Microeconomics Principles PDF

PRINCIPLES OF MICROECONOMICS 2 CHAPTER 1 - MICROECONOMICS AND MARKETS 2 1 INTRODUCTION 2 1.1 WHY CHOOSE...

PRINCIPLES OF MICROECONOMICS 2 CHAPTER 1 - MICROECONOMICS AND MARKETS 2 1 INTRODUCTION 2 1.1 WHY CHOOSE 2 1.2 THE CHOICE IN MARKET REGIMES 2 1.3 WHAT HAPPENS IN A MARKET REGIME 3 2 MICROECONOMICS AND THE DEMAND CURVE 4 2.1 THE VALUE OF A GOOD 4 2.2 THE DEMAND CURVE 4 2.3 ELASTICITY OF THE DEMAND CURVE 5 3 THE SUPPLY CURVE AND MICROECONOMICS 7 4 EQUILIBRIUM AND MICROECONOMICS 8 CHAPTER 2 - CONSUMER CHOICE 8 1 VALUE OF A GOOD AND ROLE OF PREFERENCES 8 1.1 OBJECTIVES AND RATIONALITY 8 1.2 PREFERENCES: FIRST ASSUMPTIONS 8 1.3 PREFERENCES: THE UTILITY FUNCTION 9 1.4 PREFERENCES: INDIFFERENCE CURVES 9 1.5 THE CHOICE: THE EXCHANGE TOWARDS THE OPTIMAL BASKET 11 1.6 THE CHOICE: SPENDING TOWARDS THE OPTIMUM BASKET 11 CHAPTER 3 - BUILDING A DEMAND CURVE 13 1 HOW DOES CHOICE VARY AS INCOME CHANGES? 13 2 HOW DOES CHOICE VARY WITH PRICE? 15 2.1 THE OPTIMAL CHOICE 15 3 THE DEMAND CURVE 16 3.1 THE FIRM AND THE AGGREGATE DEMAND CURVE 16 3.2 AGAIN ON THE ELASTICITY OF THE DEMAND CURVE 17 4 THE CONSUMER SURPLUS: THE MEASURE OF THE VALUE OF CHOICES 17 CHAPTER 4 - THE ENTREPRENEUR’S CHOICES 20 1 PROFIT MAXIMIZATION AND NATURE OF THE ENTERPRISE 20 2 THE NATURE OF PROFIT 20 3 THE CONSTRAINT OF TECHNOLOGY 21 3.1 THE COST CONTROL DEPARTMENT 21 3.2 THE NATURAL CONSTRAINT OF TECHNOLOGY 22 3.3 AN IMPORTANT PARENTHESIS: MARGINAL AND AVERAGE FACTOR PRODUCTIVITY 23 3.4 PROPERTIES OF ISOQUANTS 25 4 THE CHOICE OF HOW TO PRODUCE 26 1.1 FIXED INPUTS AND ISOCOSTS: THE ROLE OF TIME 26 4.2 THE CONCEPT OF ISOCOSTS AND THE LONG-TERM CHOICE 26 4.3 THE COST FUNCTION AND THE CHOICE OF HOW TO PRODUCE IN THE SHORT TERM 27 4.4 THE LONG-TERM COST FUNCTION 29 4.5 THE RELATIONSHIP BETWEEN SHORT-TERM AND LONG-TERM COSTS 31 5 THE CHOICE OF HOW MUCH TO PRODUCE: PRODUCE OR NOT PRODUCE? 32 5.1 SHORT-TERM PROFIT MAXIMISATION 32 5.2 MAXIMISING PROFIT IN THE LONG TERM 34 CHAPTER 5 - MARKET REGIMES: PERFECT COMPETITION AND MONOPOLY 34 1 THE PERFECT COMPETITION 34 1.1 MARKET REGIME DEFINITIONS AND CONDITIONS FOR PERFECT COMPETITION 34 1.2 THE SUPPLY CURVE OF THE FIRM AND THE INDUSTRY 35 2 THE MONOPOLY REGIME AND MARKET EFFICIENCY OF PERFECT COMPETITION 38 2.1 THE MONOPOLY 38 2.2 EFFICIENCY: A COMPARISON BETWEEN COMPETITION AND MONOPOLY 39 3 CONCLUDING REMARKS ON EQUILIBRIUM IN A MARKET OF PERFECT COMPETITION 44 PRINCIPLES OF MICROECONOMICS CHAPTER 1 - MICROECONOMICS AND MARKETS 1 INTRODUCTION 1.1 WHY CHOOSE Microeconomics = social science that deals with analyzing, predicting and evaluating the individual/organizations’ choices in given legislative, regulatory, social and moral contexts where they interact with other individuals/organizations → social theory of individual choices [≠ macroeconomics, that analyzes choices of communities of heterogeneous individuals] → it implies evaluating individual choices to define the ideal outcome, the optimum c Choosing implies the ability to distinguish (→ to be rational?): it means having a goal and giving up something to get something else = it generates a benefit but also a cost; the problem of choice is posed by the scarcity of resources = choice involves a renunciation, it wouldn’t be relevant if we didn’t have needs/goals What does choice mean? = satisfaction of needs/goals in the presence of scarcity of resources that poses a problem of microeconomic choice, in institutional situations that allow freedom of decision between different alternatives → institutions, preferences and resources = base of microeconomics To achieve goals, sometimes we depend on the behavior of others: a principal needs agents to which he can delegate the mission of maximizing his wellbeing → the agents have different objectives, so the principals needs to generate the right incentives so that they satisfy his objectives, through contracts → they are binding and smart (stimulate the desired results) → microeconomics can also be defined as incentive theory or contract theory/design = smart contracts (to be designed) help stimulate right incentives 1.2 THE CHOICE IN MARKET REGIMES Market = meeting place where a commodity/service can be voluntarily exchanged with other individuals for something else in return: it implies a society developed beyond a primitive world (world of auto- consumption, where each individual consumes his own resources); some markets are prohibited by law because of: an unfair/asymmetric condition of 1 of the counterparts the immorality of the trade itself the object of the exchange itself [ex: slave] would object Morality plays a role in the market, and morality standards evolve: some markets that existed before no longer exist [slave market, child labor market] → society can decide to limit the role of the market (ban/reduce it), but there are also new markets that didn’t exist before [citizenship, killing rare animals] because they had no (moral) reason to exist The existence of a market can’t be abstracted from the social context and its moral values in that particular historical moment; rules can also limit some market exchanges/delimit their areas, either good (for protecting the counterparts from excessive risk-taking) or useless (they prevent the freedom of exchange with too much bureaucracy/taxes/etc) The concept of market regime identifies the contractual strength of its participants → examples are:  monopoly = 1 seller, many buyers (or some sellers Perfect who act like 1 organization = cartel) → the seller has Competition Monopoly more bargaining power/contractual strength; leads to Entrepreneur inefficient outcomes for society (illegal now) perfect competition = many buyers and sellers → Consumer remains only an ideal to be pursued In all market regimes there is a market where the exchange between counterparties is voluntary and mutually beneficial: an exchange where parties are forced/have wrong information [misleading ads] that leads them to leave the market with regret must be avoided → regulations ensure that a trade is enforced at the agreed conditions = protecting and guaranteeing the respect of voluntary trades by enforcing the agreements made allows markets to grow and thrive If a market is dominated by a predatory behavior that goes against property rights, the incentive for victims to participate in commercial exchanges that don’t enrich them will be low: it’s easy to fight them in small and cohesive communities, but in bigger ones these behaviors are more likely to arise → institutions try to prevent them with arbiters that resolve disputes in arbitration procedures → we need protection to ensure growth of a market through mutual trust Reputation of someone in an exchange often makes the market thin up to a full disappearance [on Ebay, many non-satisfied clients don’t write bad reviews, but simply leave the market disappointed = damage to the whole market] → this happens Public Sector also when contractual obligations are not YES NO respected over a long span of time Private Sector Pure market economy Public goods = non-excludable (the buyer Market economy Incentive to produce public YES can’t exclude others from consuming it) and (prevalent goods? worldwide) Property rights enforcement? non-rival (who consumes them can’t reduce the Incentives to exchange? consumption of other goods); public and private Planned economy companies can coexist: the possibility of NO Incentive to produce Banditism and Prevarication properly - what and exchanging in them depends on effective social how much? rules that allow for mutually satisfying interactions to occur 1.3 WHAT HAPPENS IN A MARKET REGIME For exchanges to take place, the entrepreneur/producer interacts with other subjects: in the market for consumer goods = entrepreneurs desire to supply goods and consumers desire to demand those same goods [could be of deferred consumption over time = savers/ creditors → their counterparts are borrowers/debtors] in the market of production services = counterparties offer their own resources to help the entrepreneur to create the product he will sell → entrepreneurs desire to demand productive factors (to obtain resources to produce) and the productive factors themselves (workers) desire to offer their productive services → workers offer their resource of leisure time, entrepreneurs demand work time Entrepreneurs, consumers and factors of production meet in the market: whether they are able to complete an exchange or not depends on their desires, the conditions and the consequences of the exchange itself → this is the final stage of the microeconomic analysis process = the microeconomist assumes that agents have reasonably simple objectives and act by seeking the right way to achieve them = they are rational [individuals aren’t always rational, because of emotions, social norms, etc → we will study only the behavior of rational ones] Simple objectives are achieved given a certain institutional starting point (rules and institutions that protect property rights and free trade) → it can determine the structure of the market regime (usually pushing it away from monopoly); prices of goods and inputs, incomes and preferences of individuals, and the technology available to producers play a fundamental role 2 MICROECONOMICS AND THE DEMAND CURVE 2.1 THE VALUE OF A GOOD Relative price of a good (associated with the objective definition of value of a good) = expresses the exchange value of the good, the ability of a unit of the good we own to allow us to obtain other goods we don’t own / the measure of renunciation of other goods that we must accept to purchase a unit of the good in question → the relative price of a good A in terms of good B is the amount of good B that we have to give up to obtain a unit of good A Prices influence the behavior of economic agents and are influenced by their behavior at the same time: they function to allocate scarce goods and resources among individuals [if goods were free, the demand couldn’t be satisfied by any level of supply]; when the desired demand is > than the desired supply, prices increase and signal to other entrepreneurs to enter the market to eliminate excess demand Use value of a good (subjective definition of value) = the importance that the good assumes for us, because we are aware of depending from the availability of such goods to meet our needs Is there a link between exchange value and use value? When there is difficulty in the production of a certain good, the price rises [the price of water in the desert is higher than its price in other areas] → if the price depended only on the production cost, there would be no need for use value: actually, in a situation of equilibrium the price of a good (exchange value) coincides with the use value of the good for its user + the production costs of the good 2.2 THE DEMAND CURVE 2.2.1 TO READ A DEMAND CURVE Individual direct demand curve by a given consumer in a given period of time t for the good Q produced by a single producer: it tells for each relative price P of the good Q, what is the quantity that the consumer will want/desire to buy at that price given that he can afford it; the mathematical function QDi (P) associates at each price the quantity demanded by the individual i Price > Pn = desire not to consume any quantity Price < Pn = desire to demand positive quantities of the good As the relative price increases, the quantity demanded decreases: the demand curve in this case has a negative inclination and is downward sloping Economist usually represent the demand curve with prices on the Y-axis and quantity on the X-axis = inverse demand curve PDi (Q) (reversed in respect with the direct one, with the same information) → it tells for each possible price that might prevail in the market how much the consumer wishes to buy of that given good [this will happen only if there is a firm to produce that product and sell it at that price] → the curve doesn’t say what the consumer is willing to pay [he could be willing to pay much more], but how many units he wants to buy at a specific price 2.2.2 THE IMPORTANCE OF THE DEMAND CURVE The demand curve is essential for the entrepreneur: it collects the wishes of the consumer, and tells him how much he will sell of a commodity at a certain price; the demand curve is the last step of a choice process by the consumer (that considers budget and preferences) All individual demand curves summarize the desired choices of different types of individuals: there are many possible demand curves, but they all have similar characteristics → individuals express a demand to meet their objectives, giving up on something in exchange Opportunity cost of a choice = highest value of what we give up when we make that certain choice → every choice implies a renunciation: to decide whether or not to carry out a specific action, we must consider all the costs and benefits (benefits must outweigh the costs) 2.2.3 CHANGES IN THE DEMAND CURVE WITH RESPECT TO THE PRICE When drawing that inverse demand curve, we assumed that all the other relevant economic variables that influence the customer’s demand remained constant: No excessive changes in prosperity and consumer’s purchasing power (same income) No important changes in fashion/tastes A good capable of satisfying the same need is not introduced No shortage of goods consumed together with the goods in question There aren’t any new markets to sell the good/new ways of using the good itself In case any of these happen, the curve shifts to the: right (positive effects) → at the same prices as before, the firm can sell a larger quantity left (negative effects) → at the same prices as before, the firm can sell a smaller quantity Along the demand curve we see the impact of variations of price; movements of the demand curve show the impact of changes in other variables that can affect the desire [changes in income/price of other products] 2.3 ELASTICITY OF THE DEMAND CURVE At the limit of the demand curve, there is such a high price that the good will no longer be demanded: example → inverse demand function PD(Q) = 10 – 2Q tells us that when the price is 10, the entrepreneur can’t sell even a unit of the good Revenue = price X quantity sold → the entrepreneur needs to know the demand curve to obtain information on his own revenues, to know how much he will gain for each possible quantity he sold to the consumer, and what would happen to his revenues in case of price/quantity changes → revenue varies as the quantity produced/sold changes, also because the price at which this quantity can be sold varies as the quantity produced changes TR(Q) = function of the quantity sold, tells the amount of turnover in euro for every value of Q [what happens to the revenues when he expands production = the effect is ambiguous, selling more but selling each unit at a lower price can lead to different results] → its counterpart is the E(Q), expenditure function (level of expenditure by the consumer varying for every possible quantity sold) A firm that wants to find a new strategy to increase revenues must know for sure whether the variation in quantity demanded is more or less significant than the variation in prices → there is an indicator that considers the percentage variations of quantity sold and prices to understand the change in the entrepreneur’s revenue = elasticity (ε) of the demand curve (it’s a number!) Elasticity varies depending on the quantity point from which we consider the change: economists are interested in point elasticity, where the effects of infinitesimal change in prices on quantities are analyzed (using the concept of derivative); in this case, if the demand curve is downward sloping, the elasticity would be a negative number → we consider the absolute value of the elasticity to always obtain a positive number For a generic inverse linear demand curve Pd(Q) = a-bQ [or Qd(P) = a/b – (1/b)P)] the elasticity of the demand curve is equal to: Elasticity varies with the quantity: it tends to ∞ for Q which tends to 0 → even small percentage changes in price generate much larger variations in the quantity demanded → practicing discounts in price generates large gains in terms of demand = the firm will increase its revenues by decreasing prices and increasing quantities sold, it has a low market power it decreases with increases in Q it tends to 0 for a Q sufficiently large to be desired only when the price is 0 → percentage changes in prices (small) generate even smaller variations in the quantity demanded by the consumer → increasing the price generates very few losses in terms of demand, the firm has a high market power What’s the link between elasticity and total revenues? TR is price x quantity and price is related to quantity by the demand curve → TR = PD(Q)xQ; the variation of total revenues with the infinitesimal variation of the quantities can be calculated using the derivative of a product of 2 functions There are 2 contrasting effects that affect revenues when increasing very little the quantity produced: when we increase the amount sold by 1 unit, revenues increase by P(Q) but decrease because all the previous units sold (Q) are now sold at a lower price (increase in production) The marginal revenue function tells the change in total revenue due to an infinitesimal change in the quantity produced: if positive, with the increase of sales of a unit the total revenues increase if negative, with the increase of sales of a unit the total revenues decrease The marginal revenue varies with the quantity of production desired by consumers: ε > 1 → positive marginal revenue (price ↘, sales ↗, revenue ↗ // price ↗, sales ↘, revenue ↘) ε < 1 → negative marginal revenue (sales ↗, revenue ↘; sales ↘, revenue ↗) → increase in prices has a little impact on quantities: a lower volume of quantities sold (at a higher price) has a positive effect on revenues (less quantity produced means lower costs of production) The producer’s goal is to adopt corporate strategies to reduce the elasticity of demand of their customers, while an astute consumer tries not to fall into the lock-in effect (costs for a consumer who is attached to a firm and decides to go to a rival one); in case of a firm who frequently updates its menu of products over time [Apple with new iPhone models], the TR curve isn’t exhaustive = sales of the older product would drop (product cannibalization), and the TR would be really different TR for the entrepreneur is Total Expenditure [E(Q)] for the consumers, which also depends on elasticity: consumer spending and entrepreneurial revenues both depend on the structure of the demand curve 3 THE SUPPLY CURVE AND MICROECONOMICS A firm is willing to sell different quantities depending on how much it receives for each unit of goods: supply curve of the producer PS(Q)= relationship between quantity and price (for the one who offers on the market of goods), tells for each possible price that might prevail in the market of the good, what the entrepreneur will be willing to offer to the consumer The supply curve is upward sloping [note: under certain prices the entrepreneur isn’t willing to produce] (usually, sometimes it can be decreasing) and behind it there are the motivations of the entrepreneur: he is a rational individual and has a goal = maximize revenues once the total costs of production (labor/materials/capital goods) are compensated The shape of the profit function plays a key role in determining how much an entrepreneur will be willing to produce at a certain price for every possible price; production costs vary with the quantity produced = there is curve of total costs that tells how the costs vary as the quantity produced changes TC1(Q): cost independent of the quantity produced MARGINAL COST = variation of total TC2(Q): cost ↗ as quantity ↗ costs for an infinitesimal variation of TC3(Q): cost ↘ as quantity ↗ (initially) the quantity produced → the marginal cost function, for every possible value of production, tells the change in costs due to a unitary change in PROFIT = production revenue - cost The quantities that maximize revenues aren’t always the same as the ones that maximize profits (sometimes costs are so high to discourage production, in favor of an amount that guarantees < revenues but > savings) 4 EQUILIBRIUM AND MICROECONOMICS From the “abstract” market demand and market supply curve to a more concrete example: consider a credit market where those who wish to borrow will express a credit demand curve according to the cost of the credit → for very high rates no one will ask for credit, only if the rate falls sufficiently 1. rate = 30%, demand = 10 billion, supply = 25 billion → excess supply of 15 billion 2. rate drops and a war of discounts starts between banks to capture the market 3. rate = 15%, demand = 20 billion, supply = 20 billion → it converges towards equilibrium 1. rate = 10%, demand = 30 billion, supply = 15 billion → excess demand of 15 billion 2. rate rises and a rate hike war starts between consumers, that will discourage some of them and encouraging banks to offer higher credit → it converges towards equilibrium Market EQUILIBRIUM point = point where the excess demand and supply is zero: we arrive here spontaneously, without having planned this adjustment; the equilibrium price in the credit market is determined by the characteristics of the supply and demand functions If the state interferes and limits the highest rate admittable by law [ex: to 10%, so there is an excess demand of 15 billion], the credit will probably be allocated randomly/based on personal relationships of customers with banks → the others will resort to illegal markets of usurers (with lower guarantees for the debtors); the reduction of the equilibrium interest rate is supposed to satisfy equity needs towards the poor, but in reality the credit will still go to the rich (through personal/political connections) CHAPTER 2 - CONSUMER CHOICE 1 VALUE OF A GOOD AND ROLE OF PREFERENCES 1.1 OBJECTIVES AND RATIONALITY How to determine the relationship between the amount demanded by a given consumer and the price of the good? Is there a relationship between the price you pay and the use/subjective value attributed to it? Assumption of RATIONALITY = individuals have objectives and tend to choose the most appropriate way to achieve them; these goals are simple and general enough to be identified [complex goals are almost impossible to study and understand] → people act pursuing certain, simple objectives = strong hypothesis (that could sometimes be wrong) useful to guess what individuals will do + the consequences of their actions 1.2 PREFERENCES: FIRST ASSUMPTIONS The tastes and financial resources of an individual determine his desired choice; the consumer demonstrates in his behavior a considerable amount of rationality → what does this assumption require? The consumer has 2 goods available: he must choose how much to consume of each one of the 2 → we are only interested in his choice for 1 period (no inter-temporal aspect of choice like savings/debt) in a context without uncertainty; each combination of the 2 goods he may choose is called a basket of goods; each good is divisible (you can consume any fraction/multiple of it) The individual will be asked to directly classify all basket of goods according to his preferences, then examining the actual desired choice → he has to affirm whether a combination of goods is preferred or indifferent/at least as liked as to any combination (A≽B) = this means that either A is strictly  preferred to B (A≻B) or he is indifferent between A and B (A∼B); preferences have nothing to do with cost or income The hypothesis of rationality leads to 2 key assumptions on preferences preferred or indifferent to: completeness of preferences: the consumer can always evaluate whether one basket is preferred or indifferent to another o either A≽B or B≽A or both occur simultaneously o if A≻B it can’t be that B≻A = hypothesis of preferences asymmetry o it’s excluded that the framing of the alternatives influences the choice of individuals [ex pag 57] o the choice between 2 baskets doesn’t depend on what other goods we can dispose of transitivity of preferences: if you don’t prefer a basket X to a basket Y (X≽Y) and you don’t prefer a basket Z to Y (Y≽Z), then you don’t prefer Z to X (X≽Z) o in case of imperceptible differences between goods, the hypothesis of transitivity of preferences can be violated (we won’t consider this case) o [see page 59/60 with example of Ulysses where X≻Y≻Z≻X → due to irrationality] o everything that generates regret/addiction/obsession/compulsion isn’t considered (it would lead to non-transitivity) Another important assumption is that an individual, given 2 available alternatives, with one strictly preferred to the other, will consider the preferred alternative his acceptable choice → his simple objective is to consume the preferred basket 1.3 PREFERENCES: THE UTILITY FUNCTION Individual UTILITY function = mathematical function used to determine the choice of the most attractive basket for the individual → it summarizes the ordering of the various baskets by each individual, associating to each basket a number (higher for A than B if A≻B) With a maximization of this mathematical function, it would be sufficient to determine the basket with the highest number to know the individual’s choice; the assumption of continuity of preferences shows that this function exists and it’s continuous The function U(X,Y) is such that for any basket A (combination of Xa and Ya units of goods X and Y) and any basket B (combination of Xb and Yb units of goods X and Y): If A≻iB, then Ui(Xa, Ya) > Ui(Xb, Yb) → the number associated to A is bigger than the number associated to B If A∼iB, then Ui(Xa, Ya) = Ui(Xb, Yb) → the number associated to A is equal to the number associated to B Basket Books Tennis Utility It’s not important to know the value of the utility, only to be able to (quantity) (hours) indicate the ordering of the baskets according to his A 10 0 5 B 7 1 5 preferences: if A≻iB, then U(A) ≻iU(B); also, the number associated C 5 2 5 with the utility isn’t fundamental either: it could be 100000, -100, D 4 3 5 10000000 → we only need to know which baskets are preferred E 3 5 5 by the individual and between which ones he’s indifferent F 2 8 5 G 10 1 6 The individual is indifferent between A, B, C, D, E, F and is indifferent H 8 2 6 between G, H, I; he prefers G to B, which is shown but the different I 7 3 6 numbers on the utility function (G≻iB) L 9 1 ? M 7 5 ? 1.4 PREFERENCES: INDIFFERENCE CURVES 1.4.1 PROPERTIES OF INDIFFERENCE CURVES The indifference curve represents all the combinations of goods (baskets) among which the consumer is indifferent → the baskets that lie on the same indifference curve are associated to the same number by the utility function; each indifference curve is continuously decreasing, and moving along it the consumer remains indifferent with respect to the initial situation [from F to E there are fewer tennis lessons but more books] In some cases where the choice is between baskets of a good and a bad [Ferrari vs rotten food], to restore a condition of indifference we must reduce and not increase the consumption of the bad In general, we assume decreasing indifference curves and monotonous preferences (larger quantities of a good are preferred to smaller quantities of it), and we consider only goods = objects for which we are willing to give up something in exchange for an additional unit of these Monotonicity of preferences implies the concept of non-satiation: individuals never reach a stage where consuming more is harmful → satiation is relevant only in case of violence and forced choices by individuals → if he satiated, a higher indifference curve wouldn’t correspond to a higher utility and the curves would take a thick shape Through each possible basket passes an indifference curve: the individual has a complete preference ordering, he can compare any basket with any other → the more we move upwards to the right, the greater the number associated by the utility function to each specific indifference curve = for each basket on the curve there is another basket with more than 1 of the 2 goods and an equal amount of the other [D vs I = all consumer prefer I because of non-satiation; F vs I = John prefers I because he prefers all basket that lie on I indifference curve to the ones that lie on D indifference curve]; some examples go against the idea of monotonicity of preferences: income determines the level of satisfaction in the individual: below a certain level, greater wealth buys happiness individuals aren’t only interested in what they receive, also in how the quantity will be distributed (more isn’t always better) Indifference curves can’t intersect (it would go against the hypothesis of transitivity of preferences) and they are convex towards the origin = each basket made of a combination of 2 original baskets on the indifference curve is preferred to the original baskets themselves (based on the idea of moderation of the consumer) [C≻B∼E, E = xB+(1-x)E] sometimes this assumption is not very credible = there are also non- convex indifference curves: this happen if the extremes of the curve [ex: 2 beers and no car vs no beers and 2 hours driving] are preferred to a linear combination of them [driving while drinking] The more we have of a good, the less we will be willing to evaluate one more unit of it = the increase of abundance of a good X reduces the value of an additional unit of X in terms of Y, while increasing the value of a unit of Y in terms of X, to which we give up to consume more of X: if John holds D, he’s willing to give up at most 1 hour of tennis for 1 additional book (1 book = 1 tennis lesson) if John holds B, he’s willing to give up at most 1 hour of tennis for 2 additional books (1 book = ½ tennis lesson) The individual prefers linear combinations (not extremes) because of convexity/moderation = as the consumption of X increases, he’s willing to give up less and less of Y for an additional unit of X  (ΔT/ΔB) = value of 1 more unit of books in terms of tennis lessons for our consumer (marginal subjective value), decreases with the increase in consumption of books If ΔB converges towards 0, ΔT/ΔB becomes the slope of the indifference curve at the point considered, it tells us how much we should decrease the consumption of tennis lessons when there is an infinitesimal increase of books to remain indifferent to the previous situation Marginal Rate of Substitution (MRS) = - (ΔT/ΔB), opposite of the slope ΔT/ΔB, it tells us for a given amount of goods X and Y, the value attributed by the consumer to an infinitesimal additional unit of X in terms of Y Because of the convexity towards the origin, the indifference curve has negative 2nd derivative: the slope of the curve decreases as the variable increases on the x-axis; the MRS tells the additional subjective value of X in terms of Y (not the value of what we have but the value of one more unit, based on what we already have); in case of a segment parallel to one of the axes, the MRS = 0 (the consumer is satiated, remains indifferent) 1.5 THE CHOICE: THE EXCHANGE TOWARDS THE OPTIMAL BASKET How does an economic exchange take place? A consumer has a basket A (10 Books, no Tennis) and he is offered to exchange it with basket L (9 books, 1 Tennis lesson) = we don’t know the utility associated to L but we know that L≻B and A∼B, so L≻A → the exchange will take place because we can take the preferred basket This exchange had a cost (1 book for 1 additional tennis lesson) but the benefit was greater (the utility associated with L is higher → that is not the reason for the exchange, it’s the consequence!!!): exchanges happen for the improvement of human welfare and to acquire greater satisfaction; the last condition for the exchange to take place is its voluntary nature = there must be another person (someone with symmetric needs = entrepreneur) who has the opposite of our desire (L≻A isn’t true for everyone!) → the exchange must satisfy all individuals who participate in it When do we stop exchanging? When the advantage of exchanging an additional unit will be at most equal to the cost of exchanging an additional unit (M≻L, but cost > benefit); the exchange can happen only if the consumer has the means to enter it and if the wishes of the 2 counterparts are mutually compatible 1.6 THE CHOICE: SPENDING TOWARDS THE OPTIMUM BASKET Price of acquiring a good = amount of what we must give up to obtain that good (non-negotiable, the consumer has no bargaining power in a market full of other individuals like him → he only chooses how much to consume) → consider an individual with a sum of money I € (monetary income, mean of payment available to the consumer) = he would like to consume ∞ books and ∞ tennis lessons, but there is a budget constraint → he can’t buy baskets that cost more than what he has at disposal (I €) I = 50 €, PB (price of 1 book) = 5 €, PT (price of 1 tennis lesson) = 5 € → A and L are accessible, L is more advantageous; M is preferred but it’s not economically reachable o If PT = 2,5 €, M becomes reachable and concretely desirable The available alternatives must satisfy the inequality Income ≥ Expenditure (I ≥ PB x B + PT x T) → when Income = Expenditure (I = PB x B + PT x T) the individual is choosing the best basket possible (he only lives one period, so he can exhaust his income completely) The budget constraint can be synthesized as a linear constraint that tells us, for a given desired consumption of B, the max amount of T we can consume given our I and the absolute/relative P of the goods I = 500 €, PB = 50 €, PT = 100 € o 500 = 50B + 100T o T = (500/100) – (500/100)B = 5 – (1/2)B The Budget Constraint (BC) is a decreasing function that divides the plane into 2 areas = all baskets above the BC are economically unreachable, those below it are dominated by preferred baskets; the BC can move on the plane: income I ↗: the BC line moves parallel to itself upwards (slope remains the same) income I ↘: the BC line moves parallel to itself downwards (slope remains the same) price (relative price of good X with respect to Y) ↗: change in slope towards the left price (relative price of good X with respect to Y) ↘: change in slope towards the right With a decrease in price there is an increase in purchasing power (even if I = the same) G≻B, but it’s above the BC, it can’t be purchased with our income → baskets above the budget constraint are desirable but economically unattainable B and C = below the BC, they could be chosen but they don’t exhaust all the income → they are not chosen because of non-satiation D = on the BC, it exhausts the income → it’s the point on the indifference curve tangent to the budget constraint A point of tangency between an indifference curve and the BC implies that at the optimum point the slopes of these 2 curves must coincide; since the slope of the BC = opposite of the price ratio, and the slope of the Indifference Curve = opposite of MRS, the optimum basket has 2 characteristics: 1. Income is spent entirely on the purchase of the optimal basket 2. MRS = ratio of relative prices Prices are an observable variable, so at the equilibrium the MRS is too: ▪ relative price = rate at which At the optimum point, Price ≡ Objective exchange value of a we can exchange 2 goods with unit of an additional unit of a good (appropriately defined) = each other subjective value of an additional unit of a good (appropriately ▪ slope of the BC = price of good defined) ≡ MRS; but remember that price (what you have to X measured in terms of Y give up) ≠ MRS (what you are at most willing to give up) ▪ MRS = value of an additional unit of good X measured in Y ▪ Prices at equilibrium are all equal → MRS at equilibrium must be equal for all consumers = they agree on the value of an additional unit of a good in terms of the other when they consume their ideal basket o Consumers have ≠ preferences (and ≠ utility functions): they won’t buy the same amount of goods, but the MRS is still equal  All consumers won’t buy the same baskets of goods: an intellectual has to consume many more books to have the same MRS as a sportswoman (to give to an additional value of books the same value she does) → the marginal benefit at B=0 is > for the intellectual If MRS ≠ ratio of prices (in case of no tangency), the utility isn’t maximized → that isn’t the preferred basket; tangency is sufficient to guarantee an optimum, but is it necessary? Some indifference curves have the optimum point not at the tangency point: for a perfect intellectual, the marginal value of a book is higher than the cost of books in terms of tennis lessons → individuals with convex and moderated preferences can make extreme choices The choice of the individual is the combination of the marginal value of goods (tastes + MRS) and the marginal cost of goods (market price); it’s also necessary that the consumer is rational [avoid illusion of relativity, arbitrary consistency, entrepreneurs bringing a price to 0 → see examples pag 86/87] → lack of rationality isn’t always negative, often individuals follow social norms outside of economic logic (especially with free services) CHAPTER 3 - BUILDING A DEMAND CURVE 1 HOW DOES CHOICE VARY AS INCOME CHANGES? Demand grows with income: if the increase in income is not accompanied by a proportional increase in the absolute prices of all the goods consumed, the set of economically available goods increases → we can write the budget constraint as I = P x Q (I = nominal/monetary income available in €); W = real disposable income (measured in purchasable units of Q) → when I doubles, Q doubles (if P is constant) ; when income increases, tastes can change towards other goods (that the consumer couldn’t afford when he was poorer) SUPERIOR goods (or normal) = their consumption grows as real income (purchasing power) grows We can write the consumer’s budget constraint as Ia = PBBa + PTTa = PBBa + PTkBa (Ba, Ta) = favorite basket > the inclination k of the straight line, < the income spent on the good on the abscissa (T) When the income is doubled, the desired consumption and expenditure (if prices are constant) double → the share of income spent on various goods doesn’t change with change in income; if the consumer doesn’t change his preference for 1 of the 2 goods as income increases, preferences are homothetic → as income changes the % expenditure is the same  PERFECT COMPLEMENTARY goods = with 2 complement goods A and B, as priceA ↑, demandB ↓; priceA ↓, demandB ↑; perfect complements are consumed only in fixed proportions [right shoe and left shoe] → as income grows the optimum choice is always at the height of the corner point of the indifference curve → the proportion stays the same NECESSARY goods = superior goods [so their desired consumption grows with income], but the share of income spent on their consumption goes down as income increases → a greater proportion of income is spent on them for low level of income LUXURY goods = superior goods, and the share of income spent on their consumption goes up as income increases → a greater proportion of income is spent on them for higher levels of income δQ/Q = elasticity of the demand for a good with respect to income, measures the % variation in the demand for the good with a variation of 1% of the individual’s income → superior goods have an elasticity ε with respect to income > 0: Necessary goods = income ε < 1 Luxury goods = income ε > 1 Income expansion path = set of baskets chosen by the individual as his condition of real income changes → it has a positive inclination with 2 superior goods (where usually one is necessary and one is luxury) ENGEL CURVE = inverse demand curve with respect to income → it tells for each possible level of income of the consumer, how much of that good our individual will want to consume; it’s useful to firms to orient the choice of the product [who to direct the advertisement campaign to]; the Engel curve is for necessary goods: increasing and convex → higher slope for luxury goods: increasing and concave → lower slope INFERIOR goods = income ↑, demand ↓; income ↓, demand ↑: usually there aren’t any goods which are always inferior → goods that were initially superior for low levels of income can become inferior if, when the budget increases, the consumer looks for the most economically reachable substitute goods (with > quality) between all the rival ones, that he couldn’t reach before; the Engel curve for an inferior good is tilted negatively Income expansion paths and Engel curves are functions of real income, given that prices remain constant: in case absolute prices vary, the purchasing power changes (increases with lower prices, decreases with higher prices) → in case of an increase in monetary income at the same time, some individuals think their purchasing power has increased, but it’s not true (absence of monetary illusion) 2 HOW DOES CHOICE VARY WITH PRICE? 2.1 THE OPTIMAL CHOICE NORMAL goods = price ↑, demand ↓; price ↓, demand ↑ the price-consumption curve unites all the optimal combinations desired by the consumer as the price changes the demand curve is the relationship between price and desired quantity that derives from these optimal choices: for every possible price, it tells us the quantity desired by the consumer (how much he desires to consume) Example = analyze the choice of the optimal combination of CDs and classical musical concerts (M) for a given monetary income as the relative price of concerts changes: Moving from C → A: there is an increase in relative price of music concerts (they cost more in terms of CD, getting them would mean having to give up more CDs) → PM1 > PM3 The individual is reducing the consumption of M because of the increase in prices, and increasing the consumption of CDs; M = normal good (consumption decreases as price increases) From the price-consumption curve we can derive the individual demand curve of M as a function of the relative price: it’s made of indifference curves + budget constraint (that changes based on prices, income and prices of other goods are constant), transposing the tangency points found above SUBSTITUTE goods = 2 goods A and B for which as priceA ↑, demandB ↑; priceA ↓, demandB↓ (and viceversa) → they satisfy the same needs GROSS substitutes [concerts and CDs] With perfect substitutes, o the cross-demand curve links changes in price of A with indifference curves are: changes in quantities demanded of B → the slope is - downward sloping (usual) positive until prices of B decrease beyond a certain - linear threshold: substitution effect = part of A isn’t considered - not convex (fixed MRS) replaceable with B anymore PERFECT substitutes = somewhat similar goods/with a similar function → in the most extreme case, the MRS between them doesn’t depend on the amount held of the good, it’s constant o if the cost of one of the 2 changes, the consumer makes an extreme choice and holds only the one that has a marginal cost of the trade (constant, = relative price) < marginal value of the trade (constant, = MRS)  COMPLEMENT(ARY) goods = 2 goods A and B for which as priceA ↓, quantity consumed of B ↑; priceA ↑, quantity consumed of B ↓ (and viceversa) → goods we like to consume together [coffee and sugar; pasta and peeled tomatoes] → the cross-demand curve is negatively sloped GROSS complements = opposite of gross substitutes GIFFEN goods = goods are Giffen-type (economist from 19th cent) where the demand curve is positively sloped: their demand initially increases when prices decrease, but then decreases again with a further discount: 1. A → B = price ↓, demand ↑ 2. B → C = price ↓, demand ↓ The slope of their demand curve is positive only if preferences don’t depend on prices [vs Veblen goods: consumers buy them only because they are economically unattainable for most people] When goods are predominant in the overall expenditure of the consumer [a mother of many kids buys many diapers], the decrease in prices has a significant income effect = he now has more resources to buy other goods/switch to the same type of goods with a higher quality Giffen goods = INFERIOR goods: here the decrease of PPB is equivalent to a > purchasing power, which results in a lower consumption of the good → all Giffen goods are inferior goods, but not all inferior goods are Giffen 3 THE DEMAND CURVE 3.1 THE FIRM AND THE AGGREGATE DEMAND CURVE Firms sell to several consumers with different preferences: they need an aggregate indicator of the demand for the good they produce/supply = firm’s demand curve → it tells for every possible price, how much the total of the consumers demands of a good they produce in a particular period; it can be constructed by adding all individual consumer demand curves horizontally = if the different consumers are downward sloping, so will be the firm’s demand curve [as the price declines, who was demanding something will demand more, and who wasn’t demanding anything will demand something] The market demand curve is the aggregate curve for all firms that supply a product in that market → it tells for each possible price how much is demanded by consumers; what happens to the curve when price of another good changes depends on how the goods are compared with each other: Substitutes: increase in price of A = bigger consumption of B = curve moves to the right [new car models also in the same company → cannibalization] Complementary: decrease in price of A = bigger consumption of B = curve moves to the right The market demand curve is also affected by changes in the overall economy of all individuals (income could be the same, but different distribution) = some may decide to spend more on that particular good Even a increase in overall income doesn’t imply a shift in the demand curve to the right = greater overall income doesn’t imply greater demand (the re-distribution could be only a large increase in income for a few and a moderate decrease for many) → in this case the demand could even go down and the curve could shift to the left 3.2 AGAIN ON THE ELASTICITY OF THE DEMAND CURVE 2 demand curves with constant elasticity ε at every point: Completely inelastic curve = consumers are willing to buy a fixed quantity Q* regardless of the price (like a good without substitutes) → firm’s market power = very high Infinitely elastic curve = any price variation generates infinite variations in demand (price ↗ = lose all market, price ↘ = gain all market) → consumers are willing to buy any amount of the good at only 1 price P* → common in perfect competition, firm’s market power is minimal o here we assume individuals have information on where to find the same goods at lower prices, but there are also transportation costs to be considered (so for some consumers the 2 goods are different, even if they are technically the same) The existence of substitute goods influences the elasticity: the more there are, the more the consumer will shift his consumption towards them as the price of a good X increases (and desire more of good X as its price decreases) → the demand curve of a good with many substitutes is > elastic than the one of a good with no substitutes Price elasticity of a demand curve changes if we consider short term or long term effects: usually the elasticity of goods to their price is greater in the long run [new companies with lower prices that slowly take the place of old monopolies that had the trust of the consumers], but the opposite can also happen [car market, where eventually no one can postpone buying a new car and has to adapt to market prices] The cross elasticity of the demand with respect to price shows the % change in quantity demanded of a good as the price of another good changes; it’s positive for substitute goods and negative for complementary goods → antitrust authorities use it to delimit the extent of a market (relevant market) 4 THE CONSUMER SURPLUS: THE MEASURE OF THE VALUE OF CHOICES Remember that this paragraph isn’t in the final exam, this is just a recap useful to understand chapter 5 The choices of individuals entering an exchange generate a subjective value > than the objective cost = the exchange allows him to improve his wellbeing → how can we measure the subjective value of choices/the additional wellbeing derived from an exchange? At the optimum point, the consumer equalizes cost and value = in reality they are the marginal costs and the marginal values of the exchange (of the last unit that he renounces/accesses to) → when mv > mc, there is a surplus of value that is potentially acquired by the consumer in an exchange 1. assume there is a consumer that has to choose between tennis lessons T and all the remaining goods (C = composite good) also called Marshallian currency 2. assume that the price of C is 1 (𝑃𝐶 = 1) and write the Budget Constraint as 𝑰 = 𝑷𝑪 𝑪 + 𝑷𝑻 𝑻 = 𝑪 + 𝑷𝑻 𝑻 (where I = income) 3. place C on the y-axis → BC has a slope = to PT and intercepts on the axis the ordinates equal to the individual’s disposable income 4. when consuming T0, on the y-axis there is what remains of C (maximum possible residual consumption) + what you can spend on all other goods (maximum residual expenditure PCC → 𝐶 = 𝑅 − 𝑃𝑇 𝑇 0 ) → the latter is called residual income Ir 5. draw the highest indifference curve that the consumer can reach with his purchasing power 6. when T = 0, the consumer is willing to give up a max of AB of the composite good C (or to AB € of residual income on the remaining consumer goods) → area 01VZ we gave monetary value to the subjective value of the unit of a good! 7. to consume an additional unit of T the consumer is willing to give up a smaller amount of Ir (only BC €) → area 12LD 8. T1 costs 01P0H = he exchanges part of his income for it and achieves > satisfaction than he would if he didn’t participate in the exchange 9. T2 costs 12HM = lower than its marginal value (12LD) 10. T3 costs > than its marginal value: he won’t consume it The consumer trades until marginal benefit = marginal cost of the exchange Area V02DLZ (___) = total/ gross benefit of the exchange Area 02MP0 (_) = total costs of the exchange Area VP0MDLZ (__) = net cash benefit of the exchange CONSUMER SURPLUS (or net cash benefit) = minimum amount of € that the consumer would require to be willing to give up the consumption of the good he currently holds [T2] without by being damaged by the subtraction of this exchange opportunity → it’s an objective measure of the subjective value of the exchange; it’s the monetary measure of the value of the exchange: it tells us how much we must compensate a consumer if we deprive him of the possibility of entering the market The benefit comes from the fact that the consumer buys T at a total cost < than what he would be willing to pay (total value) → only the last unit consumed has no net value (because the increase in value = increase in cost necessary for the exchange) When we don’t know the indifference curve of an individual, we can represent the surplus through the Marshallian demand curve (of T), which tells that: 1. At price P0, requested Q = 0 → the 1st unit must have value < P0 2. At price P1, Q must have value at least = P1 and < P0 (_ = what we are willing to pay)  3. At price P2, Q must have value at least = P2 and < P1 (_ = what we are willing to pay) 4. At price P3, the consumer is indifferent between spending C (A + B, net benefit + cost) on Q3 units of T vs not purchasing T The rectangles leave a space (triangle) under the demand curve, that disappear more and more as the additional unit considered becomes smaller and smaller → area below the demand curve = gross surplus of the consumer for a perfectly divisible good (but part of it is the total expenditure given to the counterpart) → the higher the price, the lower the net surplus left to the consumer/benefit of the exchange Consumer surplus is important for price business strategies: entrepreneurs use it to create strategies to segment the market between individuals that evaluate a good differently → they sell the good at the highest price to individuals with the most inelastic demand curve [by selling the same good in different moments/formats → books with different covers] = process of price discrimination based on product differentiation Companies study carefully different demand curves of consumer groups and their surpluses to maximize their profits → example: 1) Sell all books at a high price → extract surplus from those willing to pay it, but lose all the others 2) Sell all books at a low price → lose a lot from the initial sale to inelastic consumers 3) Mix the 2 prices and sell at 2 different times (high for those with low elasticity, low for highly elasticity ones) → extract surplus from both categories of individuals The consumer surplus also allows us to better understand the meaning of the inverse demand curve: it shows how much Q the consumer desires at a given price + how much he is willing to pay for 1 more unit of that quantity of the good (marginal value he attributes to that additional quantity), but it doesn’t show how much you are willing to give up for a given amount of that good → only how much you are willing to pay for the last unit purchased In the Marshallian demand curve, for each quantity Q we read the max price we are willing to pay for the consumption of that quantity Q (when we have already consumed Q-1) → the demand curve has a decreasing slope because as Q ↗, the value attributed to the last unit consumed ↘; to understand this there are two ways: evaluate the marginal value of the last unit: if the 3rd tennis lesson has m.v. of 70€, it doesn’t mean that one lesson is worth 70€, but that the difference between having 2 or 3 lessons is worth 70€ per week → the value of the 3rd is lower than the one of the 1st/2nd etc. consider the characteristics of the consumed marginal unit: water can be consumed in different ways (1st for drinking, 2nd to wash yourself, 3rd to wash the ground, 4th to clean the car, etc.) → each time, the marginal value of the new liter of drinking water decreases until it becomes < than the consumption value of the 1st liter for washing Consider the choice between diamonds and water: water gives a bigger surplus, but it’s available at a low cost and in abundance (marginal value decreases); diamonds are expensive and available only in limited quantities = they are used only for few important purposes, so their marginal value is very high → concepts of price and value coincide (high price = high marginal value in this case), but the total value (S) of the good is higher for water CHAPTER 4 - THE ENTREPRENEUR’S CHOICES 1 PROFIT MAXIMIZATION AND NATURE OF THE ENTERPRISE In modern (neoclassical) economics the role of production for consumption becomes < relevant: production is for entities outside the enterprise (consumers, etc) to obtain resources to buy goods from others: new economic problem = how can quantities produced and exchanged satisfy the needs of all individuals? → focus on the concept of enterprise = unit that produces for the consumption of other individuals Neo-classical entrepreneur is rational: he has objectives and acts to achieve them = he wants to maximize profits to have more income at his disposal (for when he turns into a consumer, he isn’t necessarily selfish → he could be acting for charity); the enterprise is made by an organizational and contractual relationship between factors of production (capital + workers = company manager) and shareholders; the company manager doesn’t always have the same interests of the shareholders, but the company usually still works towards profit maximization because: 1. shareholders control the majority of the company: they can check the work of managers and remove them if needed 2. poorly managed companies are often subjected to hostile takeover bids 3. managers’ salaries increase if they generate more profits (stock options) 2 THE NATURE OF PROFIT The entrepreneur uses inputs to maximize profits (total revenue MaxQ Π(Q) = TR(Q) – TC(Q) – total costs) with the quantity produced; the derivative of the profit function creates Marginal Revenue and Marginal Cost: MΠ = MR - MC MR - MC = 0 → MR = MC MR when producing Q* = variation of TR with an infinitesimal variation of the quantity produced 𝝏𝑻𝑹(𝑸∗ ) 𝝏𝑻𝑪(𝑸∗ ) − =𝟎 MC when producing Q* = variation of TC with an infinitesimal 𝝏𝑸 𝝏𝑸 variation of the quantity produced The condition to obtain the quantity Q* that maximizes Π is that Marginal Revenue = Marginal Cost: if MR > MC, increasing production of another unit generates an increase in revenue > than the increase in costs → MΠ = positive, TΠ ↗ → it’s better to expand production if MC > MR, decreasing production of one unit generates an decrease in costs > than the decrease in revenues → it’s better to reduce production This condition is necessary but not sufficient: at the point where MR = MC, profit is not necessarily maximized; MC and MR also depend on other variables → if they change, there can be movements along the function (change of Q*) or of the function (change of other variables) PRODUCTION COST = value of everything the entrepreneur renounces to produce that quantity [it’s an opportunity cost!!]: it’s what helps him to decide whether or not to produce = he has to make more than what he could if he undertook alternative activities (TR > TC) → he has to make a rational decision to maximize profit = we can say there are 3 kinds of profits: Normal profit = profit that can be obtained in the best possible alternative available [being a professor] → opportunity cost for the entrepreneur who wants to start a new business Accounting profit = profit he actually earns, includes fixed costs, but not normal profit Economic profit = profit that considers all opportunity costs, but not fixed/sunk costs: Economic profit = Total Revenues – Total Opportunity Costs Total Opportunity Costs = Normal Profits + Total Remaining Opportunity Costs Total Remaining Opportunity Costs = costs he has to bear when becoming an entrepreneur [rent for the shed to produce, cleaning costs] The decision of the entrepreneur on whether to produce or not depends on the economic profit’s value: > 0: called extra profit, TR – TC > Normal Profit = it’s convenient to produce < 0: TR – TC < Normal Profit = it isn’t convenient to produce = 0: there is no convenience compared to the best possible alternative Sometimes, even if accounting profit < 0, economic profit > 0: economic profits don’t include fixed costs = costs he has to bear even if not producing [if accounting profit = - 10 000 and economic profit = 20 000, it’s still convenient to produce] 3 THE CONSTRAINT OF TECHNOLOGY 3.1 THE COST CONTROL DEPARTMENT Remember: the entrepreneur that wants to maximize economic profits doesn’t maximize revenues → the amount that maximizes TR causes such high TC that extra profits < 0 → maximizing profits means to produce Q* at the minimum cost; the firm can’t COST FUNCTION = created by the cost evaluation consider any Q as potentially department, it associates to each quantity produced the producible: minimum cost in units of value to produce that quantity It can’t force the market to consume the quantities it wants: it must follow the demand curve of the goods → it can’t sell more than what consumers ask for Its technical skills and managerial abilities to transform available resources and productive services into real finished products serve as a constraint The production process consists in combining resources (inputs, can be consumed in total or be durable [oven]) to create a new resource (output) → the output has a time dimension (specify how much is produced in a given unit of time → it’s a flow); durable goods have a production capacity = max amount of production services that can potentially be obtained in each period 3.2 THE NATURAL CONSTRAINT OF TECHNOLOGY TECHNOLOGY = relationship that exists between input and output available: it acts as a natural constraint → there are quantities of output that can’t be reached with certain quantities of input + a limit to the amount of input available = production choices are limited; it’s called natural because the relationship that transforms input into output derives from natural properties Technology is not immutable: technological progress = any change that allows production of a fixed output with a smaller amount of input // more output with a fixed input production set = set of all achievable combinations input-output from the available technology (area below the production function) production techniques = any combination input-output of the production process The problem of the entrepreneur is both how much to produce and how to produce: to understand how to produce, we must understand the best use of any available input in terms of production efficiency PRODUCTION FUNCTION = all the points that associate to any combination of available input the maximum level of output that can be obtained → an enterprise that operates on the production function is called OUTPUT-EFFICIENT points below the pf are output-inefficient points above the pf are technically impossible There are 3 important assumptions: perfect divisibility of input and output possibility of getting rid of goods without costs absence of the land of plenty = to produce a positive output we need a positive input (null inputs are only in the point of origin Among all output-efficient combinations there are output levels that can be produced with less input: production techniques that produce a given output with a lower use of a factor than other p.t. (with = output) are called TECHNOLOGICALLY EFFICIENT → there is no way to produce a given output with a lower level of at least one input and a constant level of all other inputs → efficient technologies are monotonous = we consider only the growing part of the production function  ISOQUANT [Y = Y0] = production function in the case of 2 inputs K (capital) and L (labor) that efficiently provide a certain level of output Y0 → it describes all the combinations of K and L that allow to produce Y0 in an efficient way = combinations on the isoquant are output-efficient [they correspond to the highest level of output that can be associated to that particular combination of inputs] The isoquant isn’t really a production function: the production function is tridimensional and is composed by a series of isoquants (one for each quantity that can be produced) → we associate a max output level with each combination of inputs, but there are more combinations of factors that reach the same max output; slope = both positive and negative Ymax = Y0 = f (K, L): isoquant = combination of all those combined factors K and L that leave the final product unchanged at a given max level Y0 MARGINAL PRODUCTIVITY OF CAPITAL MPK = (δY/δK) = impact on the quantity produced of an infinitesimal variation of capital (keeping labor constant) → δY/δK = variations of Y generated by variations of K (dK) MARGINAL PRODUCTIVITY OF LABOR MPL = (δL/δK) = impact on the quantity produced of an infinitesimal variation of labor (keeping capital constant) → δY/δL = variations of Y generated by variations of L (dL) 𝛅𝐘 𝛅𝐘 𝒅𝒀 = 𝟎 = 𝒅𝑲 × + 𝒅𝑳 × = 𝒇𝒌 𝒅𝑲 + 𝒇𝒍 𝒅𝑳 𝛅𝐊 𝛅𝐋 where f k, f l are the marginal productivity functions 3.3 AN IMPORTANT PARENTHESIS: MARGINAL AND AVERAGE FACTOR PRODUCTIVITY The shape of the marginal productivity function can be deduced from the production function if other factors are constant → we can look at the production function and obtain the marginal productivity of the factor → if the marginal productivity is positive, it means that as the factor increases, the product increases (and as factor decreases, product decreases) L↗ L↘ This example uses L and MPL, but it’s the same with K and MPK MPL + Y↗ Y↘ MPL - Y↘ Y↗ K↗ K↘ MPK + Y↗ Y↘ MPK - Y↘ Y↗  Initially, increasing L increases Y (positive MPL), and MPL increases as L increases After a certain increase in L, with each new worker, MPL declines → it still increases Y; decrease of MPL can be due to many factors: o growing organizational problems [addition of extra workers on a limited plot of land] o the entrepreneur first hires the best, only after the less good ones o organizational, motivational, technical, strategic skills of the entrepreneur become less effective as the company grows At some point, MPL becomes negative → with increase in L, Y declines (decreasing section of the production function = not considered because of hypothesis of monotonicity of technology → entrepreneur doesn’t use technologically inefficient combinations of inputs) MPL also depends on the > or < availability of other factors (K) → it increases with the increase in other factors [discovery of a new factor, buying new land] → the function rises Thomas Robert Malthus (classical economist from 18th century) was concerned with decreasing MPL = population growth would lead to product increases not sufficient to feed all the inhabitants → he is interested in income/production per capita AVERAGE PRODUCTIVITY OF LABOR (APL) = quantity of product Y available per unit of workers; it varies as the number of workers considered varies (it’s a function of the number of workers) and it has a relationship with the function of MPL; it can be measured by the ratio between 𝒀 the ordinate and the abscissa through each point of the production function → 𝑨𝑷𝑳 = 𝑳 Initially, APL increases with MPL, but it’s always lower (weighed down by initial L) When MPL begins to decrease, APL still increases (new L is still greater than average) → max APL is when APL = MPL APL begins to decrease as MPL decreases (but less = previous higher values of L still count) In recent centuries the population has increased, but also the product per capita → Malthus didn’t consider the possibility of: technological progress = same inputs provide more output, combining better with each other growth of other factors = availability of other factors like capital has increased → output increases 3.4 PROPERTIES OF ISOQUANTS (1) At least one of 2 factors [example: L] has a positive MP = when L increases (other factors constant) max product increases → we are out of the isoquant Y = Y0 and have moved to a production technique with a higher max output → to go back to the original isoquant there are 2 options: MPK > 0 = K must be decreased to reduce the max MPL + MPL - product to Y0 → decreasing isoquant decreasing increasing MPK + isoquant isoquant MPK < 0 = K must increase to reduce the max product to increasing output Y0 → increasing isoquant MPK - isoquant inefficient The entrepreneur behaves in a technologically efficient way = he produces with the least possible use of one factor given the use of the other → he wants to maximize profit = minimize cost, but on the growing part of the isoquant costs aren’t minimized [he could produce the same quantity with less input = at a lower cost] → we exclude growing parts of isoquants (technologically inefficient) (2) Since both factors have positive MP, the max quantity produced increases along isoquants that move away from the origin combinations of inputs above the isoquant are inefficient to produce Y = Y0 (they produce efficiently a > output) combinations of inputs below the isoquant can’t technically produce Y0 [these concepts seem similar to indifference curves and utility functions, but they are different → utility/marginal utility weren’t measurable, the output/marginal productivity are] (3) The set of inputs needed to produce Y0 is convex: if there are 2 combinations of inputs (K1, L1) and (K2, L2) that produce a certain quantity Y0, then any combination of the 2 produces at least a quantity equal to Y0 → [∝ 𝐾1 + (1−∝)𝐾2 ; ∝ 𝐿1 + (1−∝)𝐿2 ], 0 quantities of product] Convexity of technology and convexity of isoquants imply that the slope is negative and decreasing → it can be 𝛅𝐘 𝛅𝐘 deduced from the condition 𝒅𝒀 = 𝟎 = 𝒅𝑲 × + 𝒅𝑳 × = 𝒇𝒌 𝒅𝑲 + 𝛅𝐊 𝛅𝐋 𝒅𝑲 𝒇𝒍 𝑴𝑷𝑳 𝒇𝒍 𝒅𝑳 which implies that on the isoquant = − 𝒇𝒌 = − 𝒅𝑳 𝑴𝑷𝑲 MARGINAL RATE OF TECHNICAL SUBSTITUTION (MRTS) = absolute value of the slope of the isoquant, ratio of marginal productivity → it tells how much capital we can do without, when we increase the use of the labor factor by one unit, to keep the maximum production unchanged This rate is decreasing in absolute value (implied by convexity of the isoquant) = as we increase L by one unit at a time, we need smaller and smaller reductions of K to get the same Y as we increase L in the input combinations → decrease in MRTS is based on factors of production that gradually become less and less capable of generating additional product as their use decreases 𝑴𝑷𝑳 𝑴𝑹𝑻𝑺 = − 𝑴𝑷𝑲 Decrease in MRTS is due to: a. decreasing MPL and MPK = as L ↗ and K ↘, the increase in output generated by a given and small increase in L becomes gradually smaller, and the reduction in K will become gradually smaller b. decreasing MPL and increasing MPK (only a little) and vice versa  c. if MPL and MPK were both increasing, the MRTS couldn’t be decreasing → we exclude it when we exclude convex isoquants towards the origin 4 THE CHOICE OF HOW TO PRODUCE 4.1 FIXED INPUTS AND ISOCOSTS: THE ROLE OF TIME VARIABLE costs VC(Q) = costs that vary with the variation of production FIXED costs FC = costs that don’t vary with the variation of production, they don’t depend on the choice of how much will be produced→ linked to the time horizon to which the entrepreneur refers in making his decisions = they can become variable TOTAL cost = minimum cost of producing any quantity Q → TC (Q) = FC + VC (Q) Fixed costs exist because of fixed inputs [rent for a shed, cleaning services] = inputs for which it isn’t possible to vary the max level of use → the company has to bear these costs regardless of the level of production → fixed inputs generate a fixed cost (not economic cost = doesn’t affect the firm’s decision on whether and how much to produce) If the entrepreneur was able to use only part of a certain fixed input without paying for the services he doesn’t use, TC would vary until the max amount of services available is used [possibility of subletting the shed/to pay only the cleaning for the spaces used] → the input even if fixed doesn’t generate fixed costs SHORT term = there is at least one factor of production that can’t be modified (there is a fixed input) LONG term = all the levels of production factors can be varied (there are only variable costs) → in the long term each production factor can be modified in its maximum amount of services it provides to the enterprise → there are no fixed inputs and no fixed costs Problem of how to produce in short and long term: the firm takes input prices as given [salary, workers’ income, interest on capital, etc] → we assume that the company is a price-taker on the input market [even if unrealistic] = no market power 4.2 THE CONCEPT OF ISOCOSTS AND THE LONG-TERM CHOICE ISOCOST curve = place of combinations of production techniques labor-factor and capital-factor that all have the same cost for the 𝑇𝐶 0 𝑤0 entrepreneur → 𝑻𝑪𝟎 = 𝒘𝟎 𝑳 + 𝒓𝟎 𝑲 or 𝐾 = − ( 𝑟0 ) × 𝐿 𝑟0 it’s a straight line with slope equal to the negative of the relative costs of the factors it tells the maximum K (ordinate) we can use for each given use of L (abscissa) when the factor costs are w0 and r0 and the cost is TC0 it’s downward sloping = for a given TC0, the more you use of one factor, the less you have to use of the other one [w0 and r0 are the unit remuneration of the factors L and K] ECONOMICALLY EFFICIENT = technique that allows the production of a given quantity at the lowest possible cost → it’s the tangency point between isoquant and iso-cost There are many output/technologically efficient techniques, but less economically efficient ones = each combination on the same isoquant has a different cost, so the entrepreneur chooses the combination of factors that minimizes production costs for a given unit cost of factors 4.3 THE COST FUNCTION AND THE CHOICE OF HOW TO PRODUCE IN THE SHORT TERM In the short term the choice of how much to produce considers that not all inputs are variable → the firm chooses the production technique with a limit of use for the fixed factor, but fixed inputs and fixed costs don’t necessarily occur simultaneously: A. Fixed input – Recoverable costs = the company only pays for what it actually uses → the cost of producing these quantities is higher in the short term than in the long term because we don’t have full availability of all the inputs B. Fixed input – Sunk costs = the company pays regardless of the amount of factor used → it’s always better to fully use the factor at production capacity TECHNOLOGY EXPANSION PATH = curve that combines all optimal input combinations as production changes and input prices remain constant: A. combinations of productive factors where slope of the iso-cost = slope of the isoquant o when Y>Y2, the best combination becomes (Ln, K2) B. combinations of productive factors along the straight line parallel to the abscissa axis = production capacity of the fixed factor SHORT-TERM COST FUNCTION We now know for each quantity the minimum cost of producing it: we can construct the minimum cost functions → it’s an increasing function [the more you produce, the higher the total minimum cost]; we assume that K=K0 is the production capacity of a fixed input with a fixed cost r0K0 (r0 € = unit cost of 1 hour of rental of machines): 1. Rewrite the equation of the minimum short-term TC necessary to produce Q when unit costs are w0 and r0: o 𝑻𝑪(𝑄(𝐿, 𝐾 0 ), 𝑤0 , 𝑟0 , 𝐾0 ) = 𝑭𝑪 + 𝑽𝑪 (𝑸, 𝒘𝟎 ) = 𝒓𝟎 𝑲𝟎 + 𝑽𝑪 (𝑸, 𝒘𝟎 ); FC ≠ economic cost 2. Determine the minimum average cost per unit of production that the entrepreneur has to bear to produce any quantity Q 𝒓𝟎 𝑲𝟎 𝑽𝑪 (𝑸,𝒘𝟎 ) o ATC = AFC + AVC → 𝑨𝑻𝑪(𝑄, 𝑤0 , 𝑟0 ) = + 𝑸 𝑸 o Minimum average total cost = minimum average fixed cost + minimum average variable cost → 𝑨𝑻𝑪 = 𝑨𝑭𝒊𝒙𝑪 (𝑸, 𝒓𝟎 ) + 𝑨𝑽𝑪 (𝑸, 𝒘𝟎 ); AFixC ↘ as Q ↗ 3. Examine a simple economic profit equation + fixed costs o 𝛱(𝑄, 𝑤0 , 𝑟0 , 𝐾0 ) = 𝑇𝑅(𝑄) − 𝑇𝐶(𝑄, 𝑤0 , 𝑟0 , 𝐾0 ) = 𝑝(𝑄)𝑄 − 𝑄 𝐴𝑇𝐶 (𝑄, 𝑤0 , 𝑟0 , 𝐾0 ) o 𝜫(𝑸, 𝒘𝟎 , 𝒓𝟎 , 𝑲𝟎 ) = (𝒑(𝑸) − 𝑨𝑻𝑪(𝑸, 𝒘𝟎 , 𝒓𝟎 , 𝑲𝟎 ))𝑸 By comparing ATC and price the entrepreneur understands if profit is > 0 → he can face competition by keeping AVC low (and can wipe out competition by lowering price thanks to low AVC) 4. Determine the Variable Cost function: if to produce Q1 we minimize costs and use the economically efficient technique L1 we have  o 𝑽𝑪 (𝑸𝟏 , 𝒘𝟎 ) = 𝒘𝟎 𝑳𝟏 € 5. Using this equation, the minimum ATC is: 𝒓 𝑲 𝒘 𝑳 o 𝑨𝑻𝑪(𝑄, 𝑤0 , 𝑟0 ) = 𝟎 𝟎 + 𝟎 𝟏 𝑸𝟏 𝑸𝟏 6. The AVC depends on how many units of product the worker will generate → it’s linked with APL: 𝑸(𝑳,𝑲𝟎 ) o 𝑨𝑷𝑳 (𝑳, 𝑲𝟎 ) = [Q(L, K0) is the production function] 𝑳 𝟎 𝒘 𝑳 𝒘𝟎 ×𝑳 𝒘𝟎 o 𝑨𝑽𝑪 (𝑸(𝑳, 𝑲𝟎 ), 𝒘𝟎 ) = 𝑸(𝑳,𝑲 = = ) 𝟎 𝑳 ×𝑨𝑷𝑳(𝑳,𝑲𝟎 ) 𝑨𝑷𝑳(𝑳,𝑲𝟎 ) o AVC ↘ as APL of the workers ↗ [AVC reaches a min at the max of APL] 7. We draw the APL function and AVC function starting from the production function, then derive the TC curve by shifting it by an amount = to FC; note that the production function is a counterpoint to the TC function [convex → concave VS concave → convex] The same relationship exists between APL and AVC functions // between MC and MPL: MC = minimum cost increase we need to produce an infinitesimal extra unit of product → MC = derivative of the TC function 𝜹𝑻𝑪(𝑸(𝑳,𝑲𝟎 ),𝒘𝟎 ) o 𝑴𝑪(𝑸(𝑳, 𝑲𝟎 ), 𝒘𝟎 ) = = 𝜹𝑸 𝜹(𝒘𝟎 𝑳+𝒓𝟎 𝑲𝟎 ) 𝜹(𝒘𝟎 𝑳) 𝜹(𝒓𝟎 𝑲𝟎 ) 𝜹𝑳 = + = 𝒘𝟎 𝜹𝑸 + 𝟎 = 𝜹𝑸 𝜹𝑸 𝜹𝑸 𝟏 𝒘𝟎 𝒘𝟎 𝑴𝑷𝑳 (𝑸,𝑲 ) = 𝟎 𝑴𝑷𝑳((𝑸(𝑳,𝑲𝟎 );𝑲𝟎 ) MC = inversely linked to technology, ≠ to FC → it doesn’t influence the decision of producing 1 more/less unit: 𝑇𝐶(1)−𝑇𝐶(0) 𝑉𝐶(1) o 𝑴𝑪(𝟏) = = 𝐹𝐶 + 𝑉𝐶(1) − 𝐹𝐶 − 𝑉𝐶(0) = = 𝑨𝑽𝑪(𝟏) 1−0 1 1. MC and AVC curve start at the same point, they are both initially decreasing [but AVC at a smaller pace → AVC remain > MC] 2. When MC stop decreasing [producing 1 more unit is > expensive than producing the previous one], AVC continue to decrease 3. AVC reach a minimum when AVC = MC (at Q0) → point of efficient production scale 4. AVC start to increase again, but MC > AVC, and ATC will continue to decrease because AVC increases < than AFixC decrease 5. min of ATC when ATC = MC (at Q1) 6. ATC start to increase again (the increase in AVC outweighs the decrease in AFixC) Note that AVC first ↗ and then ↘ as Q ↗, while AFixC continues to ↘ going towards 0 → FC are irrecoverable, so the entrepreneur will decide whether to produce or not in the short term based on the comparison between AVC and price [he compares the cost of producing each unit with the revenue he gets from selling each unit] → lowering the minimum costs of producing allows for greater profits 4.4 THE LONG-TERM COST FUNCTION A) TECHNOLOGY In the long run all factors of production are variable [≠ FC]: all factors vary simultaneously, so we distinguish based on returns to scale CONSTANT returns to scale = if the use of all production factors increases by a certain proportion, there is an exactly proportional increase in output [double L and K → double Y] → skill of producing independent from the size of production/company = same technical efforts whatever the size INCREASING returns to scale = if the use of all production factors increases by a certain proportion, there is a more than proportional increase in output → the company expands by improving, combines factors in an even better way DECREASING returns to scale = if the use of all production factors increases by a certain proportion, there is a less than proportional increase in output → as the size of the company grows, it becomes more difficult to coordinate the activity of the various factors of production; it denotes possible future business issues in the growth process Don’t confuse returns to scale with marginal COBB-DOUGLAS function [𝒀 = 𝑨𝑳∝ 𝑲𝜷 ] productivity!! → decreasing MPK and MPL: impact on Y of MP Short term variations of 1 factor L↑ MPL ↓ MPK ↑ Returns impact on Y of K↑ MPK ↓ MPL ↑ Long term to Scale variations of all factors α + β = 1 → constant returns to scale α + β > 1 → increasing returns to scale B) THE COMPANY’S COSTS IN THE LONG TERM α + β < 1 → decreasing returns to scale In the long run, the entrepreneur will choose the combination of input that guarantees the lowest TC (tangency between isoquant and isocost) → at the optimum point, the condition is that the MRTS is equal to the ratio between the unitary factor costs 𝑴𝑷𝑳 𝒘 𝑴𝑷𝑳 𝑴𝑷𝑲 𝑴𝑹𝑻𝑺 = = ⇒ = 𝑴𝑷𝑲 𝒓 𝒘 𝒓 Economic efficiency means there is no further way to economize on the expenditure for the factors necessary to produce that Q; if we aren’t at a point of tangency, we aren’t