ECON1020/ECON1022 Foundations/Principles of Microeconomics Lecture Notes PDF

ECON1020/ECON1022 Foundations/Principles of Microeconomics Lecture Notes Maksymilian Kwiek1 18th September 2024 1 University of Southampton ...

ECON1020/ECON1022 Foundations/Principles of Microeconomics Lecture Notes Maksymilian Kwiek1 18th September 2024 1 University of Southampton  1 This study guide is more than PowerPoint slides, but less than a textbook. Use these notes to check what is covered, but you will benefit from using a regular textbook. There are 12 chapters corresponding to 12 broad topics, and they are covered in 12 teaching weeks of the semester. Technical terms are introduced in italics. Table 1: Tentative plan Part Week Topic ECON1020 extras 1 Behavioural functions 2 Competitive equilibrium I 3 Normative properties Core 4 Externalities, public goods Incentives 5 Monopoly Rationing 6 Game theory, oligopoly Congestion 7 Consumers Cooperation 8 Firms Money Dive 9 Competitive equilibrium II Costs 10 Welfare & equality Economic systems 11 Exchange General Equilibrium Review 12 Central messages, method Chapter 1 Behavioural functions 1.1 Agents and their behaviour Economic agents have agency, which means they possess the ability to make their own decisions. These decisions are made based on their preferences and within the limits of external constraints. Therefore, an agent’s behaviour is influenced by these external factors. The relationship between behaviour and external incentives can be described as a behavioural function. External F actor → Behaviour 2 1.2. DEMAND 3 Agent External Factor Behaviour consumer price of the good quantity demanded consumer price of another good quantity demanded worker wage effort firm price of the product quantity supplied family child tax credits fertility decision student difficulty of exam option choice driver congestion commuting decision government political protest political reform political activist political reform political protest firm other firm’s price this firm’s price firm other firm’s investment this firm’s investment Table 1.1: Examples of behavioural functions 1.2 Demand 1.2.1 Definition and properties One of the most prominent behavioural functions is the demand function. This function summarizes how consumers’ purchasing decisions react to prices. In other words, the quantity of a good that a consumer intends to purchase (behaviour) changes with the price of that good (external factor). Shape: the demand function is postulated to be downward sloping, indicating that the higher price causes the consumer to want to buy less. This ‘law of demand’ is confirmed empirically and has strong theoretical grounds. There are theoretical caveats that will be discussed later. 1.2. DEMAND 4 Price Price of of apples apples Quantity of apples Quantity of apples Figure 1.1: Change of price triggers the change in quantity demanded (left), change of other things is illustrated as a shift of the demand curve (right) Remarks 1. Notation could be any of these and more: q = Q (p), q = q (p), q = D (p),... 2. Note the ‘reversed’ axis. The price (exogenous parameter) is on the vertical axis, and the quantity (dependent variable) is on the horizontal axis, which is the opposite of the usual convention! 3. The quantity demanded may depend on other factors such as income, prices of related goods, tastes, expectations, etc. 4. Demand (function or curve) is the relationship between price and quantity (the entire curve). Quantity demanded is a number of units demanded at one price (a point on the curve). See Figure 1.1: both pictures show that the quantity demanded increased, but only the picture on the right shows that the demand changed. The effect of a change in the price of this good 1.2. DEMAND 5 results in a change in quantity demanded, causing a movement along the curve. The effect of a change in other exogenous factors results in a change in demand, causing the movement of the curve itself (shifts). For example, if income increases, the demand shifts (maybe to the right so that quantity demanded is greater than before for all prices). 5. Ceteris paribus means ‘keeping everything else constant’. The picture on the left shows a change of price ceteris paribus (that is, income and other things staying as before). The picture on the right shows a possible effect of changing income ceteris paribus (that is, keeping other things constant, in particular the price of this good) 6. Quantity demanded is not the same as quantity needed since the concept of needs is not defined. Quantity demanded is not the same as quantity purchased as there could be rationing. 7. Market demand is the horizontal sum of individual demands. 1.2.2 An alternative interpretation We looked at the demand as a behavioural function, p → q. But we can look at its inverse, q → p. The demand function seen this way depicts the highest price the consumer is willing to pay to voluntarily buy the marginal q’th unit of this good after all inframarginal units have already been secured. Thus, this reservation price can be interpreted as a marginal value, where the term marginal refers to the last or incremental unit. Marginal Value: this is the value to a consumer of the last unit of consump- tion expressed in monetary terms (also known as marginal willingness to pay). Downward-sloping demand shows that Marginal Value diminishes as the consumer has more and more of that good. 1.3. SUPPLY 6 Notation could be any of these and more: p = M V (q), p = v (q), p = p (q), p = P (q),... 1.3 Supply 1.3.1 Profit-maximizing competitive firms The cost function describes the minimal cost of producing q units of final output. The cost function is denoted C (q). It conveniently summarizes technology and input prices. Two assumptions: 1. We assume that these firms cannot change the market price p. Such firms are called competitive firms,1 or price-takers. 2. We assume that firms want to maximize profit, which is just the difference between the revenue and costs, π = pq − C (q). The variable that is under firms’ control is the production level q. Thus, they solve max pq − C (q) q Mathematically, the first order condition is dπ/dq = 0, or simply p = C ′ (q), where the right hand side is the derivative (or slope, rate of change) of the cost function. This is a key object in the producer theory, called the Marginal Cost, M C (q). It says how fast the cost changes, if the production increases by one (or infinites- imal unit). All of the following are essentially the same: M C (q), C ′ (q), ∆C/∆q, 1 Be aware of a possible terminology confusion: "Competitive" in this context does not imply that the firms are aggressive or have lower costs than others in the industry. Instead, "compet- itive" is used to differentiate from firms with market power, such as monopolies. 1.3. SUPPLY 7 Marginal Cost of q, marginal willingness to accept. The profit maximizing con- dition can be written as p = M C (q).2 The term marginal willingness to accept comes from the fact that M C (q) is the minimal price that the seller will accept to produce qth unit. Interpretation: Notice how the Marginal Cost is a mirror image of the con- sumer’s Marginal Value. M C represents the minimum amount of money needed to cover the cost of producing the q’th unit. If the market price (which is exo- genous) is greater than the Marginal Cost, p > M C (q), then the firm will earn more than it costs to produce this extra unit. This results in pure profit, making it profitable for the firm to increase production. Conversely, if the price is lower than the Marginal Cost, the firm will save money by reducing production. The firm will continue to adjust production q until these two forces balance out, reaching a point where p = M C (q). Increasing Marginal Cost: Recall that for this condition to describe firm’s behaviour, it must be that M C is increasing. This often makes sense in real life because it costs more and more to produce each extra unit as we run into diminishing returns and run out of ‘low-handing fruit’. However, this does not have to happen for all technologies. If it does not, then this analysis does not apply (we will discuss this later). 1.3.2 The supply function Therefore, the condition p = M C (q) can be viewed as a behavioural function that tells us firm’s quantity supplied q as a function of exogenous market price p. That is, when the price on the left-hand side changes, the firm will reassess its situation and will react by adjusting q on the right-hand side so that the equality is Recall the mathematical second order condition: it must me that C ′′ (q) < 0. That is, the 2 Marginal Cost must be increasing. 1.3. SUPPLY 8 Price Price of of corn corn Quantity of corn Quantity of corn Figure 1.2: Left - the supply does not change but the quantity supplied does. Right - the supply changes restored. Since M C is increasing, the behavioural relationship is positive, meaning the increase in price will compel the firm to increase the quantity supplied, as seen in the left picture on Figure 1.2. Remarks 1. Quantity supplied is a point on a curve, the amount of the good that the firm intends to sell at a given price, holding other factors constant. Supply refers to the entire curve, indicating the quantity supplied at each price. See Figure 1.2: a change in the price of corn results in a movement along the curve, whereas a change in technology or input prices results in a shift of the curve. 2. Market supply is the horizontal sum of individual supplies (see Figure 1.3). For instance, let the price be p′ and suppose that at this price, firm 1 supplies 1.4. ELASTICITY OF BEHAVIOURAL FUNCTIONS 9 £ Firm 1 Firm 2 Market Supply p’ q q1 q2 q1 + q 2 Figure 1.3: Market supply quantity q1 and firm 2 supplies quantity q2. Then, the total quantity supplied at this price by the market, consisting of these two firms, is q1 + q2. 1.4 Elasticity of behavioural functions 1.4.1 General definition Consider any behavioural function f : p → q, that is q = f (p). It is important to know how much the behaviour q responds to a change of the exogenous factor p. We could use the slope, ∆q/∆p, but slopes depend on units. Thus, we will use a similar notion called elasticity, which is like a slope but it uses percentage changes 1.4. ELASTICITY OF BEHAVIOURAL FUNCTIONS 10 rather than changes in physical units. Definition: ”%∆q” ϵ= ”%∆p” ∆q/q ∆q/∆p slope of the tangent = = = ∆p/p q/p slope of the secant 1.4.2 Examples and properties Suppose that the price goes up from £1000 to £1010 causing the consumer to change their behaviour so that the quantity demanded falls from 50 to 47.5 units. Then ”%∆p” is the percentage change of price, ”%∆p” = 10/1000 = 1%, while ”%∆q” is the percentage change of quantity, ”%∆q” = −2.5/50 = −5%. There- fore, the price elasticity of demand is −5%/1% = −5 (see Figure 1.4). Observations: Elasticity has no units, as opposed to slope. Hence, it is irrelevant whether one uses € versus £, or litres versus pints. In the example, the slope is −0.25, but if we expressed the price in pennies instead of pounds, the slope would change by a factor of 100. Elasticity is independent of units. Elasticity can be measured between two points (before the change and after the change), or at a point (when the change is infinitesimal). The numerical values could be different. Elasticity can change along the behavioural function. A constant slope func- tion (linear) has a changing elasticity. A constant elasticity function has a changing slope. Note: Demand and supply functions are drawn ‘the other way round’. The endo- genous behaviour is on the horizontal axis and the exogenous factor on the vertical. 1.4. ELASTICITY OF BEHAVIOURAL FUNCTIONS 11 price Demand ∆p p ∆q q Quantity Figure 1.4: Elasticity 1.4. ELASTICITY OF BEHAVIOURAL FUNCTIONS 12 So, a flat/horizontal demand function indicates a very responsive demand. Ter- minology: Perfectly elastic demand ϵ = −∞, Elastic demand ϵ < −1, Unit elasticity demand ϵ = −1, Inelastic demand ϵ > −1, Perfectly inelastic ϵ = 0. ‘Price elasticity of demand’ where q is the quantity of a good and p is the price of the same good, is not the only elasticity. Some important elasticities include: Price elasticity of demand: qapple is quantity demanded, papple is the price of the same good. Cross-price elasticity of demand: qapple is quantity demanded, pbanana is the price of some other good. Income elasticity of demand: the behaviour is quantity demanded, the ex- ternal factor is consumer’s income. Price elasticity of supply: the behaviour is quantity supplied, the external factor is the price of this good. You can define elasticity for any function, behavioural or not. 1.4. ELASTICITY OF BEHAVIOURAL FUNCTIONS 13 price price Demand (inelastic) Demand (elastic) p p q q Quantity Quantity Figure 1.5: Expenditure 1.4.3 Expenditures/Revenue and elasticity Total consumers’ expenditure (and thus firms’ revenue) is R = pq. If the price goes up, then there are two offsetting effects: p increases and q decreases. Fact: if the demand is inelastic ϵ > −1 then total R goes up (as price increases), otherwise it goes down. Graphically, R is the shaded rectangle in Figure 1.5