Review for the Second Exam Intermediate Microeconomics Fall 2010

Transcription

1 Review for the Second Exam Intermediate Microeconomics Fall Matt recently moved to New York City. To model his behavior, assume he only consumes rental housing (H) and a composite good (X, P X = 1). His income is $5,000/month and the price of housing = $5/unit. At these prices he would maximize his utility consuming H 0 = 450 units of housing and the rest of his income on the composite good. Give the values for H 0 and X 0 below. Matt has been offered a unit of rent controlled housing that offers H RC = 700 units of housing at a total cost of RENT RC = The single point in the below graph shows this bundle. a. Give the values for H RC and X RC (the consumption of the composite good) that describe his consumption if he accepts the rent controlled unit. b. Would Matt accept this rent controlled unit? Explain. c. Using the graph, show the benefit of the rent controlled unit to Matt. [You cannot find an exact dollar value.] Explain the intuition behind your measure of the benefit of this program. d. Using the graph, show the cost of the rent controlled unit to the owner of the unit. [You CAN find an exact dollar value.] Explain the intuition behind your measure of the benefit of this program.

2 2. The demand for apples can be given as follows: P = @Q If the goal is to maximize revenue, what price would you charge? How many apples would you sell? 3. Briefly discuss the merits of the following statement. You should start your discussion with either "I agree with this statement" or "I disagree with this statement." You should then explain why you agree or why you disagree. For simplicity, assume that the price of milk = $1. "If all of a rational economic agent's income is spent on milk and CDs, and the demand for CDs is elastic, then a decrease in the price of CDs will decrease the consumption of milk." 4. Give an example of two goods with a negative cross-price elasticity. What relationship exists between these two goods? 5. You allocate $1,000 to spend on books and other goods. The price of other goods is $1 and the price a book is $10. Currently I maximize my utility at 50 books and spending the rest on other goods. a. Show the above information in a properly labeled graph. b. If the price of books increased by 20%, I would be indifferent between 50 books and consuming no books. Given the above information determine a measure of your consumer surplus. Show this in your graph. [Note: You can find a specific value for this measure of consumer surplus.] 6. Ana currently has no auto insurance. She knows that the probability of her getting in an accident is 5% and that an accident would cost her $1,700. If Ana s initial wealth is $8,100 and she is risk averse (U = M 1/2 ), what is the maximum Ana is willing to pay for auto insurance? Assume the policy will cover all of her costs of the accident ($1,700). Show you work and briefly explain how you found this value. If the insurance company charges their expected cost, what is the level of consumer surplus to Ana? Briefly explain how you determined the level of consumer surplus (be sure to clearly define consumer surplus in your answer). 7. Consider the following demand curve: P = Q. a. What is the elasticity of demand at price = $20? b. If the firm wanted to increase total revenue, should they increase or decrease their price? 8. Ken spends all of his income on two goods, potatoes and steak. He considers potatoes an inferior good. If potatoes are inferior, what must be true about the income elasticity of steak? Be as specific as possible. Briefly explain your logic. 9. Andrew has offered you the opportunity to play the following game. He will flip a coin. If it lands heads, he will pay you $25 and if it lands tails you will pay him $30. a. What is the expected value of Andrew s offer? b. Assume your initial wealth is $100 and you are a risk taker (U = M 2 ). Would you accept this offer from Andrew? Explain. c. Assume you accept his offer. However, Andrew has second thoughts. What is the minimum payment you would accept to give up this offer? Show your work and briefly explain how you found this value.

3 10. The space to the right gives a budget constraint and an indifference curve for someone who consumes just two goods, juice and bananas. This person s demand for juice is inelastic (but not perfectly inelastic). Adding the necessary budget constraints and indifference curves, show two additional points on this person s price consumption curve for juice. Briefly explain the logic behind how you determined the shape of the PCC. 11. Don currently spends all of his income (M) on food (F) and a composite good (X) (P X = 1). His income is $2,000/month, the price of food = $4, and he currently maximizes his utility by consuming 200 units of food. The government has decided to offer the following program. All households will be given a food voucher worth $500. [A voucher is identical to cash, except that it can only be spent on food.] To fund this program a tax is placed on food consumption. This increases the price of food to $5. a. Show the budget constraint associated with this program. Clearly indicate the values at all intercepts, kinks, and end points. b. Would Don be willing to enter this program? Explain. c. Using the tools of economics (Hint: The Income and Substitution Effects), what prediction can you make regarding Don's food consumption. Explain carefully. d. Show an indifference curve that represents the highest utility attainable under the program. e. Show graphically an appropriate measure of the benefit of this program to Don. Briefly explain. 12. Your current wealth, M, is $64 and your utility function can be represented by U =. You have been given a ticket that entitles you to the following gamble. A coin will be flipped, if it lands heads, you will receive $36, but if it lands tails you will pay $15. a. What is the expected value of this gamble? Show your work for partial credit. b. What is the expected utility of this gamble? Show your work for partial credit. c. What is the minimum price that would induce you to sell this ticket. Explain. Show your work for full credit.

4 13. The SU bookstore currently sells books at $20/each. They are thinking about implementing a frequent buyers program where you can pay to join and then purchase books at only $10 each. If your demand for books from the SU bookstore is: P B = 100-2@Q B what is the maximum you would pay to join this program? You can find an exact dollar amount. [Hint: A graph may help, but is not required.] Show your work for partial credit. 14. Under the current meal plan at SU (pretend this is true) you are able to purchase any number of Marriott meals at a price of $5. You budget $100 per week for food at SU and all other goods. Assume that the price of other goods is $1. a. Under this plan you maximize utility by eating 5 meals per week. Show the budget constraint and indifference curve associated with the utility maximizing consumption of Marriott meals and all other goods. Be sure to determine how much you are spending on all other goods and show that in your graph. b. If the price of a meal increased to $15, you would be indifferent between eating 5 Marriott meals per week and no Marriott meals. Given this information, determine the level of consumer surplus. c. Show this in your graph. 15. Dane spends all of his income ($250/month) on two goods, Spam (an inferior good, P SPAM = $5) and a composite good (X, P X = $1). The space below shows Dane s budget constraint and the indifference curve associated with his most preferred point (X 0,S 0 ). Add values for both intercepts. Assume Dane lobbies congress and is able to have a $3/unit subsidy placed on Spam. This drops the price of Span to $2. Given the current trend towards fiscal irresponsibility, no tax is levied to pay for this program. a. Show the new budget constraint in the space above. Be sure to clearly indicate values at both intercepts. b. Using the Income and Substitution Effects, predict what will happen to his consumption of Spam. c. Using the Income and Substitution Effects, predict what will happen to his consumption of the composite good (X).

5 16. Consider a person with the following utility function: U = X " Y 1-" Assume the price of X is $4, the price of Y is $2, and the person spends $100 on these two goods. Find the utility maximizing consumption of X as a function of ". 17. Jack needs help determining how many eggs he wants to eat. You know the following about Jack. He has $400 to spend on eggs (E) and bacon (B). Eggs are $2 each and a strip of bacon is $1. His utility function is given by the following: U(E,B) = E@B. To help him along the way, answer the following questions: a. What is Jack s marginal utility of bacon? b. What is Jack s MRS between bacon and eggs? c. How many eggs would maximize his utility? 18. Martha s preferences for Scented Bath Fizzie Soaps (S) and Fritz Knipschildt Chocolates (C) is described by the following utility function: U = S 1/4 C 3/4. Prices are P S = $5 and P C = $10 and she allocates $200/day on these two items. a. What two conditions must hold is Martha is maximizing her utility? Explain the meaning behind each. b. Determine Martha s utility maximizing quantities of S and C. Show your work for full credit. 19. Consider the following production function: Q = K L 4/3 a. Define Constant Returns to Scale. b. Determine whether this production function has increasing, decreasing, or constant returns to scale. Explain. Show your work for full credit. c. Define Law of Diminishing Marginal Product. d. Does this production function obey the law of diminishing marginal product in Labor? Explain. Show your work for full credit.