University of Ghana AGEC 211 Microeconomics Past Paper 2014/2015 PDF

( UNIVERSITY OF GHANA (All rights reserved) COLLEGE OF BASIC AND APPLIED SCIENCES FIRST SEMESTER EXAMINATIONS: 2014/2015 LEVEL 200: BACHELOR...

( UNIVERSITY OF GHANA (All rights reserved) COLLEGE OF BASIC AND APPLIED SCIENCES FIRST SEMESTER EXAMINATIONS: 2014/2015 LEVEL 200: BACHELOR OF SCIENCE IN AGRICULTURE AGRICULTURAL ECONOMICS AND AGRIBUSINESS AGEC 211: MICROECONOMICS: PRINCIPLES AND APPLICATIONS TO HOUSEHOLDS AND FIRMS TWO (2) HOURS INDEX NUMBER,_ _ _ _ _ _ _ _ __ ANSWER ALL QUESTIONS. Do Sections A and B on the Question Paper. Use the Answer Booklet for Sections C and D. ATTACH BOTH and submit SECTION A: (25 MARKS) /25 MINUTESI Choose the most appropriate answer by indicating the correct alphabet. A. Increase the price of the good. ~..... elasticity of demand of a product is less than 1, then to increase total revenues: J. If the price B. decrease the price of the good C. ho Id the price of the good constant D. decrease the demand for the product ,.. 2. The slope of the indifference curve measures the A. the slope of the budget line B. total utility of a good C. space on an indifference curve D. marginal rate of substitution 3. Which of the following best describes the long run position ofa firm: A. all the inputs of the firm is variable 8. all the inputs of the firm is fixed C. an input of the firm is fixed D. production is in equilibrium 4. Which of the following could not cause a shift of the demand curve for product M? A. a decrease in consumer income B. an increase in the prices of goods which are substitutes for product M C. a decrease in the price of goods which are complements for product M D. an increase in the price of product M 5. Which of the following is a characteristic of a monopoly in a specific market? A. the firm is a price-taker B. a small number of buyers in product markets C. many sellers and buyers of all products D. no market entry into this market by other producers is possible Page 1 of5 Prof. Daniel Bruce Sarpong 6. li ~lkh will be most characteristic of an oligopoly: A. easy entry into the industry B. a few large producers C. product standardization D. no control over price 1. tm whe equilibrium condition of the producer, the slope of the isoquant would equate A. the slope of the isocost line B. total product of a good C. ratio of the marginal utilities of the commodity D. ratio of the marginal functions of the factor inputs S..¢\~] individual's labour supply curve will bend backwards when: A. the substitution effect of a higher wage is greater than income effect B. the income effect of a higher wage is greater than the substitution effect C. the income effect of a higher wage is equal to the substitution effect D. the demand for labour is in the short run I). ~ ltJe government guarantees a minimum price to maize producers that is above the market price A. producer surplus decreases C. the quantity demanded increases B. the economy as a whole always gains D. it has to buy the surplus produced Figure I Q No. of Workers H:."\l. l efer to figure). Marginal product is zero: A) at point A B) at point B C) at point C D) none of above t.l. Refer to figure I. Marginal product reaches a maximum at: A ) at point C B) at point B C) at point A D) the origin 112. Most goods can be classified as normal goods rather than inferior goods. The definition of a normal: good means that A. the percentage change in consumer income is greater than the percentage change in price B. the percentage change in quantity demanded of the good is greater than the percentage change jn consumer income C. as consumer income increases, consumer purchases of the good increase D. the income elasticity of demand is negative B. Ama's income is held constant in the face of increases in the price of good Z. Ama's demand for good Z however decreases. Good Z is: A. normal good C. a Giffen good B. inferior good D. a complement ¥4. Suppose the price of fish decreases and Ama discovers that she can eat more fish because they are cheaper than beef. This is an example of a) the substitution effect. b) the f10rmal good effect. c) the law of diminishing marginal utility d) the law of increasing demand. Page 2 of 5 Prof. Daniel Bruce SIITp4.f: g ·15. Which of the following best expresses the la\v of diminishing marginal utility?.3 A. The more a person consumes of a product, the smaller becomes the utility which he receives from its consumption. B. The more a person consumes of a product, the smaller becomes the additional utility which she receives as a result of consuming an additional unit of the product. C. The less a person consumes of a product, the smaller becomes the uti lity wh ich she receives from its consumption. D. The less a person consumes of a product, the smaller becomes the additional utility which he receives as a result of consuming an additional unit of the product. 16. Which of the following statements is true? A. The substitution and income effect of a higher wage both cause a worker to work less B. The substitution and income effect of a higher wage both cause a worker to work more C. The substitution effect of a higher wage causes a worker to work more, while the income effect of a higher wage causes a worker to work less D. The substitution effect of a higher wage causes a worker to work less, while the income effect of a higher wage causes a worker to work more 17. [fthe quantity supplied of a product is in excess of the quantity demanded for the product, then A. there is a surplus of the product B. there is a shortage of the product C. the product is a normal good D. the product is an inferior good 18. A schedule which shows the different amounts of a commodity suppliers are willing and able to put on the market at each price is: A. Supply B. Demand C. Quantity supplied D. Quantity demanded 19. If the supply curve shifts from left to right on a graph, this indicates: A. a increase in supply B. an increase in quantity supplied C. a decrease in supply D. a decrease in quantity supplied 20. If two goods are substitutes for each other, an increase in the price of one will necessarily A. decrease the price for the other B. increase the price for the other C. decrease the quantity demanded of the other D. increase the quantity demanded of the other 21. If a 1% fall in the price of a product causes the quantity demanded of the product to increase by 2%, demand is A. inelastic C. unit elasticity B. elastic D. perfectly elastic 22. Which of the following could cause an increase in the supply of maize in Ghana? A. an increase in the price of maize B. deterioration in the production technology for maize C. a decrease in the price of maize in the market D. none of the above 23. The isoquant is A. concave C. linear B. convex D. positive Page 3 ofS Prof. Daniel Bruce Sarpong 24. Which of the following is not an essential assumption of the theory o f consumer behavior? A. The consumer has a sufficient income. B. The consumer is rational. C. Goods and services are not free. D. Goods and services yield decreasing amounts of marginal utility as the consumer buys more of them. 25. A study shows that the coefficient of the cross price elasticity of PZ and FR is positive. This information indicates that PZ and FR are A. normal goods C. substitute goods B. independent goods D. complementary goods SECTION B: [20 MARKS] /20 MINUTESj Indicate whether each of the following statements is TRUE or FALSE 26. In production theory, an isoquant is the locus of input combinations, all of which give the same output. 27. An individual consumer's demand curve is more price elastic relative to the market demand curve. 28. Profit-maximisation behaviour implies that a competitive firm will hire a factor input beyond the point where the Value Marginal Product (VMP) of the factor equals the price of the factor. 29. The Marginal Revenue Product is the extra revenue produced by hiring an extra unit of a facto r, other factors held constant. 30. Monopsony is the case of a market dominated by a single seller of the good exchanged in the market. 31. In the long run all inputs are variable; in the short run all inputs are fixed. 32. If the MU,.IPa > MUt/Pb, an individual should choose to cons ume more of good B. 33. A shift in a supply schedule is not the same as a change in quantity supplied when all oth er factors are held constant. 34. In a perfectly competitive economy, it is assumed th at the firm has no market power to a lter its product price but may influence the wage rate. 35. The quantity demanded of a Giffen good decreases as income increases, ceteris paribus. 36. According to the law of demand, only the price of a good influences the amount people will choose to purchase. 37. A change in the price of carrots will cause a movement alon g the demand for carrots curve and a shift in the demand for substitute vegetables. 38. The law of supply states that more of a good wi II be suppl ied the low er its price, ceteris paribus. 39. An increase in demand causes equilibrium price and quantity to rise, ceteris paribus. 40. Price elasticity of demand is the ratio of the percentage change in quantity demanded to the percentage change in income. 41. If the price of a good goes up by 5% and the quantity demanded falls by 15% , the price e lasticity of demand is 1/3. 42. The principle of diminishing marginal utility states that people enjoy consuming more of a good. 43. Technical efficiency is achieved in production when the fewest amount of inputs poss ible are used to produce a given output. 44. The higher the wage, the lower the quantity of labor supplied, ceteris paribus 45. The demand for labour is based on the worker' s trade-off between income and leisure. Page 40fS Prof. Daniel Bruce Sarpong SECTION C [40 MINUTES! s You have an income ofGHC 50 to spend on two commodities, PZ and FR. FR costs GHC 12.5 46. per unit, and PZ cost GHC 10 per unit. Using this information, and by showing working, answer the following: a) Write down your budget equation. b) Write down your budget line b) If you spent all your income on FR, how much could you buy? c) If you spent all your income on PZ, how much could you buy? d) Suppose that the price of PZ increases to GHC IS. ceteris paribus. Write down your new budget I ine. What is the new price ratio of PZ to FR? (10 Marks) 47. Using the information on the Utility functions provided, derive by showing working, the marginal utilities (MU) and the marginal rate of substitution (MRS (.-':"X2) of each function: 1 (a) 2x ]+3x/ (b).JX,+6Xl (c) Xz+X/ (d) --Jx/--Jxz 1 (e) X(,(; (10 Marks) 48 Translate this table onto the answer booklet and fill in the blanks Price Percentage change Percentage Interpretation of the Impl ication of the Elasticity in Quantity change in Price magnitude in the estimated elasticity demanded price elasticity to the Total Revenue position of the Firm 0.73 12.5 13.8 20.6 1.10 1.10 2.36 18.6 10.2 10.6 15 marks SECTION D (35 MINUTES) 8 O5 49. Assume the following Cobb-Douglas production function (Pj) for maize: Q = KO. L , where Q is the number of bags of maize produced, K is the units of capital used and L the units of labour employed. If each input is increased proportionally by 1.5 amount a) Compare the pjofthe firm after the increase to the firm's initial pj b) Derive the MRTS K L. c) Estimate the factor intensity of the production function and interpret your results. d) What is the magnitude of the degree of homogeneity? Explain. (10 Marks) 50 The total cost (TC) of repairing X tractors by the Agricultural Engineering Department, College of Basic and Applied Sciences (CBAS), University of Ghana, Legon, is given by TC = 4X2 + 2X + 25 Compute the following: (a) Total Variable Cost (TVC) (b) Total Fixed Cost (TFC) (c) Average Variable Cost (AVC) (d) Average Fixed Cost (AFC) (e) Average Total Cost (ATe) (f) Maginal Cost (MC) (10 marks) Page S ofS Prof. Daniel Bruce SlIrpong  DEPARTMENT OF AGRICULTURAL ECONOMICS & AGRIBUSINESS FIRST SEMESTER 2019/2020 ACADEMIC YEAR AGEC 211: MICROECONOMICS — PRINCIPLES AND APPLICATIONS TO HOUSEHOLDS AND FIRMS Credits: 2 Lecture Period(s) and Venue: Tuesdays, 7.30am – 9.20am Central Cafeteria Course Instructors: Prof. Daniel B. Sarpong Dr. Freda E. Asem 10/10/2019 1  INTRODUCTION Economics: Science/field of study of the HOW to allocate scarce resources among the unlimited/numerous competing ends/needs/wants. These needs include; food, recreation clothing, shelter, education, judiciary etc. “goods” – needed to meet these  Resources have to be expended Economics is also concerned with the efficient use/management of limited productive resources to achieve maximum satisfaction of human material wants 10/10/2019 2  ALL Resources  Production process (by firms) Distribution/ Consumption  Commodities + Services process HH/ (Gov’t  Policies) Several levels of human study:  Sociology: inter-relationships between the society (how society organizes the norms, culture, etc.)  Psychology: the attitude of individual society The economic problem:  what? (cars, bombs, bread?)  How? (what combination)  For whom? 10/10/2019 4 Theory: a systematic/logical/cogent/plausible explanation for the occurrence of a given phenomenon. A model: a simplified picture of reality, an abstract generalization of how relevant data actually behave. A mathematical representation, based on economic theory of an economic unit, usually for prediction purposes. Economics:  Microeconomics  Macroeconomics (total output, total level of employment, total income, aggregate expenditures, the general level of prices) 10/10/2019 5  INTRODUCTION CONT’D Microeconomics deals with the behaviour of individual economic units: consumers, workers, investors, owners of land, business firms, i.e. any individual or entity that plays a role in the function of an economy. Macroeconomics concerns itself with how these economic units interact to form larger units – markets and industries 10/10/2019 6  The Use and Limitations of Microeconomic Theory/Principle Like any science, economics is concerned with the explanation and prediction of observed phenomena. These explanations and predictions are based on theories. These theories are also the basis for making predictions. For example, the “theory of the firm” tells us whether a firm’s output level will increase or decrease in response to an increase in wage rate or a decrease in the price of raw materials. 10/10/2019 7  The Use and Limitations of Microeconomic Theory/Principle Cont’d These theories can be used to construct models using the application of statistics and econometrics – from which quantitative predictions can be made  No theory is “perfectly” correct even in physics, chemistry, economics! The usefulness and validity of a theory depend on whether it succeeds in explaining and predicting the set of phenomena that it is intended to explain and predict 10/10/2019 8  The Use and Limitations of Microeconomic Theory/Principle Cont’d  Hence theories are continually tested against observation for refinements or discarded Do all firms maximize profit all the time? So when evaluating a theory, it is important to keep in mind that it is invariably imperfect! 10/10/2019 9  Methodology of Economics The procedure/approach that economists use to formulate plausible/coherent/consistent/objective/authentic explanation for the occurrence of various economic phenomena. “Economic scientist” use the scientific enquiry to generate the coherent/authentic explanations for the occurrence of various economic phenomena. 10/10/2019 10  Positive vs. Normative Economics Positive economics – issues related to “what is” (“what can be done”) actually the situation in an economy. An increase in tax (ad-valorem) on a good increases price of that good and decreases quantity demanded. Normative economics – “what ought to be” issues in the economy. “What ought to be” – depends on the moral whims/caprices or political whims of whoever is determining what ought to be in the economy. 10/10/2019 11 Normative economics: Subject to value (moral/political) judgement of whoever is doing the decision on what ought to be the case. Positive economics – “what is” is largely devoid of subjective value judgements. Why economists disagree! Economists will mostly “agree” on positive issues but “disagree’ on normative issues on the economy. 10/10/2019 12  Fallacies (Economic) 1) The false-cause fallacy – the fact that Event A occurs with or precede Event B does not mean that A has caused B. 2) The fallacy of composition – what is true for each part taken separately is also true for the whole, or reverse. 3) The ceteris paribus fallacy – if the relationship between two variables is to be established, the effects of other factors that are changing as well must not be allowed to confuse the relationship or the ceteris paribus fallacy will occur. 10/10/2019 13  Graphs and their meanings  Direct/inverse relationships  Dependent/independent variables dependent – the effect independent – the cause  Slope of a line  Intercept  Equation form Marginal concept 1) Graphs are tools used to illustrate economic models – visual schemes for picturing the quantitative relationship between 2 variables. 10/10/2019 14  AGEC 211: MICROECONOMICS — PRINCIPLES AND APPLICATIONS TO HOUSEHOLDS AND FIRMS WEEK 2 RECAP Intermediate and Final Goods Concept of a Market Mechanics of Demand and Supply Course Instructors: Prof. Daniel B. Sarpong Dr. Freda E. Asem 10/10/2019 1  Concept of an Intermediate Good  An intermediate good is a product used to produce a final good or finished product.  These goods are sold between industries for resale or the production of other goods.  Examples of intermediate good is salt, wheat, steel, wood, glass, gold and silver, tires etc. 10/10/2019 2  Concept of a Final Good  Final goods refer to those goods which are used either for consumption or for investment.  Example; a bicycle, car, microwave, phone, laptop, a bag of chips etc. 10/10/2019 3  Concept of a Market Market  Any arrangement that makes it possible for buyers and sellers to exchange a commodity/service.  The arrangement could be at a location i.e. supermarket (one seller & several buyers) or Makola (several sellers & several buyers)  The arrangement is not necessarily a physical location. It could be on the telephone/fax/telex/internet or on any means of communication. 10/10/2019 4 Markets can be classified first by:  The type of commodities/services that are exchanged on the market  Cocoa market  Coffee market  Maize market  Whether transaction takes place within the economy or between two (2) different economies  Domestic market  Foreign market: foreign producer in touch with a domestic buyer or vice versa. 10/10/2019 5  Concept of a Market Cont’d  Transaction takes place now or future date for a particular commodity  Spot market  Forward/futures market  Whether the commodity is a final product or intermediate product  Intermediate product market (input market/factor market) e.g. agricultural credit market, rubber market, etc.  Final product market: Consumers derive utility 10/10/2019 6  The Structure of the Market  On the basis of the structure of the market, there are a set of characteristics. a) Number of buyers b) Number of sellers c) Access to information in the market. i.e. technology available, cost structure d) Types of goods exchanged in the market (homogenous/differentiated) e) Ease of exit or entry f) Gov’t or any type of intervention 10/10/2019 7  The Structure of the Market Cont’d  On the basis of the conduct of the market – i.e. the behaviour of the market is influenced/determined by the structure of the market.  Performance of the market  Product is in the right form (quality) right time right place 10/10/2019 8 Market Structure  The number and relative size of firms in an industry. The market structure illustrate the range of market power a firm might possess. Market Power  The ability to alter the market price of a good or service Market Structure Spectrum: Sellers/Producers New competition New products Constantly changing Changes in technology the structure of the Gov’t interventions markets 10/10/2019 9  Perfect Competition  Many firm selling  Many buyers  Firms have no power over the price of goods they produce to sell.  In perfectly competitive markets no single producer/consumer has any control over the price and quantity of the product (Firm’s quantity is small relative to market quantity)  Ease of entry/exit  Relatively no gov’t controls  Profit maximization  Complete access to information 10/10/2019 10  Market Demand Demand for Individual Producer Demand facing single firm in Perfect Competition 10/10/2019 11  Monopolistic Competition  There are many firms  Keen competition  They have some degree of monopoly because of their differential products  Products differentiation  Product of each seller is branded and identified Oligopoly  A few large firms supply all or most of a particular product. E.g. Airline industry, pharmaceuticals, computer and software industry, auto industry 10/10/2019 12  Duopoly  Only two (2) firms supply particular product. E.g. Visa and MasterCard (electronic payment processing market), Airbus and Boeing in the market of large commercial airplanes Monopoly  Single seller/producer supplies entire quantity for the market.  Has power to set market prices, hence are price setters (price maker) e.g. ECG, GWCL 10/10/2019 13  Mechanics of Supply and Demand Demand function  Relationship describing how quantity of a specified commodity/service are related to the price of that commodity/service i.e. (own price) and other factors which determine this quantity. Demand  Quantities buyers are willing and able to purchase. Demand is in reference to a final commodity/service purchased by household. 10/10/2019 14  Mechanics of Supply and Demand Cont’d Hence:  Final Demand (demand by households of final commodity/service) to consume to derive satisfaction or utility.  Intermediate Demand (demand for factor inputs)  Firms purchase goods and services to aid in further production of commodities/services 10/10/2019 15  Utility Function 10/10/2019 16 10/10/2019 17 Demand is the quantity of a good that buyers are willing and able to purchase under a given set of conditions over an specific period of time. Supply is the quantity of a good that sellers are willing and able to sell under a given set of time. 10/10/2019 18  Shortage and Supply in Market 10/10/2019 19  ELASTICITY OF DEMAND It refers to the degree to which consumers change their demand in response to price or income change. Concept of Elasticity  Price Elasticity of Demand: This measures the responsiveness of quantity demanded of a product to changes in its own price. E.g. if the price of alcohol increases, what happens to the quantity of alcohol demanded?  Cross-price Elasticity: This measures the responsiveness of quantity demanded to changes in the prices of other goods (both complements and substitutes). E.g. if the price of one brand of coffee rises, what happens to the demand for another coffee brand? Determinants of Elasticity of Demand (Own Price) 3. The time period  Demand more elastic goods in the long run 4. The number of uses to which a commodity can be put  The more the possible uses, the greater its price elasticity 5. The proportion of income spent on the particular commodity 6. Where demand can be postponed  The commodity, purchase and use of which can be deferred have a highly elastic demand  Determinants of Elasticity of Demand (Income)  Basic determinants of income elasticity  AGEC 211: MICROECONOMICS — PRINCIPLES AND APPLICATIONS TO HOUSEHOLDS AND FIRMS WEEK 2 RECAP Intermediate and Final Goods Concept of a Market Mechanics of Demand and Supply Course Instructors: Prof. Daniel B. Sarpong Dr. Freda E. Asem 10/10/2019 1  Concept of an Intermediate Good  An intermediate good is a product used to produce a final good or finished product.  These goods are sold between industries for resale or the production of other goods.  Examples of intermediate good is salt, wheat, steel, wood, glass, gold and silver, tires etc. 10/10/2019 2  Concept of a Final Good  Final goods refer to those goods which are used either for consumption or for investment.  Example; a bicycle, car, microwave, phone, laptop, a bag of chips etc. 10/10/2019 3  Concept of a Market Market  Any arrangement that makes it possible for buyers and sellers to exchange a commodity/service.  The arrangement could be at a location i.e. supermarket (one seller & several buyers) or Makola (several sellers & several buyers)  The arrangement is not necessarily a physical location. It could be on the telephone/fax/telex/internet or on any means of communication. 10/10/2019 4 Markets can be classified first by:  The type of commodities/services that are exchanged on the market  Cocoa market  Coffee market  Maize market  Whether transaction takes place within the economy or between two (2) different economies  Domestic market  Foreign market: foreign producer in touch with a domestic buyer or vice versa. 10/10/2019 5  Concept of a Market Cont’d  Transaction takes place now or future date for a particular commodity  Spot market  Forward/futures market  Whether the commodity is a final product or intermediate product  Intermediate product market (input market/factor market) e.g. agricultural credit market, rubber market, etc.  Final product market: Consumers derive utility 10/10/2019 6  The Structure of the Market  On the basis of the structure of the market, there are a set of characteristics. a) Number of buyers b) Number of sellers c) Access to information in the market. i.e. technology available, cost structure d) Types of goods exchanged in the market (homogenous/differentiated) e) Ease of exit or entry f) Gov’t or any type of intervention 10/10/2019 7  The Structure of the Market Cont’d  On the basis of the conduct of the market – i.e. the behaviour of the market is influenced/determined by the structure of the market.  Performance of the market  Product is in the right form (quality) right time right place 10/10/2019 8 Market Structure  The number and relative size of firms in an industry. The market structure illustrate the range of market power a firm might possess. Market Power  The ability to alter the market price of a good or service Market Structure Spectrum: Sellers/Producers New competition New products Constantly changing Changes in technology the structure of the Gov’t interventions markets 10/10/2019 9  Perfect Competition  Many firm selling  Many buyers  Firms have no power over the price of goods they produce to sell.  In perfectly competitive markets no single producer/consumer has any control over the price and quantity of the product (Firm’s quantity is small relative to market quantity)  Ease of entry/exit  Relatively no gov’t controls  Profit maximization  Complete access to information 10/10/2019 10  Market Demand Demand for Individual Producer Demand facing single firm in Perfect Competition 10/10/2019 11  Monopolistic Competition  There are many firms  Keen competition  They have some degree of monopoly because of their differential products  Products differentiation  Product of each seller is branded and identified Oligopoly  A few large firms supply all or most of a particular product. E.g. Airline industry, pharmaceuticals, computer and software industry, auto industry 10/10/2019 12  Duopoly  Only two (2) firms supply particular product. E.g. Visa and MasterCard (electronic payment processing market), Airbus and Boeing in the market of large commercial airplanes Monopoly  Single seller/producer supplies entire quantity for the market.  Has power to set market prices, hence are price setters (price maker) e.g. ECG, GWCL 10/10/2019 13  Mechanics of Supply and Demand Demand function  Relationship describing how quantity of a specified commodity/service are related to the price of that commodity/service i.e. (own price) and other factors which determine this quantity. Demand  Quantities buyers are willing and able to purchase. Demand is in reference to a final commodity/service purchased by household. 10/10/2019 14  Mechanics of Supply and Demand Cont’d Hence:  Final Demand (demand by households of final commodity/service) to consume to derive satisfaction or utility.  Intermediate Demand (demand for factor inputs)  Firms purchase goods and services to aid in further production of commodities/services 10/10/2019 15  Utility Function 10/10/2019 16 10/10/2019 17 Demand is the quantity of a good that buyers are willing and able to purchase under a given set of conditions over a specific period of time. Supply is the quantity of a good that producers are willing and able to sell under a given set of time. 10/10/2019 18  Shortage and Supply in Market 10/10/2019 19  AGEC 211 MICROECONOMIC PRINCIPLES AND APPLICATIONS Week 4  PRICE ELASTICITY OF DEMAND Two different types of price elasticity(Ed) can be calculated as follows:  Arc elasticity of demand  Point elasticity of demand Point Method This method uses the original quantity and price as the denominator for their respective variables. Arc/Midpoint Method In this method, we take the averages of original and new prices and quantities to measure elasticity.  Elasticity of Demand cont’d (𝑄2 −𝑄1)/𝑄1 (𝑄2−𝑄1) 𝑃1 Point Ed = = X (𝑃2−𝑃1)/𝑃1 (𝑃2−𝑃1) 𝑄1 (Q2 −Q1) 0.5∗(Q2+Q1) (𝑄2−𝑄1) (𝑃2+𝑃1) Arc Ed = (P2−P1) = X (𝑃2−𝑃1) (𝑄2+𝑄1) 0.5∗(P2+P1) Degrees of Elasticity of Demand Products with price elasticity of demand of less than 1 are said to have a relatively inelastic demand with respect to price; thus they are said to be price inelastic. i.e.0< Ed 1⇒ price elastic Products with a price elasticity of demand exactly equal to 1 are said to have a unit(or unitary) elasticity of demand P P Ed=0 Ed=(-)∞ Q Q Perfectly inelastic demand Perfectly elastic demand  Elasticity and Total Revenue When Ed>1, demand is elastic (Q is strongly responsive to changes in P). When Ed1,% ∆ in Q > % ∆ in P, thus, TR will move in the opposite direction of price.  Elasticity and Total Revenue cont’d i.e P↑ TR↓ P↓ TR↑ So it is better to decrease price to increase revenue for elastic goods Inelastic demand If Ed < 1,% ∆ in Q < % ∆ in P, thus, TR will move in the same direction of price. P↑ TR↑ i.e P↓ TR↓ So it is better to increase price to increase revenue for elastic goods  Elasticity and Total Revenue cont’d Unitary Elasticity If Ed=1,% ∆ in Q=% ∆ in P, thus, TR will not change. Hence, we can use “TR test” to check on the elasticity of a product. 1. If price and TR move in different directions, Ed>1 (demand is elastic). 2. If price and TR move in same directions, Ed>>> Qf Pf (Quantity and “other” price move opposite, -ve) Kenkey & Gari (Substitutes) Qi Pk >>>> Qg Pg  AGEC 211: MICROECONOMICS — PRINCIPLES AND APPLICATIONS TO HOUSEHOLDS AND FIRMS WEEK 2 RECAP Intermediate and Final Goods Concept of a Market Mechanics of Demand and Supply Course Instructors: Prof. Daniel B. Sarpong Dr. Freda E. Asem 10/10/2019 12  Price Elasticity of Supply It is a measure of the extent to which quantity supplied of a good changes when the price of the good changes. %∆𝑄𝑠 Es= %∆𝑃 Perfectly Elastic Supply: A small rise in price increases the quantity supplied by a very large amount hence, supply is perfectly elastic. P S Q  Price Elasticity of Supply Cont’d Elastic Supply: P S Q A 10% rise in the price of a book increases the quantity of books supplied by 20%. Hence, the supply of books is elastic.  Unit Elastic Supply Supply is unit elastic if the percentage change in quantity supplied equals the percentage in price. P S Q A 10% rise in the price of fish results in an increase in quantity of fish supplied by 10%  Price Elasticity of Supply cont’d Inelastic Supply: Supply is inelastic if the percentage change in quantity supplied is less than the percentage change in price. P S Q Example: A 20% rise in the price of a hotel room increases the quantity of hotel rooms supplied by 10%  Price Elasticity of Supply cont’d Perfectly Inelastic Supply: Supply is perfectly inelastic if the percentage change in the quantity supplied is zero when the price changes. P S Q  Cross-Price Elasticity of Supply The cross-price elasticity of supply of two goods X and Y can be given as: %∆QX percentage change in the quantity supplied of X Es= = %∆PY percentage change in the price of Y  Consumer Choice: Utility curve, Utility Surface, Indifference Curve and Indifference Surface Theory of Consumer Behaviour Starts with the examination of the behavior of the consumer since market demand is assessed to be 𝚺 of the demand of individual consumers *This begins with examining the derivation of demand for an individual consumer The consumer is rational if he plans the spending of his income so as to attain the highest possible level of satisfaction or utility given his income and the market prices of the various commodities(axiom of utility maximization) It is assumed that the consumer has full knowledge of all information on prices, his income and the commodities to be consumed and that;  Consumer Choice: Utility Curve, Utility Surface, Indifference Curve and Indifference Surface cont’d. In order to attain this objective ,the consumer must be able to compare the utility (satisfaction) of the various baskets of goods which he /she can buy with his/her income. *There are 2 approaches to the problem of comparison of utilities Cardinalist: postulate that utility can be measured in monetary units by the amount of money the consumer is willing to sacrifice for another amount of a commodity. Other economists suggest a subjective unit- UTILS Ordinalist: postulate that utility is not measurable, but an ordinal magnitude. It suffices for the consumer to rank the various basket o goods according to the satisfaction that each bundle gives him. That is determined by his order of preference. Consumer Choice: Utility Curve, Utility Surface, Indifference Curve and Indifference Surface cont’d. There are 2 ordinal theories: 1. Indifference curves approach 2. Revealed preference approach In examining these approaches 1. State the assumptions underlying each 2. Derive the equilibrium of the consumer and firm 3. Determine the consumer’s demand for the individual product Cardinal Utility Theory Maintained Assumptions /Axioms /Self Evident truths  Cardinal Utility Theory cont’d. 1. Rationality ⇒ aims at maximization of utility subject to the budget constraint 2. Cardinal Utility ⇒ utility measured as a cardinal concept. A convenient measure is money :monetary units one is prepared to pay for another unit of the commodity 3. Constant Marginal Utility of Money⇒ if MU of money changes as income(Y) changes ,then it is an inappropriate measuring rod. 4. Diminishing marginal utility(axiom of diminishing marginal utility)⇒MU decreases as more is consumed 5. Total utility depends on the quantities of the individual commodities : U= f(X1,…..Xn) Equilibrium of the Consumer Starts with the utility function U=U(qx) Where: Utility is measured in monetary units. If the consumer buys qx ,his expenditure is qx. Px=Y Now the consumer seeks to maximize the difference between his utility.  AGEC 211 MICROECONOMIC PRINCIPLES AND APPLICATIONS WEEK 7  RECAP Markets/Market Structure Mechanics of Demand and Supply Elasticities (Own Price, Cross Price, Income Elasticities) Total Revenue  THEORY OF DEMAND (1) Purpose: determine the various factors that affect demand (2) Demand is a multivariate relationship 3 𝐷𝑖 = 𝑓(𝑃𝑖 , 𝑌, 𝑃𝑥 , 𝑇𝑎𝑠𝑡𝑒, 𝐼𝑛𝑐𝑜𝑚𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛, 𝑃𝑜𝑝. , 𝐶𝑜𝑛𝑠𝑢𝑚𝑒𝑟 ′ 𝑠 𝑤𝑒𝑎𝑙𝑡ℎ, 𝑐𝑟𝑒𝑑𝑖𝑡 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦, 𝑔𝑜𝑣 ′ 𝑡 𝑝𝑜𝑙𝑖𝑐𝑦, 𝐷𝑡−1 𝑌𝑡−1 ) Consumer dd (Theory of consumer Total final good demand behavior) Demand Intermediate good Firms dd for investment good 𝟏 𝒒𝒏 = , given 𝒀, etc ⇒ 𝐿𝑎𝑤 𝑜𝑓 𝑑𝑒𝑚𝑎𝑛𝑑 10/10/2019 𝑷𝒅 3  Theory Of Consumer Behavior Starts with the examination of the behaviour of the consumer, since market demand is assumed to be the summation of the demand of individual consumers. We will first examine the derivation of demand for an individual consumer. We assume that: Consumer is rational: Given his income and the market price of the various commodities, he plans the spending of his income so as to obtain the highest possible satisfaction or utility (axiom of utility maximization). 10/10/2019 4  Assumed that the consumer has full knowledge of all information on prices, his income and the commodities to be consumed and that… In order to attain this objective the consumer must be able to compare the utility (satisfaction) of the various “basket of goods” which he can buy with his income. There are two approaches to the problem of comparison of utilities. 10/10/2019 5 Cardinalists – postulate that utility can be measured in monetary units by the amount of money the consumer is willing to sacrifice for another unit of a commodity. Other economists suggest a subjective unit – UTILS. Ordinalists – postulate that utility is not measurable, but an ordinal magnitude. It suffices for the consumer to rank the various “basket of goods” according to the satisfaction that each bundle gives him. That is determine his order of preference. Indifference curves approach There are two ordinal theories Revealed preference approach 10/10/2019 6  In examining these approaches: 1) State the assumptions underlying each 2) Derive the equilibrium of the consumer and from here… 3) Determine the consumer’s demand for the individual product. CARDINAL UTILITY THEORY Maintained assumptions/axioms/self-evident truths (1) Rationality: aims at maximization of utility s.t the budget constraint (2) Cardinal utility: utility measured as a cardinal concept. Convenient measure is money: monetary units one is prepared to pay for another unit of the commodity. (3) Constant marginal utility of money: if MU of money changes as Y changes then an inappropriate measuring rod. 10/10/2019 7 (4) Diminishing marginal utility (axiom of diminishing marginal utility): 𝑀𝑈 ↓ as more is consumed (5) Total utility depends on the quantities of the individual commodities 𝑼 = 𝒇(𝒙𝟏 , 𝒙𝟐 , 𝒙𝟑 , … 𝒙𝒏 ) 10/10/2019 8 Equilibrium of the Consumer (intuition) For a single commodity 𝒙, the consumer can either buy commodity 𝒙 or keep his income. Under these conditions there is equilibrium when the marginal utility is equated to its market price 𝑴𝑼𝒙 = 𝑷𝒙. 𝑴𝑼𝒙 > 𝑷𝒙 , ↑ satisfaction (welfare) by buying more of 𝒙. 𝑴𝑼𝒙 < 𝑷𝒙 , ↑ satisfaction by buying less of 𝒙 and keeping more of his income. Therefore, equilibrium is at where 𝑀𝑈𝑥 = 𝑷𝒙 10/10/2019 9  Equilibrium Of The Consumer (algebra) Start with the utility function: 𝒖 = 𝑼 (𝒒𝒙 ) Where utility is measured in monetary units. If the consumer buys 𝒒𝒙 his expenditure is 𝒑𝒙𝒒𝒙 = 𝒀 Now the consumer seeks to maximize his utility s.t the difference between his utility and his expenditure/income. 10/10/2019 10 The necessary condition for a maximum is that the partial derivative of the function with respect to 𝒒𝒙 be equal to zero. Thus, 𝛿𝑍 𝛿𝑢(.) 𝛿 𝑝 𝑥𝑞 𝑥 𝛿𝑢 𝛿 𝑝 𝑥𝑞 𝑥 = − =0 ⇒ − =0 𝒑𝒙 is a 𝛿𝑞𝑥 𝛿𝑞𝑥 𝛿𝑞𝑥 𝛿𝑞𝑥 𝛿𝑞𝑥 constant 𝜹𝒖(.) 𝜹 𝒒𝒙 𝜹𝒖(.) 𝜹 𝒒𝒙 𝛿𝑢(.) ⇒ − 𝒑𝒙 =𝟎 − 𝒑𝒙 =𝟎 − 𝒑𝒙 = 0 𝜹𝒒𝒙 𝜹𝒒𝒙 𝜹𝒒𝒙 𝜹𝒒𝒙 𝛿𝑞𝑥 𝜹𝒖(.) 𝜹𝒒𝒙 = 𝒑𝒙 ⇒ 𝑴𝑼𝒙 = 𝑷𝒙 10/10/2019 11 If there are more commodities, the equilibrium for the consumer is the equality of the ratios of the marginal utilities of the individual commodities to their prices. 𝑴𝑼𝒙 𝑴𝑼𝒚 𝑴𝑼𝒏 = =⋯= 𝑷𝒙 𝑷𝒚 𝑷𝒏 𝑀𝑈𝑥1 𝑀𝑈𝑥1 = 𝑃𝑥1 ⇒ =1 𝑃𝑥1 𝑀𝑈𝑥2 𝑀𝑈𝑥2 = 𝑃𝑥2 ⇒ =1 𝑃𝑥2 𝑀𝑈𝑥3 𝑀𝑈𝑥3 = 𝑃𝑥3 ⇒ =1 𝑃𝑥3 𝑴𝑼𝒙𝟏 𝑴𝑼𝒙𝟐 𝑴𝑼𝒙𝟑 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, = = 10/10/2019 𝑷𝒙𝟏 𝑷𝒙𝟐 𝑷𝒙𝟑 12 That is the utility derived from spending an additional unit of money must be the same for all commodities. If a consumer derives greater utility from any one commodity, he can increase his satisfaction by spending more on that commodity and less on the others until the above equilibrium condition is fulfilled or satisfied. 10/10/2019 13  Derivation of the Demand of the Consumer ⇒ Based on the axiom of diminishing marginal utility. (use geometry) 𝑼𝒙 𝑴𝑼 𝑷 𝑻𝑼 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑏𝑦 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑀𝑈1 𝑃1 𝜹𝒖 𝜹𝒒 = 𝑴𝑼 𝑀𝑈2 𝑃2 𝒙 0 𝑥1 𝑥2 𝑥 𝑞𝑥 𝑥1 𝑥2 𝑞𝑥 Marginal utility of 𝒙 is the slope of the total utility function 𝑼𝒙 = 𝒇(𝒒𝒙 ) 10/10/2019 14 Total utility ↑ but at a decreasing rate up to 𝒙 and then starts to decline. Negative segment ignored “Do not make economic sense” If 𝑴𝑼𝒙 is measured in monetary units the demand curve for 𝒙 is identical to the positive segment of the 𝑴𝑼 curve 10/10/2019 15  Critique Of The Cardinal Approach (1) *Satisfaction cannot be measured objectively. (2) *The assumption of constant utility of money is also unrealistic. As 𝑌 ↑, 𝑀𝑈 of 𝑌 changes. Hence, money cannot be used as a measuring rod since its own utility changes. (3) The axiom of diminishing marginal utility is an established concept and not derived from the cardinal approach, i.e. it must be taken for granted. 10/10/2019 16  AGEC 211 MICROECONOMIC PRINCIPLES AND APPLICATIONS WEEK 8  AGEC 211 CONSUMER CHOICE –THEORY OF DEMAND (2) WEEK 8  RECAP…. Cardinalists – postulate that utility can be measured in monetary units by the amount of money the consumer is willing to sacrifice for another unit of a commodity. Other economists suggest a subjective unit – UTILS. Ordinalists – postulate that utility is not measurable, but an ordinal magnitude. It suffices for the consumer to rank the various “basket of goods” according to the satisfaction that each bundle gives him. That is determine his order of preference. There are two ordinal theories Indifference curves approach Revealed preference approach 10/10/2019 3  The Indifference-Curves Theory ASSUMPTIONS (1)Rationality: maximization of utility s.t Y + assumption that the consumer has full knowledge of all information. (2)Utility is ordinal: He can rank his preferences according to the satisfaction derived from the consumption of each basket. (3)Diminishing marginal rate of substitution: Preferences are ranked in terms of indifference curves which are said to be convex to the origin implying that the slope of the indifference curves increases. 10/10/2019 4 The slope of the indifference curve is called the MRS of the commodities. Indifference-curve theory is based, thus on the axiom of diminishing MRS: the amount of one good a consumer will give up to obtain more of another good. (4) Total utility of the consumer depends on the quantities consumed 𝑼 = 𝒇(𝒒𝟏 , 𝒒𝟐 , … 𝒒𝒏 ) (5) Consistency and transitivity of choice: The consumer is consistent in his choice. If in period (1) he chooses A over B he will not choose B over A in another period if both are available to him. i.e. If 𝑨 > 𝑩 , 𝒕𝒉𝒆𝒏 𝑩 ≯ 𝑨 10/10/2019 5 Transitivity: If 𝑨 > 𝑩, 𝑎𝑛𝑑 𝑩 > 𝑪, 𝑡ℎ𝑒𝑛 𝑨 > 𝑪 Monotonicity: more is better. Goods not bads Completeness: Any two bundles can be compared 10/10/2019 6  Equilibrium of the Consumer To define the equilibrium of the consumer (the choice of bundle that maximizes his utility), we need the basic tools of a) The concept of indifference curves b) Slope of the indifference curve, MRS c) The concept of the budget line Indifference Curves Locus of points – particular combinations or bundles of goods – which yield the same utility (level of satisfaction) to the consumer, so that he is indifferent as to the particular combination he consumes. 10/10/2019 7  U = 𝑓 𝑥, 𝑦 = k where k is a As quantity of 𝑦 ↓ x ↑ to maintain constant the same level of satisfaction 𝑈 𝑥1 , 𝑥2 = 12 ⇒ 𝑥1𝑥2 = 12 hence 𝑠𝑙𝑜𝑝𝑒 = −𝒗𝒆 𝑈 3,4 = 12 𝒚 𝒚 𝛿𝑦 𝐼𝐼𝐼 𝐼𝐼 𝛿𝑥 𝑰 0 𝒙 0 𝒙 Indifference Curve Indifference Map 10/10/2019 8  Indifference map shows all the indifference curves which rank the preferences of the consumer. Combinations of goods situated on an indifference curve yield the same utility. ⇒ Combination of goods lying on a higher indifference curve yield higher level of satisfaction and are preferred. Combination of goods on a lower indifference curve yield lower utility. ⇒ The negative of the slope of an indifference curve at any one point is called the MRS of the two commodities, X2 and X1, and is given by the slope of the tangent of that point. 10/10/2019 9  Slope o𝑓 𝑎𝑛 𝑖𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑐𝑢𝑟𝑣𝑒 𝑋1 𝜹𝑿𝟏 =− , 𝑴𝑹𝑺𝐱𝟐, 𝐱𝟏 𝜹𝑿𝟐 𝑋2 10/10/2019 10 It is assumed that 𝑿𝟏 and 𝑿𝟐 can substitute one another to a certain extent but are not perfect substitutes. 𝑴𝑹𝑺𝒙𝟐, 𝒙𝟏( 𝒙𝟐 𝒇𝒐𝒓 𝒙𝟏) ⇒ the number of units of commodity 𝑿𝟏 that must be given up in exchange for an extra unit of commodity 𝑿𝟐 so that the consumer maintains the same level of satisfaction. The concept of 𝑴𝑼 is implicit in the definition of MRS since it can be proven that the 𝑴𝑼𝒙𝟐 𝑴𝑼𝒙𝟏 MRSx2,x1 = 𝑜𝑟 𝑴𝑹𝑺𝒙𝟏, 𝒙𝟐 = 𝑴𝑼𝒙𝟏 𝑴𝑼𝒙𝟐 10/10/2019 11  Total utility in case of 𝑿𝟏 and 𝑿𝟐 is 𝑼 = 𝒇 𝒙𝟏, 𝒙𝟐. The equation of an indifference curve is 𝐔 = 𝐟 𝐱𝟏, 𝒙𝟐 = 𝒌 where 𝑘 is constant Total differential of the utility function is 𝜹𝒖 𝜹𝒖 𝜹𝒖 = 𝐝𝐲 + 𝐝𝐱 = 𝐌𝐔𝐲 𝒅𝒚 + 𝐌𝐔𝐱 𝒅𝐱 = 𝟎 𝜹𝒚 𝜹𝒙 Along any particular indifference curve the total differential is by definition equal to zero. 10/10/2019 12 Thus, 𝛿𝑢 = MUy 𝛿𝑦 + MUx δx = 0 𝑀𝑈𝑦 𝛿𝑦 = − 𝑀𝑈𝑥 𝛿𝑥 𝑀𝑈𝑦 𝛿𝑥 =− 𝑀𝑈𝑥 𝛿𝑦 𝑴𝑼𝒙 𝜹𝒙 OR 𝑴𝑼𝒙 𝜹𝒙 = − 𝑴𝑼𝒚 𝜹𝒚 =− 𝑴𝑼𝒚 𝜹𝒚 Rearranging 𝜹𝐲 𝑴𝑼𝒙 𝛿x 𝑀𝑈𝑦 − = = 𝑴𝑹𝑺𝒙,𝒚 𝑂𝑅 − = = 𝑴𝑹𝑺𝒚,𝒙 𝜹𝒙 𝑴𝑼𝒚 𝛿𝑦 𝑀𝑈𝑥 10/10/2019 13  Properties of the Indifference Curve (1)Has negative slope: as quantity of one commodity ↓, the quantity of the other must increase for the same utility (satisfaction). (2)The farther away from the origin of the IC, the higher the level of utility it denotes. (3)Indifference curves do not intersect. If they did, the point of their intersection would imply 2 different levels of satisfaction which is impossible. 10/10/2019 14  Indifference Curves do not intersect II At A, IC 𝑰𝑰 > 𝑰𝑪 𝑰 X1 A But at C 𝑰𝑰 = 𝑰 At B ⇒ 𝑰𝑪 𝑰𝑰 < 𝑰𝑪 𝑰 ?? 𝑪 I B X2 (4) IC are convex (non-perfect substitutes) to origin – slope of IC decreases (in absolute terms) as we move along the curve from the left towards the right, i.e. MRS is diminishing. The axiom of decreasing MRS expresses the observed behavioural rule that the number of units of x2 the consumer is willing to sacrifice in order to obtain an additional unit of x1 increases as the quantity of x1 decreases. It becomes increasingly difficult to substitute x2 for x1 as we move along the IC. 10/10/2019 16 → 𝑷𝒆𝒓𝒇𝒆𝒄𝒕 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆𝒔 Complementary goods y y Straight line with negative slope x x  The Budget Constraint of the Consumer Consumer has a given income (Y) which sets limits to his maximizing behaviour. Hence Y act as a constraint in attempting to maximize utility. 1) In the case of commodities x1, x2 𝒀 ≧ 𝑷𝟏𝑿𝟏 + 𝑷𝟐𝑿𝟐 2) We can present the BL (Income constraint) by solving for one 𝟏 𝑷𝟏 of the quantities consumed. 𝑿𝟐 = 𝒀 + 𝑿𝟏 𝑷𝟐 𝑷𝟐 𝒀 𝐩𝒚 𝒀 𝐩𝐱 𝒑𝒙𝒒𝒙 = 𝒀 − 𝒑𝒚 𝒒𝒚 𝒒𝒙 = − 𝐪𝐲 𝐪𝐲 = − 𝐪𝐱 𝒑𝒙 𝐩𝐱 𝒑𝒚 𝐩𝐲 10/10/2019 18  𝑌 qy 𝑃𝑦 A Budget Line 𝑌 𝑃𝑥 B qx  𝒀 When qx = 0, 𝒒𝒚 = 𝒑𝒚 𝒀 qy = 0, 𝒒𝒙 = 𝒑𝒙 When 𝐏𝐱 ↓ / 𝐏𝐲 , 𝐘 (1)Y (purchasing power) ↑ (although Y is fixed or given) (2) 𝒒𝒙 ↑ (𝑞𝑦 ↑) ceteris paribus (3)The budget line pivot around the fixed price 𝒑𝒙 (4)Since slope = − and 𝐏𝐱 ↓ slope of budget line falls. 10/10/2019 𝒑𝒚 20  Derivation of the Equilibrium of the Consumer The consumer is in equilibrium when he maximizes his utility, given his income and the market prices. 2 conditions must be fulfilled for the consumer to be in equilibrium 𝑀𝑈𝑥1 𝑃1 𝛿𝑥2 (1)MRSx1, 𝑥2 = = = [Necessary Condition] 𝑀𝑈𝑥2 𝑃2 𝛿𝑥1 (2)IC be convex to the origin. Fulfilled by the axiom of diminishing MRSx1,x2 ⇒ the slope of the IC decreases (in absolute terms) as we move along the curve from the left to the right. Lets demonstrate this equilibrium using (a) graphical presentation and (b) mathematical derivations 10/10/2019 21  Graphical Presentation At e, the slope of the 𝑃𝑥2 x1 budget line ( ) and of 𝑃𝑥1 A the indifference curve 𝑴𝑼𝒙𝟐 (𝐌𝐑𝑺𝒙𝟐, 𝒙𝟏 = ) are 𝑴𝑼𝒙𝟏 ∗ 𝑥1 e equal 𝑴𝑼𝒙𝟐 = 𝑷𝒙𝟐 = 𝑴𝑼𝒙𝟏 𝑷𝒙𝟏 𝜹𝒙𝟏 𝑴𝑹𝑺𝒙𝟐,𝒙𝟏 = 𝜹𝒙𝟐 ∗ 𝑥2 B x2 Given the IC map of the consumer and his budget line, the equilibrium is defined by the point of tangency of the budget line with the higher possible IC (point e). 𝑃𝑥2 At e, the slope of the budget line ( ) and of the indifference 𝑃𝑥1 𝑴𝑼𝒙𝟐 curve (𝐌𝐑𝑺𝒙𝟐, 𝒙𝟏 = ) are equal 𝑴𝑼𝒙𝟏 𝑴𝑼𝒙𝟐 𝑷𝒙𝟐 𝜹𝒙𝟏 = = 𝑴𝑹𝑺𝒙𝟐,𝒙𝟏 = 𝑴𝑼𝒙𝟏 𝑷𝒙𝟏 𝜹𝒙𝟐 Thus the first order condition is denoted graphically by the point of tangency of the 2 indifferent curves. The second order condition is implied by the convex slope of the IC. The consumer maximizes his utility by buying x1* and x2* of the 2 commodities. 10/10/2019 23  **For level 300** Mathematical derivation 𝑚𝑎𝑥𝑼 = 𝑓 𝑞1, 𝑞2, … 𝑞𝑛 s.t 𝑛𝑖=1 𝑞𝑖𝑝𝑖 = 𝑞1 𝑝1 + q2p2 + 𝑞𝑛 𝑝𝑛 = Y Solution: we use the Lagrangian multipliers method for the solution of this constraint maximum (a)Rewrite the constraint the in the form 𝑞1𝑝1 + q2p2 … + 𝑞𝑛 𝑝𝑛 − Y = 0 or (Y − q1p1 − q2p2 … 𝑞𝑛 𝑝𝑛 ) = 0 (b) Multiplying the constraint by a constant, called the Lagrangian multiple 𝝀 𝒒𝟏𝒑𝟏 + 𝐪𝟐𝐩𝟐 … + 𝐪𝐧𝐩𝐧 − 𝒀 = 𝟎 (c) Obtain the composite function by subtracting (b) from the utility function 10/10/2019 24 𝛷 = 𝑢. − 𝜆 𝑞1𝑝1 + q2p2 … + 𝑞𝑛 𝑝𝑛 − Y For maximization, its partial derivative be equal to zero. Differentiate 𝛷 with respect to q1…qn and 𝜆 and equating to zero. 𝛿𝛷 𝛿𝑢. = − 𝜆𝑝1 = 0 𝛿𝑞1 𝛿𝑞1 𝛿𝛷 𝛿𝑢. = − 𝜆𝑝2 = 0 𝛿𝑞2 𝛿𝑞2 𝛿𝛷 𝛿𝑢. = − 𝜆𝑝𝑛 = 0 𝛿𝑞𝑛 𝛿𝑞𝑛 𝛿𝛷 = −(𝑞1𝑝1 + 𝑞2𝑝2 + ⋯ 𝑞𝑛 𝑝𝑛 − 𝑌) = 0 𝛿𝜆 10/10/2019 25  𝛿𝑢(.) 𝛿𝑢. But = 𝑀𝑈1, = 𝑀𝑈2 … 𝛿𝑞1 𝛿𝑞2 Substitute and solving for 𝜆 we find Equilibrium conditions are identical with the Cardinalists approach 𝑴𝑼𝟏 𝑴𝑼𝟐 𝑴𝑼𝒏 𝑀𝑈1 𝑀𝑈2 𝝀= = =⋯ = MU1𝑃2 = 𝑀𝑈2𝑃1 𝑷𝟏 𝑷𝟐 𝑷𝒏 𝑃1 𝑃2 𝑴𝑼𝟏 𝑷𝟏 ⇒ = 𝑴𝑼𝟐 𝑷𝟐 Alternatively, we may divide the preceding equation corresponding to x by the equation which refers to commodity y and obtain 𝑴𝑼𝒙 𝑷𝒙 = 10/10/2019 𝑴𝑼𝒚 𝑷𝒚 26  Derivation of the Demand Curve Using the IC Approach (a) Graphical derivation of the demand curve: First Approach 𝒒𝒚 Price-consumption line A (Price offer curve) 𝑦3 𝑒3 𝑦2 𝑒2 𝑦1 𝑒1 𝐼𝐼𝐼 𝐼𝐼 𝐼 0 𝑥1 B 𝑥 2 𝑥3 𝐵𝐼 𝐵𝐼𝐼 𝒒𝒙 10/10/2019 27 Assume price of 𝒙 to fall, the budget line shifts to right due to ↑ in purchasing power of the money income. More of 𝒙 and 𝒚 are bought. The new budget line is tangent to a higher IC. New equilibrium occurs to the right of the original showing that as price falls more of the commodity will be bought. If we allow the price of 𝒙 to fall continuously and we join the points of tangency of successive BL and higher IC we form the so called price-consumption line from which we derive the demand curve for commodity x. 10/10/2019 28 At point 𝒆𝟏 , 𝒙𝟏 is bought at price 𝒚𝟏. At point 𝒆𝟐 the price, 𝒚𝟐 is lower than 𝒚𝟏 and the quantity demanded has increased to 𝒙𝟐 , and so on. We may plot the price-quantity pairs defined by the points of equilibrium (on the price-consumption line) to obtain a demand curve. The demand curve for a normal good will always have a negative slope, denoting the ‘law of demand’ Demand curve for a NORMAL GOOD 𝑷𝒙 𝑃1 𝑃2 𝑃3 𝑥1 𝑥2 𝑥3 𝒒𝒙  𝜹𝒙 For a normal good, > 𝟎. Demand changes in the same 𝜹𝒚 direction as Y i.e. as 𝑌 ↑ 𝑄𝐷 ↑ ⇒ 𝑃𝑄 ↓ 𝜹𝒙 For inferior goods, < 𝟎. Demand changes in the opposite 𝜹𝒚 direction as Y. As 𝑌 ↑ 𝑄𝐷 ↓ For giffen goods, ↓ 𝑖𝑛 𝑃 leads to ↓ 𝑖𝑛 𝑄. ⇒ 𝒀 held constant or same money income. Possible but mostly unlikely in each individual behaviour. A normal good can be a luxury/necessity. 10/10/2019 31  %Δ𝑋 Normal good: >0 %Δ𝑌 %𝜟𝑿 i. Luxury goods: >𝟏 %𝜟𝒀 %𝜟𝑿 ii. Necessary goods: 0 2Q or 𝐿 0 2Q or 𝐾 0  Cobb-Douglas 𝑄 = 𝐴𝐾 𝛼 𝐿𝛽 𝛼, 𝛽 > 0  Constant Elasticity of Substitution (CES)  Translog  Leontif 10/26/2019 4 MRTS: The slope of the isoquant defines the degree of substitutability of factors of production. The slope of the isoquant decreases 𝜕𝐾 K 𝑆𝑙𝑜𝑝𝑒 = − (in absolute terms) as we move 𝜕𝐿 downwards along the isoquant, showing the increasing difficulty in substituting 𝑲 for 𝑳. 𝜕𝐾 The slope of the isoquant is called 𝜕𝐿 the Marginal Rate of Technical 𝜕𝐾 Substitution (MRTS) of the factors. 𝜕𝐿 𝜹𝑲 𝑴𝑷𝑳 − = 𝑴𝑹𝑻𝑺𝑳,𝑲 = 𝜹𝑳 𝑴𝑷𝑲 10/26/2019 L 5  Proof: Given Q= 𝒇(𝑲, 𝑳) along an isoquant, the quantity of output, 𝑄 is constant. Totally differentiating the production function. If we should change 𝑲, 𝑳 by small amounts, 𝑑. 𝝏𝑄 𝝏𝑄 d𝑌 = 𝑑𝐾 + 𝑑𝐿 = 0 𝝏𝐾 𝝏𝐿 𝑀𝑃𝐾 𝑑𝐾 + 𝑀𝑃𝐿 𝑑𝐿 = 0 𝑑𝐾 𝑀𝑃𝐿 𝝏𝑄 ⁄ 𝝏𝐿 − = = = 𝑀𝑅𝑇𝑆𝐿,𝐾 𝑑𝐿 𝑀𝑃𝐾 𝝏𝑄 ⁄ 𝝏𝐾 𝑑𝐿 𝑀𝑃𝐾 𝝏𝑄⁄𝝏𝐾 − = = = 𝑀𝑅𝑇𝑆𝐾,𝐿 𝑑𝐾 𝑀𝑃𝐿 𝝏𝑄⁄𝝏𝐿 10/26/2019 6 MRTS as a measure of the degree of substitutability suffers from units of measurement problem. A better measure is the elasticity of substitution. % 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑲/𝑳 𝝈= % 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑴𝑹𝑻𝑺 𝑑(𝐾/𝐿)/(𝐾/𝐿) 𝜎= 𝑑(𝑀𝑅𝑇𝑆)/(𝑀𝑅𝑇𝑆) 10/26/2019 7 Given Q= 𝜱𝑲𝜶 𝑳𝜷 𝛼, 𝛽 serves as relative factor shares 𝜶 Ratio ↑ ⇒ more capital intensive Factor intensity = Ratio ↓ ⇒ more labour intensive 𝜷 Efficiency of production = 𝜱 Returns to scale = 𝜶 + 𝜷 𝒗 = 𝜶 + 𝜷, 𝒗 = 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 ℎ𝑜𝑚𝑜𝑔𝑒𝑛𝑒𝑖𝑡𝑦 𝐼𝑓 𝜶 + 𝜷 = 𝟏, 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑅𝑇𝑆 𝜶 + 𝜷 < 𝟏, 𝑫𝒆𝒄𝒓𝒆𝒂𝒔𝒊𝒏𝒈 𝑅𝑇𝑆 𝜶 + 𝜷 > 𝟏, 𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒊𝒏𝒈 𝑅𝑇𝑆 10/26/2019 8  𝑄0 = 𝑓(𝐾, 𝐿) ↑ both proportionality by 𝒔 𝑄0∗ = 𝑓(𝑠𝐾, 𝑠𝐿) 𝑄0∗ = 𝑠 ∗ 𝑓(𝐾, 𝐿) 𝑄0∗ = 𝑠 ∗ 𝑄0 If 𝒔 can be factored out , production = homogenous If 𝒔 cannot be factored out, Non−homogenous Example 𝑸 = 𝑨𝑲𝜶 𝑳𝜷 Doubling 𝑲 and 𝑳 ∗ 𝛼 𝛽 ∗ 𝑄 = 𝐴(2𝐾) (2𝐿) 𝑄 = (2𝛼+𝛽 )𝑄 When 𝜶 + 𝜷 = 𝟏, output doubled 𝜶 + 𝜷 > 𝟏, more than doubled 10/26/2019 9 𝒀 = 𝜱𝑲𝜶 𝑳𝜷 Let 𝐾 and 𝐿 ↑ by 𝒔 ∗ ∗ 𝑌 = 𝛷(𝑠𝐾)𝛼 (𝑠𝐿)𝛽 𝑌 = 𝛷𝑠 𝛼 𝐾 𝛼 𝑠𝛽 𝐿𝛽 ∗ ∗ 𝑌 = (𝛷𝐾 𝛼 𝐿𝛽 )𝑠 𝛼+𝛽 𝑌 = (𝑌)𝑠 𝛼+𝛽 Assignment Given 𝑌 = 𝛷𝐾 𝛼 𝐿𝛽 −Derive the 𝑀𝑃𝐿 , 𝑀𝑃𝐾 −Derive 𝑀𝑅𝑇𝑆 −Derive elasticity of substitution 10/26/2019 10  Factor Intensity Relative proportions of the various factors of production used to make a given product. K If 𝜶 = 0.6 𝜷 = 0.35 𝐴1 Upper part – more capital intensive 𝐾1 Lower part – more labour intensive Factor intensity of any process is 𝐾2 B measured by the slope of the line through the origin representing the particular process. 𝐿1 𝐿2 L 10/26/2019 11  Hence it is the 𝑲⁄𝑳 𝑟𝑎𝑡𝑖𝑜 𝑲𝟏 𝑲𝟐 𝑨𝟏 = 𝐁= K 𝑳𝟏 𝑳𝟐 𝐴1 For the 𝑲⁄𝑳 𝑟𝑎𝑡𝑖𝑜 𝑨 > 𝑩 𝐾1 𝑲𝟏 𝑲𝟐 =𝑨> =𝑩 𝑳𝟏 𝑳𝟐 𝐾2 B 𝐿1 𝐿2 L 10/26/2019 12  Isocost Line / Curve In the Q= 𝒇(𝑲, 𝑳) assume 𝒘 = 𝑐𝑜𝑠𝑡 𝑜𝑟 𝑝𝑟𝑖𝑐𝑒 of 𝐿 (wage rate) 𝒓 = 𝑐𝑜𝑠𝑡 𝑜𝑟 𝑝𝑟𝑖𝑐𝑒 of capital services Isocost line is defined by the cost equation: Total cost ⇒ 𝑪 = 𝒓𝑲 + 𝒘𝑳 → [Cost equation] Similar to the budget line situation 𝑪 𝒘 𝑲= − 𝑳 10/26/2019 𝒓 𝒓 13  Slope of isocost line/curve K 𝑪⁄ 𝒓 𝒘⁄ 𝒓 𝑪⁄ L 𝒘  OBJECTIVES OF PRODUCERS All firms produce with the objective of max 𝝅 in the optimal combination of factors. All these firms incur costs in their production process Hence firms faced with a single decision 1) Can choose a given cost and maximize output. → 𝑶𝒖𝒕𝒑𝒖𝒕 𝒎𝒂𝒙. 2) Can choose a given output and minimize cost. → 𝑪𝒐𝒔𝒕 𝒎𝒊𝒏. All these scenarios are possible depending on the firms market position (new, 𝑳𝑹 position, 𝑺𝑹 position, pressure of demand, etc.) NB: Some firms produce in the 𝑺𝑹 with the objective of capturing market share, etc. 10/26/2019 15 In all cases certain assumptions are made For a perfectly competitive market situation 1) Firm has a goal of 𝝅 max. 𝝅= 𝑅−𝐶 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝑃 ∗ 𝑄 𝜕𝑅𝑒𝑣𝑒𝑛𝑢𝑒 𝝅 = 𝑝𝑟𝑜𝑓𝑖𝑡𝑠 =𝑃 𝜕𝑄 𝜕𝑅𝑒𝑣𝑒𝑛𝑢𝑒 𝑅 = 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝑀𝑅 𝜕𝑄 𝐶 = 𝑐𝑜𝑠𝑡 ⇒ 𝑴𝑹 = 𝑷 2) Price of output is given, 𝑷𝒙 3) Price of factors are given, 𝒘, 𝒓 [A] Maximize Output s.t Cost Constraint: Isocost line given from the cost constraint Given Q= 𝒇(𝑳, 𝑲, 𝒗, ɣ) and prices of factor inputs 𝒘, 𝒓 Maximum level of output defined by tangency of the highest ISOQUANT and the ISOCOST LINE, given the cost constraint. 10/26/2019 17  Graphically: At 𝒆𝟏 : slope of isocost line (𝒘/𝒓) is equal to slope of isoquant K 𝑀𝑃𝐿 𝜕𝐾 𝑀𝑃𝐾 = = 𝑀𝑅𝑇𝑆 𝜕𝐿 𝜕X w MPL 𝜕L 1) = = 𝜕X = r MPK 𝜕K 𝜕K K1 𝑒1 MRTSL,K = 𝜕L (F.O.C) Q3 2) The isoquant must be convex Q2 to the origin (S.O.C) Q1 L1 L  Factor Demand Curves → These are markets demand for labor, raw materials and other inputs to production by firms. → Factor markets could be in: Perfectly competitive markets Where almost competitive Producers/sellers have market power 10/26/2019 19  Competitive Factor Markets Assumptions: Large number of sellers/buyers of the factor of production No single person can influence price hence all are price takers (A)Demand For A Factor Input Demand curves for factors of production are downward sloping just like demand curves for final goods. However, it is downward sloping for reasons different from consumers demand 10/26/2019 20 → Factor demands (e.g. demand for Labor) are DERIVED DEMAND ⇒ They depend on and are derived from THE FIRMS LEVEL OF OUTPUT AND THE COSTS OF INPUTS (such as the wage rate) E.g. Demand of Ghanair for stewardess is a derived demand that depends not only on the current salary of stewardess, BUT also on how many passengers and how many aircrafts Ghanair expects.  + − 𝑫𝑳 = 𝒇(𝑸 , 𝒘 ) + − 𝑫𝑲 = 𝒇(𝑸 , 𝒓 ) 10/26/2019 22  Analysis of Factor Demand for One Variable Recall 𝑀𝑃𝐿 𝑐𝑢𝑟𝑣𝑒 MP L 10/26/2019 23 Assumptions: Firms produce output using 𝑲, 𝑳 at price 𝒓, 𝒘 Assume that the firm has its plants/equipment in place (as in 𝑺𝑹 analysis) and must decide how much LABOR to hire. The firm has already hired a certain number of workers and wants to know whether it is profitable to HIRE ONE ADDITIONAL WORKER Hiring this additional worker is worthwhile if: 𝑨𝑫𝑫𝑰𝑻𝑰𝑶𝑵𝑨𝑳 𝑹𝑬𝑽𝑬𝑵𝑼𝑬 > 𝑻𝑯𝑬 𝑪𝑶𝑺𝑻 : Firm should hire more labor The additional revenue from an incremental unit of labor is called MARGINAL REVENUE PRODUCT of labour → 𝑴𝑹𝑷𝑳 𝑴𝑹𝑷𝑳 = 𝑴𝑷𝑳 𝑴𝑹 → Holds for any competitive factor market, whether output market is competitive or not. 10/26/2019 25 However, in a perfectly competitive market (output/input) A firm sells all its output at the market price, 𝑷 The MR from the sale of an additional unit of output is then equal to 𝑷 i.e. 𝑴𝑹 = 𝑷 Hence 𝑴𝑹𝑷𝑳 = 𝑴𝑷𝑳 ∗ 𝑷𝑿 (X = product/output) 𝑽𝑴𝑷𝑳 𝑴𝑷𝑳 𝑽𝑴𝑷𝑳 𝑽𝑴𝑷𝑳 = 𝑴𝑷𝑳 ∗ 𝑷𝑿 𝑴𝑷𝑳 L 1) 𝑀𝑃𝐿 ↓ as number of hours of labor ↑ (diminishing returns) 2) 𝑀𝑅𝑃 curve then slopes downwards, even though the price of the product is constant. 10/26/2019 27 → The concept of 𝑴𝑹𝑷 is applied in the hiring of labour by firms. However competitive the OUTPUT MARKET, the 𝑀𝑅𝑃 tells us how much the firm will pay to hire an additional unit of labour. As long as 𝑴𝑹𝑷𝑳 > 𝒘𝒂𝒈𝒆 𝒓𝒂𝒕𝒆 (𝒘) Firm should hire an additional unit of labour If 𝑴𝑹𝑷𝑳 < 𝒘 → firm should lay off workers Only when 𝑴𝑹𝑷𝑳 = 𝒘 will the firm have hired the 𝝅 − 𝒎𝒂𝒙𝒊𝒎𝒊𝒛𝒊𝒏𝒈 amount of Labour  Price of labour (w) 𝒘∗ 𝑆𝐿 𝒘𝟐 𝑆𝐿2 𝑀𝑅𝑃𝐿 = DL 𝐐∗𝐋 𝐐𝟐𝐋 𝐐𝐋 10/26/2019 29  As 𝑤 ↓ 𝑄 ↑ Since Labor market is perfectly competitive, the firm can hire as many workers as it wants at the market wage, 𝒘∗. Supply of labor curve facing firm, 𝑺𝑳 is a horizontal line 𝑸∗𝑳 is the 𝝅 − 𝒎𝒂𝒙. amount of labour that the firms hires When wage rate ↓ (𝑺𝑳 facing the firm shifts to 𝑺𝟐𝑳 ) and firm maximize 𝝅 by moving along the demand curve for labour until the new wage rate (𝒘𝟐 ) is equal to the 𝑴𝑹𝑷 = 𝑫𝑳 and 𝑸𝟐𝑳 of labor is hired. 10/26/2019 30 (C) MARKET DEMAND CURVE: factor inputs like labour is demanded by firms in many different industries. (a) Determine each industry’s (collection of firms producing similar goods) demand for labour (b)Add the industry demand curves for labor to obtain the market demand curve for labour  Difficult because of the possible interaction among firms. Easiest when there is a single producer of the product. Then the 𝑴𝑹𝑷 𝒄𝒖𝒓𝒗𝒆 is the industry demand curve for the input. 10/26/2019 31