Intermediate Microeconomics Midterm

Transcription

1 Econ 201 Spring 2016 Name: Student ID: Intermediate Microeconomics Midterm Thursday April 21, 2016 Beomsoo Kim There are 7 questions and 130 possible points. There are 2 pages to this exam. Please write all answers on the examination booklet. You will have 75 minutes to complete the exam. During the exam, you may use calculator and a dictionary. Use of hand-held electronic devices (such as cell phones, electronic dictionary, etc.) during the exam is strictly prohibited. For all questions, please show all your work to get full credit. Please make your diagrams clear and label the relevant parts of the graph. Once you ve completed the exam, please sign the pledge on page 2 1. (20 points) Compute the MRS for the following utility functions: ( a and b are strictly positive constants). a. U(X,Y) = aln(x)+bln(y), b. U(X,Y)=XaYb, c. U(X,Y)=aX+bY, d. U(X, Y)=(X ρ + Y ρ ) 1/ ρ 2. (10 points) John is indifferent between canned soup and fresh soup. Canned soup sells for $1 per serving and fresh soup sells for $2 per serving. Assuming that John has allocated $4 toward soup, how will he spend it? Explain your answer by drawing John's budget line and indifference curves. 3. (20 points) ) A consumer has $100 of income to spend on books and other goods (a composite good). Books cost $20 each and the consumer s optimal bundle is to consume purchase three books while spending the rest of the income on the composite good. The consumer is then given a gift of a book. Assume the consumer is unable to sell the book. Use two separate graphs to demonstrate each of the two possible scenarios: i. A consumer that is indifferent between the book gift and a cash gift of $20. ii. A consumer that strictly prefers a $20 cash gift to a book. To get full credit, accompany each graph with a brief explanation and draw your graphs clearly and well labeled.

2 Econ 201 Spring 2016 Beomsoo Kim 4. (15 points) For what values of a and b will the following production function exhibit increasing, decreasing or constant returns to scale? q = (La + Ka) 1/b 5. (10 points) Suppose that products can be produced according to the production function Q=5KL, where MP l =5K and MP k =5L, and assume the input prices are P l =$1 and P k =2. If the firm wishes produce 20 units of output, what cost minimizing combination of K and L should the firm utilize? (HINT: There are 2 unknowns (K and L), so you need 2 equations to answer the question.) 6. (10 points) The ABX Corporation determines that at current prices the demand for its computer chips has a price elasticity of 1.5 in the short run, while the price elasticity for its disk drive is 0.8. a. If the corporation decides to raise the price of both products by 20%, what will happen to its sales? b. What will happen to its sales revenue? 7. (45 points) Ed's utility from vacations (V) and meals (M) is given by the function U(V,M) = V 2 M. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, the price of vacations remained the same. Both years, Ed had an income of $1500. a. (5 points) Set up a Lagrangian to solve utility maximization problem with initial price and find equilibrium. b. (5 points) When price of meals increased repeat the a and find equilibrium. c. (5 points ) Show both equilibrium in the graph. Place vacation on the vertical axis and meals on the horizontal axis. d. (5 points) show the compensating variation for price change in meals in the graph. e. (13 points) Calculate compensating variation as numeric number for the price change in meals. (Hint: Use expenditure function) f. (12 points) Calculate the equivalent variation as numeric number for the price change in meals. Honor Pledge: I pledge on my honor that I have not given or received any unauthorized assistance on this examination. Signature:

3 Econ 201Beomsoo Kim Spring 2015 Name: Student ID: Intermediate Microeconomics Midterm Monday April 20, 2015 There are 7 questions and 130 possible points. There are 2 pages to this exam. Please write all answers on the examination booklet. You will have 75 minutes to complete the exam. During the exam, you may use a simple calculator(no Scientific or Graphic Calculators) and a dictionary. Use of hand-held electronic devices (such as cell phones, electronic dictionary, etc.) during the exam is strictly prohibited. For all questions, please show all your work to get full credit. Please make your diagrams clear and label the relevant parts of the graph. Once you ve completed the exam, please sign the pledge on page 2 1. (25 points) Julia s utility function is U.. A. Calculate marginal utility for B. Calculate marginal utility for C. Calculate marginal rate of substitution of for $0.5, $1, and income is $30 D. Write the budget constraint as mathematical form. E. How many and will Julia consume if she intends to spend all her money? 2. (10 points) The price elasticity of demand for agricultural products is normally estimated to be less than 1 in absolute value (inelastic). Use this fact to explain why farmers as a group succeed financially in years when productivity is low. 3. (30 points) The Federal government provides financial assistance to farmers who grow certain crops through a system of price supports. The price support system for tobacco works as follows: Tobacco farmers sell their crops to wholesalers, who in turn sell the tobacco to cigarette manufactures. The government establishes a target price for a product, P o, which is set above the market clearing price P e. To insure that prices reach the target level P o, the government guarantees to buy any unsold crops at the target level P o. By purchasing the unsold tobacco, the government, in effect, establishes a minimum price of P o. A. Graphically illustrate the price for and the amount of tobacco that will be purchased by wholesalers and by the government under this support program. On your graph indicate the total revenue that will be paid by wholesalers and by the government for the tobacco. As an alternative to the current support system, consider the following program: The government will no longer purchase unsold tobacco at the price P o. However, the government will subsidize farmers for any goods sold at prices below P o. For

4 Econ 201Beomsoo Kim Spring 2015 example, if a farmer sells his crop for P a and P a <P o the government writes a check for P o -P a for each unit sold. B. On a separate graph, indicate the price at which the farmers will sell tobacco to wholesalers and the quantity of tobacco sold. On your graph, also indicate the revenues paid by the Federal government. What pricing system would consumers prefer? What pricing system would farmers prefer? 4. (15 points) For each of the production functions listed below, determine whether the production technology exhibits constant, increasing, or decreasing returns to scale: A. Q = L 1/3 K 1/3 B. Q = L 1/2 + K 1/2 C. To produce each unit of output, a firm must use exactly 3 units of L and 5 units of K. 5. (10 points) Suppose the quantity of fish caught can be described by the production Q=K + 5L, where Q pounds of fish and K is the number of boats. Suppose that in the short-run, capital is fixed at 20 boats. A. Graph short-run output as a function of labor. B. Graph the average productivity of labor and marginal productivity of labor. 6. (10 points) Suppose that a firm s production function is Q=F(L)=L 3-200L 2 +10,000L. A. What is marginal product of labor? B. At what amount of labor input are the firm s average and marginal product of labor equal? 7. (30 points) Catherine has a monthly income of $210, which she spends on pizzas and a composite of all other goods. The price of a pizza is $3. A. Draw Catherine s budget constraint. Label your values of the intercepts and the slope of the budget constraint. (Place pizza on the horizontal axis). B. Assume Catherine maximizes her utility by spending $84 on pizzas and the rest of income on AOG. Show the bundle that maximizes her utility and the indifference curve through this bundle. C. The price of pizzas increases to $6. Show her new budget constraint and the substitution effect of this price change. Label your diagram appropriately. D. Assume pizzas and all other goods are both normal goods, show the income effect of the price change. Indicate Catherine s new utility level (indifference curve) after the price change. E. (10 points) How much additional income would Catherine need to be as well off as she was at her initial optimal bundle? (This requires a graphical answer, not a numeric answer.) What is the special name that is given to this additional income? Honor Pledge: I pledge on my honor that I have not given or received any unauthorized assistance on this examination. Signature:

5 Econ 201Beomsoo Kim Spring 2014 Name: Student ID: Intermediate Microeconomics Midterm Monday April 21, 2014 There are 6 questions and 130 possible points. There are 2 pages to this exam. Please write all answers on the examination booklet. You will have 75 minutes to complete the exam. During the exam, you may use a simple calculator(no Scientific or Graphic Calculators) and a dictionary. Use of hand-held electronic devices (such as cell phones, electronicdictionary, etc.) during the exam is strictly prohibited. For all questions, please show all your work to get full credit. Please make your diagrams clear and label the relevant parts of the graph. Once you ve completed the exam, please sign the pledge on page 2 1. (32 points) Jane s income is $300 per month. She spends all of it on tickets to concerts and films. A concert ticket costs $15 and a film ticket costs $10. Her marginal rate of substitution for concerts with films, MRS CF, is F/C, where C stands for the number of concert tickets and F stands for the number of films. (Calculate as a continuous function. Meaning Jane can buy 0.5 concert ticket. It make sense if she goes to concert every other month) A. Write the budget constraint as algebraic expression (place Concert tickets on the left hand side). B. Find equilibrium. How many concert tickets and how many film tickets will she purchase? To get full credit show your work. C. Price of film ticket decreased as $5. How many film tickets will she purchase? D. Draw price-consumption curve (place film tickets on the horizontal axes and allowing the price of film tickets, P f, to vary). E. (8 points) Draw film ticket demand curve (show two points in the demand curve driven in the above). 2. (16 points) Jane can spend $100 and her indifference curve is F=U/C. F means film and C means concert. Concert ticket costs $5 per ticket. The price of film ticket falls from $5 to $1.25 per ticket. A. (4 points) Calculate the equilibrium bundle with $5 and $1.25 respectively. What is the utility level respectively? B. (6 points) What is the compensated effect? Compensated effects means that how many concert tickets and film tickets she will purchase when she wants to keep her original utility level after price change. C. (6 points) How much money do we need to take away from Jane to compensate for the price cut?

6 Econ 201Beomsoo Kim Spring (16 points) Water's Edge is a small company in Minnesota that makes high-quality, hand-made sweaters. To produce each sweater, the company must use exactly 1 unit of capital, 20 hours of labor, and 50 yards of wool. If labor costs $5/hour, wool is $1/yard, and P k =$50. A. Does this production technology exhibit constant, increasing, or decreasing returns to scale? B. Here is another production function q = L 1/3 K 2/3. Does this production technology exhibit constant, increasing, or decreasing returns to scale? (Show how you get an answer in detail for full credit) 4. (24 points)use supply and demand curve shifts to illustrate the effect of the following events on the market for apples. Make clear the direction of the change in both prices and quantity sold. A. Scientists find that an apple a day does indeed keep the doctor away. B. The price of pears triples. C. A bad weather shrinks the apple crop to one-third its normal size. D. A popular pesticide used on apples for which there are no close substitutes, is suddenly banned by the government 5. (26 points) In this problem, you are to analyze the effects of the December 1973 OPEC oil embargo. Since 1974, the world oil market has been dominated by the OPEC cartel. By collectively restricting output, OPEC has succeeded in pushing world oil prices well above what they would have been in a competitive market. In 1974 OPEC accounted for about two-thirds of the world oil supply. Suppose the supply of oil provided by non-opec members can be described by the linear equation Q= P where demand is measured in billion barrels of oil per year and price is the price per barrel (in 1974 dollars). In 1973, OPEC supplied a fixed amount of 12 billion barrels of oil per year. A. Provide an equation for and graph the world supply of oil. B. Suppose the world demand for oil can be described by the linear equation Q= P. Given the supply and demand, what is the world price for oil? C. At this price, what is the elasticity of demand for oil? D. (8 points) In December of 1973, OPEC members agreed to reduce output by 25% or to 9 billion barrels per year. What was the short-run price for oil after the reduction in output? 6. (16 points)mike derives utility from the consumption of cheeseburgers (C) and Pepsi (P). If P c =$1.50/burger, P p =$1/glass, and income=$25/day, Mike chooses to consume 10 cheeseburgers and 10 Pepsi's per day. If P c falls below $1.50, Mike will still consume 10 cheeseburgers/day. (explain your reasoning in detail to get full credit) A. Does Mike consider cheeseburgers to be a normal or an inferior good? B. Is Pepsi a normal or inferior good? Can you tell? Honor Pledge:I pledge on my honor that I have not given or received any unauthorized assistance on this examination. Signature:

7 Econ 201 Spring 2013 Name: Student ID: Beomsoo Kim Intermediate Microeconomics Midterm Tuesday April 22, 2013 There are 5 questions and 130 possible points. There are 2 pages to this exam. Please write all answers on the examination booklet. You will have 75 minutes to complete the exam. During the exam, you may use a simple calculator (No Scientific or Graphic Calculators) and a dictionary. Use of hand-held electronic devices (such as cell phones, electronic dictionary, etc.) during the exam is strictly prohibited. For all questions, please show all your work to get full credit. Please make your diagrams clear and label the relevant parts of the graph. Once you ve completed the exam, please sign the pledge on page 2 5 points for each sub questions unless specified. 1. (25 points) Consider Jen, a consumer with preferences U(H,F)=F1/3H2/3, where H is the quantity of housing and F is the quantity of food (per month). Suppose Jen has a stipend of $600/month which she uses to purchase food at a price of $1/unit and housing at a price of $10/unit. (place housing on the horizontal axes) a. Calculate Marginal Utility of housing. b. Calculate Marginal Utility of food c. Calculate Marginal Rate of Substitution of food for housing. d. Compute Jen's utility-maximizing bundle of goods. e. Suppose that Jen's employer subsidizes housing by paying 50% of her total housing costs, thereby effectively lowering the price Jen pays for housing to $5/unit. Compute Jen's new optimal consumption bundle. f. How much does Jen's employer pay in total for this subsidy? How much utility does Jen enjoy with this subsidy (compute her utility at the optimal bundle). g. Suppose that her employer simply gave Jen the dollar cost you found in (c) as a lump sum (instead of subsidizing housing). Calculate Jen s utility with lump sum. Will Jen gain a higher utility from the housing subsidy or the lump-sum equivalent transfer? 2. (30 points) ) Lisa has an income of $100. She spends all of her income on pizza and burritos. A pizza costs $10 and a burrito costs $5. However, the store where Lisa buys her burritos has a special deal. After you've bought six burritos, then you can buy each burrito for $2.50. Draw Lisa's opportunity set.

8 Econ 201 Spring 2013 Beomsoo Kim 3. (10 points) Suppose that the demand curve for pigs is given by Z=10-2p, where Z is the number of pounds demanded per year and p is the price per pound. Suppose that the price is $1 per pound. a. Find the quantity demanded. b. Find the total expenditure c. Calculate the consumer surplus Now suppose that the government initiates a program to limit the supply of pigs. Suppose further that, as a consequence of the plan, the price per pound goes up to $2. d. What is consumer surplus after the price increase? e. What is the maximum amount that pig consumers would be willing to bribe legislators to repeal the supply limitation program? 4. (25 points) Midcontinent Plastics makes 80 fiberglass truck hoods per day for large truck manufacturers. Each hood sells for $ Midcontinent sells all of its product to the large truck manufacturers. Suppose the own price elasticity of demand for hoods is 0.4 and the price elasticity of supply is 1.5. a. Compute the slope and intercept coefficients for the linear supply and demand equations. b. If the local county government imposed a per unit tax of $25.00 per hood manufactured, what would be the new equilibrium price of hoods to the truck manufacturer? c. Would a per unit tax on hoods change the revenue received by Midcontinent? 5. (25 points) For what values of a and b will the following production function exhibit increasing, decreasing or constant returns to scale? q = (La + Ka)1/b Honor Pledge: I pledge on my honor that I have not given or received any unauthorized assistance on this examination. Signature: