Midterm #1 Exam Study Questions AK AK AK Selected problems

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1 Midterm #1 Exam Study Questions AK AK AK Selected problems Practice Short Answer for Microeconomic Concepts A subset of these questions will be on the exam. 1. What is the Ceteris Paribus assumption? 2. What is the definition of Opportunity Cost? 3. How do Positive and Normative economics differ? 4. What are two of the three basic assumptions concerning Utility? 5. What is an Indifference Curve and what does it represent? 6. What is the definition of Marginal Rate of Substitution? 7. What is meant by the term Diminishing Marginal Rate of Substitution? 8. What are the definitions of Substitute and Complement goods? Give examples of both. 9. If a normal good X s price decreases, do the Income Effect and the Substitution Effect predict an increase/decrease in consumption of good X and why? 10. What does the the Lump-Sum principle refer to in terms of the Substitution and Income effects? 11. What s the difference between a shift in vs. movement along an individual s demand curve? 12. What is the definition of Income elasticity of demand (eq,i)? What is the sign of eq,i for an inferior good? 13. What is the definition of Cross-price elasticity of demand (eq,p )? If you always eat biscotti with your coffee, what is the sign of the Cross-price elasticity of coffee prices and biscotti demand and why? 14. What can be said about expenditures on a good X with inelastic demand? Give examples of goods with inelastic and elastic demand curves. 15. How are price elasticity of demand for a good and the substitution effect related? 16. How does price elasticity differ between normal goods and luxury goods? 17. What is meant by the term: Marginal Physical Productivity? 18. What is the definition of the Rate of technical substitution? 19. What does it mean when a production function exhibits Increasing Returns to Scale? 20. What s the difference between Technical progress and Input substitution in terms of production?

2 Practice Multiple-Choice Questions 1. Normative economic analysis a. involves the study of what comprises a normal firm. b. involves how resources are actually used in an economy. c. involves judgments on how resources should be used in an economy. d. is usually thought to be a waste of time. 2. If bundles of goods A and B lie on the same indifference curve, one can assume the individual a. prefers bundle A to bundle B. b. prefers bundle B to bundle A. c. enjoys bundle A and B equally. d. bundle A contains the same goods as bundle B. 3. An increase in an individual s income without changing relative prices will a. rotate the budget constraint about the X-axis. b. shift the indifference curves outward. c. shift the budget constraint outward in a parallel way. d. rotate the budget constraint about the Y axis. 4. If income doubles and the quantity demanded of good X more than doubles, then good X can be described as a a. substitute good. b. complement good. c. necessity. d. luxury. 5. If good X is a normal good and its price rises, then quantity demanded a. may or may not fall. b. will always fall. c. will always rise. d. will remain unchanged. 6. The price elasticity of demand for a horizontal demand curve is a. 0. b. 1. c. 1. d. infinity. 7. The price elasticity of demand for a linear demand curve follows the pattern (moving from high prices to low prices) a. elastic, unit elastic, inelastic. b. unit elastic, inelastic, elastic. c. inelastic, unit elastic, elastic. d. elastic, inelastic, unit elastic.

3 8. A firm s isoquant shows a. the amount of labor needed to produce a given level of output with capital held constant. b. the amount of capital needed to produce a given level of output with labor held constant. c. the various combinations of capital and labor that will produce a given amount of output. d. none of the above. 9. A firm s rate of technical substitution is represented graphically by a. the slope of the line connecting the origin with the relevant point on the isoquant. b. the negative of the slope of the line connecting the origin with the relevant point on the isoquant. c. the slope of the isoquant at the relevant point. d. the negative of the slope of the isoquant at the relevant point. 10. The slope of the budget constraint line is a. the ratio of the prices (P x /P y ). b. the negative of the ratio of the prices (P x /P y ). c. the ratio of income divided by price of Y (I/P y ). d. none of the above. Answer Sheet for multiple-choice 1. c 6. d 2. c 7. a 3. c 8. c 4. d 9. d 5. b 10. b

4 Practice Quantitative Questions: Constrained Utility Maximization: 1) a) State the conditions for Utility Maximization Given a consumer s budget constraint (BC) and indifference curves (ICs) derived from that consumer s utility function, utility is maximized where: i. Consumption is on the BC ii. An IC is tangent to the BC where the iii. Negative of the Marginal Rate of Substitution (MRS) = slope of the BC iv. The tangency of the IC to the BC indicates the highest affordable utility with respect to the BC b) If an individual s utility function is U u(x,y) from the consumption of two goods X and Y and her budget constraint is given by I = PxX + PyY, (where Px and Py are the prices of goods X and Y respectively), show the constrained utility-maximizing condition algebraically, indicating which condition stated above goes with the algebraic equivalent. BC: I = P X *X + P Y *Y Rearranging yields: i. Y = I/ P Y (P X /P Y ) * X ii. MRS = MU X /MU Y iii. Max Utility where (P X /P Y ) = -MU X /MU Y Can now solve for X and Y via two equations (i. and iii.) and two unknowns (X and Y)

5 c) Draw a carefully labeled graph indicating the constrained utility-maximizing condition. 2) A person can consume two goods, X and Y with prices PX = $4 and PY = $10 and a total of budget of $200. Given the following Utility function for goods X and Y: U(X,Y) = 8X ½ Y ½ a) Determine the utility maximizing levels of consumption for X and Y From BC: 200 = 4X + 10Y Y = 200/10 (4/10)X = X Slope of BC is given by PX/PY = -0.4 From Utility function: MUX = (8 * ½)X -1/2 Y 1/2 = 4(Y/X) 1/2 MUY = (8 * ½)X 1/2 Y -1/2 = 4(X/Y) 1/2 MUX/MUY = Y/X

6 Set PX/PY = -MRS = -MUX/MUY -.4 = -Y/X Y = 0.4X Plug above equation into BC: 200 = 4X + (10)(0.4X) 200 = 8X X = 25 and Y = 10 b) Construct a figure showing the budget constraint and drawing in where the indifference curve for utility maximization would be. Y I/PY = IC where utility = 40(10) 1/2 25 BC I/PX = 50 X c) What is the person s maximum utility given a budget of $200? Given Maximum Utility where X = 25 and Y = 10 just plug these values into the utility function: U(X,Y) = 8X ½ Y ½ = 8(25) ½ (10) ½ = 8*5*(10) ½ = 40(10) 1/2

7 Elasticity: Question 1: A firm faces a market demand curve given by: P + 8Q = 1000 (where P is the market price and Q is the market quantity) The firm sells its product at a price of P = $800 a) If the firm wants to increase revenue should it consider raising or lowering the price of its product? Explain. At P = $800, Q = 25 Rearranging demand curve yields: Q = 1000/8-1/8P = 123 1/8P εq,p = P/Q*(dQ/dP) = (800/25) * -(1/8) = -4 The price elasticity of the product is < -1 so ε Q,P is elastic. This means lowering the price will increase revenues. b) If the firm changes prices by 5% in the direction you indicated, how much will their revenue increase? Revenue at original price and quantity = $800 * 25 = $20,000 From definition of own-price elasticity eq,p = % Q/ % P -4 = 20/-5 So a 5% decrease in price is accompanied by a 20% increase in quantity resulting in new price and quantity: P = 760, Q = 30 Revenue at new price and quantity = $760 * 30 = $22,800 Change in revenue: $22,800 $20,000 = $2,800

8 Question 2: Good X has a price elasticity of εq,p = -4.2 and an income elasticity of εq,i = 6.5 Good Y has a price elasticity of εq,p = -0.8 At current prices 500 units of Good X are sold at $15 a unit and 1000 units of Good Y at $50 a unit. Revenue for Good X = 500 * $15 Revenue for Good Y = 1000 * $50 = $7,500 = $50,000 a) If PX increases by 10%, how much will sales change? εq,p = % QX/ % PX -4.2 = -Z/10 Z = So a 10% increase in PX is associated with a 42% decrease in QX. New Q = 290 Sales change = 42% 0f 500 = drop in sales of 210 b) How much will total revenue from X change and in what direction? New PX = $16.50 New QX = 290 New Revenue = $4,785 Sales change = $4,785 - $7,500 = -$2,715 c) Answer a) and b) for Good Y εq,p = % QY/ % PY -0.8 = -Z/10 Z = -8.0 So a 10% increase in PY is associated with an 8% decrease in QY. New Q = 920 Sales change = 8% 0f 1000 = drop in sales of 80 New PY = $55 New QY = 920 New Revenue = $50,600 Rev. change = $50,600 - $50,000 = -$600

9 d) If PX = $15 a unit and income decreases by 2% how will sales of X be affected? εq,i = % Q/ % I 6.5 = -Z/-2 Z = Question 3: So a 2% decrease in Income is assoc. with an -13% decrease in QX. New QX = 870 Sales change = 13% 0f 1000 = drop in sales of 130 You are the manager of a retail auto parts store and you sell windshield wipers, SqueejeeMagic (SQM) and SpeedyClean (SC) windshield wiper fluid. From your own market research you ve determined that i) SqueejeeMagic has an own price elasticity of demand of 1.6, ii) SpeedyClean has an own price elasticity of demand of 1.0, and iii) the cross-price elasticity of SpeedyClean prices and SQM windshield wiper demand is 1.2. Given the elasticity estimates, answer the following questions. a) What kind of good is SQM (normal, inferior) and why? Is the price elasticity of SQM elastic, inelastic or unit elastic? εq,p = % QSQM/ % PSQM = -1.6 SQM is, by definition, a normal good since a(n) increase(decrease) in the price is associated with a(n) decrease(increase) in quantity Since ε Q,P < -1 the demand is elastic. b) If you lowered the price of SQM windshield wipers, how would you expect your revenue from that product to change? Illustrate your answer with a carefully labeled graph of the demand curve for SQM. Since ε Q,P for SQM is elastic and SQM is a normal good, a lower price results in a proportionately larger increase in quantity. This results in a higher revenue if the price is lowered. PSQM P1 P2 Q1 Q2 QSQM

10 c) As a result of foreign competition, your supplier of SpeedyClean wiper fluid lowers the price to you. In response you lower the price to your customers of a gallon of SC wiper fluid from $2.00 to $1.50. Will sales of SC increase or decrease? Will happen to revenues from sales of SC? εq,p = % QSC/ % PSC = -1.0 Since own-price elasticity of SpeedyClean,, is < 0 SpeedyClean is a normal good. For a normal good when price decreases quantity increases so sales will increase. However, since the elasticity is unit elastic, a 25% decrease in price is matched by a 25% increase in sales resulting in no change in revenue. d) What will the lower SC price do for sales of SQM and why? The cross-price elasticity of SpeedyClean prices and SQM windshield wiper demand is ε Q,P = -1.2 This indicates that a 1% decrease in P SpeedyClean results in a 1.2% increase in sales of SQM. So, as would be expected, SpeedyClean and SQM are complements

11 Math review: Derivative rule: Given the function F(X,Y) = ax b Y c where X and Y are variables The partial derivative of F() with respect to X is: δf(x,y)/δx = abx (b-1) Y c The partial derivative of F() with respect to Y is: δf(x,y)/δy = acx b Y (c-1) Problem 1: Given the utility function U(X,Y) = 5X 1/5 Y 2/3 for goods X and Y respectively: a) Calculate the Marginal utility of X (MUX). MUX = 5(1/5)X (1/5 1) Y 2/3 = X -4/5 Y 2/3 b) Calculate the Marginal utility of Y (MUY). MUY = 5(2/3)X 1/5 (2/3 1) Y =(10/3) X 1/5 Y -1/3

12 Problem 2: Given the Production function Q(K,L) = 15K 2 L 3/2 for capital K and labor L: a) Calculate the Marginal Productivity of Labor (MPL). MPL = 15(3/2)K 2 (3/2 1) L = (45/2)K 2 L 1/2 b) Calculate the Marginal Productivity of Capital (MPK). MPK = 15(2)K (2 1) L 3/2 = 30KL 3/2