Microeconomic Theory (Econ 210) 1st Midterm Exam

Transcription

1 Microeconomic Theory (Econ 210) 1st Midterm Exam Professor Guse Tuesday, October 18, 2005 You have 2 hours to complete the exam. There are a total of 80 points available. It is designed to take about 1 minute per point. You are allowed to reference a single page of notes. You may use a calculator, if you like, but only to do simple calculations; you may not use any symbolic or graphing capabilities which your calculator may have. There is space provided for each question. If you need additional space, you may write on the back of the pages or use additional sheets and staple them to your exam when you turn it in. Please show all of your work. Please turn in your cheat sheet when you turn in your exam. If you have questions, please raise your hand during the first 10 minutes and I will respond to the whole class. I will return after about 75 minutes to respond to any additional questions you may have. Good luck and have fun. 1

2 1. (14 points) Fella has rational preferences over bundles of yarn and catnip, (y,c). When presented with a choice between one bundle containing 1 ball of yarn and no catnip (1,0) and another containing 1 ounce of catnip and no yarn (0,1), Fella is indifferent. Fella would strictly prefer ( 3 4, 1 4 ) to either of those and would strictly prefer ( 3 4, 1 4 ) to ( 3 4, 1) as well. (a) (4 pts) Fella s preferences could... i. be monotonic and convex ii. be monotonic but not convex iii. not be monotonic but could be convex iv. not be monotonic and could not be convex (b) (4 pts) Explain your answer. (c) (6 pts) Draw a picture of Fella s preferences consistent with the story above. 2

3 2. (26 points) Cookie Monster (CM) has preferences over bundles of milk (L) and cookies (C) which are represented by u(l, C) = 1 3 log L log C. (a) (4 pts) What are CM s demands for L and C as a functions of income (m), the price of milk (p L ), and the price of cookies (p C )? (b) (6 pts) The price of milk is p L = $1.00 per gallon and the price of cookies is p C = $2.00 per pound. Draw a picture which shows Cookie Monster s income expansion path in L C space out to an income level of $15 per week. (c) (2 pts) Due to cutbacks at PBS, Cookie Monster has fallen on hard times and his weekly income is only $9 per week. In the same picture, draw CM s budget line and optimal consumption bundle. (d) (4 pts) Grover approaches Cookie Monster and offers to give Cookie Monster a gallon of milk in exchange for a half-pound of cookies. How does CM respond? Explain. 3

4 (e) Cookie Monster continued (6pts) Once the public sees the television images of Cookie Monster and Grover, both emaciated and desperately hungry, reduced to bargaining over crumbs, the outcry is too much for Congress. However, instead of cash-assistance, they decide to give Cookie Monster milk stamps. (Research sponsored by the dairy industry has shown that too many cookies may cause diabetes in muppets.) Every week they give him 6 stamps, each good for one gallon of milk. Futhermore, he is forbidden from trading his milk stamps (or his milk) for cookies. Draw CM s new budget and optimal bundle. (f) (4 pts) At the optimal choice, what rate would CM be willing to accept cookies in exchange for giving up milk? How does this relate to the MRT in the market? Explain. 4

5 3. (10 points) Sven consumes only bacon and eggs. Furthermore, he eats exactly 2 eggs for every 3 strips of bacon and will not eat them in any other ratio. (a) (2 pts) write down a utility function which represents Sven s preferences over bundles of strips of bacon (B) and eggs (G). (b) (4 pts) Draw a picture of Sven s optimal choice if his income is 100, the price of bacon is $1 per strip and eggs are $0.50 each. (c) (4 pts) What is Sven s demand for eggs as a function of income and prices? 5

6 4. (14 points) The picture below shows three different budgets, I, II, and III, faced by an individual with rational, monotone, convex preference over bundles of good x and good y. The price of good x is equal to p x across all three budgets; only the price of good y and the income level are changing. Y II Summary of Budgets Price Price Income of X of Y I M p x p H II M p x p L III m p x p L III I X (a) (4 pts) Assume that the bundles indicated on each budget line are the consumer s optimal choice for those respective budgets. (The bundle at the intersection of I and III goes with budget I.) Would the consumer prefer I or III? Explain. (b) Consider the transition from budget I to II. i. (3 pts) Label the income and substitution effects of this price change for good x. ii. (3 pts) Label the income and substitution effect of this price change for good y. iii. (2 pts) Good x is ( Normal Inferior and Ordinary Giffen ). Circle one. iv. (2 pts) Good y is ( Normal Inferior and Ordinary Giffen ). Circle one. 6

7 5. (16 points) Jean-Paul makes goat cheese. His short-run cost curve - that is, the total cost as a function of output - is given by C(q) = q 3q 2 + q 3 where 40 is the fixed cost and q is output in pounds. Showing your work, answer the questions below and explain your answers using any diagrams you see fit. (a) Write down the marginal cost and average variable cost functions. (b) In the short-run, How many pounds should JP produce when the price of goat cheese is $5 per pound? (c) In the short-run, How many pounds should JP produce when the price of goat cheese is $10 per pound? 7