MIC Unit 1 Practice Exam 1 and Solns

MIC Unit 1 Practice Exam 1 and Solns - NAME , Student ID...

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Unformatted text preview: NAME , Student ID Number Northwestern University First Midterm Economics 310-1 _ Winter Quarter, 2000-2001 Professor Braeutigam INSTRUCTIONS: (1) Write your name and student ID number in the Spaces at the tog of this gage. (2) This a 50 minute. closed-book examination..Answer all questions. (3) The examination is worth 100 points. The potential score on each question is indicated in parentheses at the beginning of each question. ' .(4) Show all work clearly and concisely in the sgace provided after each Question. ' You must support your answer with clearly demonstrated reasoning to receive any credit. However, for work in the right direction partial credit will be given. Question 1 (25 points possible )- Question 2 (25 points possible) Question 3 (25 points possible ) V Question 4 (25 points possible ) Total Score (100 points possible) Circle the nameof your Teaching Assistant and Section Day: Marc Fusaro - Thursday - Marc Fusaro - Friday Nick Kreisle - Thursday Nick Kreisle - Friday 209 Economics 310-1, Professor Braeutigam Page 2 First Midterm, Winter 2000-2001 -1) Suppose the supply curve for cotton is given by ClS = 2P, where QS is the quantity offered for sale when the price is P. The demand curve for cotton is QD = 200(M/P), where O0 is the quantity purchased when M- is the income in the market andP is the price. Assume M is exogenous. a) (8 points) What are the equilibrium price and quantity of cotton when income is 100? .b) (9 points) What are the following elasticities at the equilibrium you determined in (a)? v The own price elasticity of demand The income elasticity of demand The own‘price elasticity of supply c) (8 points) Find the reduced form equation that shows how the equilibrium price depends on the level of income. Use this reduced form to determine how you would expect a small increase in income to affect the equilibrium price when M = 100 (Le. find the value of dP/dM when M = 100). 210 Economics 310—1, Professor Braeutigam Page 3 First Midterm, Winter 2000-2001 2) Sam consumes two goods. food (measured by F) and clothing (measured by C). To survive, he needs at least 10 units of clothing and 20 units of food each year. If he receives less clothing than 10 units or less food than 20 units, he dies (and gets infinitely negative utility). When F320-and 0310, his utility function is _ . . .. . JF-ZO #010 U 2JF 20JC 10, With the marginal utilities MUC m and MUF m . The price of food (P;) is 1, and he has an income of l = 200 per year. The price of clothing is PC. a) (7 points) If"the price of clothing is too high. Sam will not be able to survive. What is the range of prices V for clothing for which he can survive? - For the rest of this problem assume that the price of clothing is low enough so that Sam can purchase more than the minimum amounts of food and clothing necessary to survive. b') '(8 points) Show whether he has a diminishing marginal rate of substitution of clothing for food. c) (10 points) Derive an algebraic expression for Sam's demand for clothing. that is, express C as a function of Pc (assuming l=200 and PF = 1). 211 Economics 310-1, Professor Braeutigam Page 4 First Midterm, Winter 2000-2001 3) a) (7 points) A consumer buys only goods x and y. Her indifference map is shown below. She has an income of $100 per week and the price of y is $1, Using the graph. draw the price consumption curve between the lowest and highest indifference curves on the graph. 'y Indifference curves ' 10% -. i , ‘\ i t : 1 -‘ 0246810121416182022 b) (10 points) Using the information contained in the optimal choice diagram in (a), draw a picture of the consumer's demand curve for x. Your demand curve should contain 4 points, one corresponding to each indifference curve. Label the coordinates of the points. 212 Economics 310—1, Professor Braeutigam Page 5 ,First Midterm. Winter 2000-2001 c) (8 points) The graph is repeated below for your convenience. On the graph show how you would measure the equivalent variation resulting from an increase in the price of x from $5-to $10. Provide a numerical estimate of the equivalent variation (an exact measure is not necessary. but be clear in showing how you arrive at your estimate). y » Indifference curves 10 ‘ i l l. l mm...— , , x O246810121416182022 4) Answer each of the following in the space provided. a) (10 points) A consumer buys two goods, X and Y. and always likes more of both goods. When he faces budget line BL1, his optimal choice is A. Given budget line BL2. he chooses B. Using revealed preference, what can you say about the way the consumer ranks A and B? If you cannot infer a ranking, explain why not. 213 Economics 310—1. Professor Braeutigam Page 6 First Midterm. Winter 2000-2001 b) (7 points) Joe likes root beer and ice cream in his root beer floats. but he wantsthe ratio of ice cream and root beer to be fixed: exactly one scoop of ice cream for each 8 ounces of root beer. On a graph with scoops of ice cream on the horizontal axis and ounces of root beer on the vertical axis. draw two indifference curves. Label the lower indifference curve U1 and the higher indifference curve U2. c) (8 points) Alexis consumes root beer (R) and cokes (C). Her preferences are characterized by a constant marginal rate of substitution of root beer for cokes, MRSRC = 4. The price of a Coke is 1 and the price of a root beer 3. To maximize her satisfaction. should she buy only cokes. only root beer, or a combination of the two? Explain. ' ' 214 Economics 310-1, Professor Braeutigam Page 7 First Midterm. Winter 2000-2001 Solutions: 1) a) When M = 100. demand is_ QD = 200(100/P) = 20,000/P. ln equflibrium Qs = Q0. Thus 2P=20,000/P, or P2 = 10,000, with P = 100. _ - . The equilibrium quantity can be calculated either by looking at the supply curve or the demand curve at the . equilibrium price. Using the supply curve. Qs = 2P = 2(100) = 200. Equivalently, using the demand curve we see that QD = 200(M/P) = 200(100/100) =' 200. b) The demand curve is a constant elasticity curve, of the form Q = APEM’.. where e is the own price elasticity of demand and f is the income elasticity of demand (i.e.. Q = 200P'1M‘). The own price elasticity of demand is -—1, and the income elasticity of demand is 1. Supply elasticity: Em, = (dQs/dPXP/Q) = 2(100/200) = 1. c) In equilibrium Qs = 00. Thus 2P=200M/P, or P2 = 100M. This means that P = 10M”. As M increases, the demand curve shifts out and the equilibrium price rises. The rate of change in P as M increases is dP/dM = 5/M°‘5. So, for example. when M = 100, dP/dM = 5/(100)°'5 = 5/10 = 0.5. So when M rises by 1 unit, P will rise by about 0.5. _____—_—_—_______——— 2‘) a) Using the budget line, we know that PFF + PCC 5 I, or F + PCC 5 200. When he just receives enough food and clothing to survive, F = 20 and C = 10. So 20+ Pc(10) 5 200. This means that Pc 5 18. If the price of clothing exceeds 18, he cannot purchase enough of the two goods to survive. b) F-20 MRSCF JAE: V010 =12. - MUF i/c.1o (>10 JF-ZO the MRS” diminishes. Therefore he has a diminishing MRS”. As he consumes more clothing (and less food) along an isoquant, 0) At an optimum, two conditions must be satisfied: F-20 P F—20 7 ~ 1 MRS =——=—° => —=P =5 F=P c-1o +2 H C" c-1o PF c-1o ° °( ) 0 (2) F+PCC=200 90+5Pc Substituting (1)into (2) :> Pc(C-10)+20+PCC=200 :> C= . c 3) a) x 8 10 '12 14 16 18 20 22 215 Economics 310-1, Professor Braeutigam Page 8 First Midterm, Winter 2000-2001 b) When P)( = 20, the optimal basket is A, with x = 2. When P, = 10, the optimal basket is B, with x = 4. When P, = 6.67, the optimal basket is C, with x = 6. When P, = 5, the optimal basket is E, with x = 8. The demand curve appears as follows: PX 22 20 18 16 14 12 10 ' 0 2 4 - 6 8 10 Baskets A, B, C, and E in the optimal choice diagram correspond respectively to Points A, B, C, and E on the demand curve. c) The graph below shows: _a) the initial budget line and optimal basket A. b) the final budget line and the final basket C. c) the decomposition budget line for determining the equivalent variation (parallel to the initial budget line and tangent to the final indifference curve) and the decomposition basket D. Since p, = 1, the difference between the vertical intercept of the initial budget line and the decomposition budget line is the equivalent variation, or about -$24 in this example. The equivalent variation is negative because the higher price decreases the consumer’s welfare. ' y-E Equivalent 1 0 “Variation about -$24 Decomposition BL for equivalent variation Initial BL 0 246810121416182022 216 Economics 310-1; Professor Braeutigam Page 9 First Midterm, Winter 2000-2001 4) a) We cannot infer a ranking. Given BL1, the consumer selects A when he could have chosen F. So A is weakly preferred to F. Since F lies to the northeast of B, F is strongly preferred to 8. Thus. on the basis of his behavior given BL1, the consumer must strictly prefer A to B. However, given BL1, the consumer selects B when he could have chosen E. 80 B is weakly preferred to E. Since E lies to the northeast of A, E is strongly preferred to E. Thus. on the basis of his behavior given ' 8L2, the consumer must strictly prefer B to A. ' It cannot be true simultaneoUsly that A is strongly preferred to B and B is strongly preferred to A. This violates the axiom of transitivity. The consumer cannot simultaneously be choosing an optimal basket given each budget line.’ b) Ounces of root beer m Scoops of ice cream c) MRSRC = 4 = MUR/MUC > PR/Pc = 3/1. Cross multiplying tells us that MUR/PR >MUc/Pc. Therefore, the , marginal utility per dollar spent on root beer will always be greater than the marginal utility per dollar spent on coke. She should substitute root beer for coke until she consumes only root beer. 217 ...
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MIC Unit 1 Practice Exam 1 and Solns - NAME , Student ID...

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