Midterm 1 exam answers Managerial economics PDF

Preview

Summary

Midterm 1 exam answers Managerial economics MBA course...

Description

Economics 100A Answers Midterm #1 Amjad Toukan July 9, 2014 Student Name:______________________________Student ID#:__________________ You have 1 hour 15 minutes for this examination. It is a closed note/book exam. You may use a calculator, no cell phones. Explain all of your answers and show all of your work. A complete answer illustrates how you arrived at that answer. Label all graphs and axes. The points for each question are listed in parentheses. Be sure to write your name, and student ID# above. Good luck! You might find the following information useful: MU C 

 U (C , F ) ...Additional satisfaction from consuming 1 additional unit of C

clothing MRS 

PF …………Marginal rate of substitution of food for clothing PC

 U ( X , Y )   ( PX X  PY Y  I ) ……Lagrangian for utility maximization

The arc price elsaticity formula is : E p [

 Q (P1  P2 ) / 2 ][ ]  P (Q1 Q2 ) / 2

The arc income elsaticity formula is : E I [

Q ( I1  I2 ) / 2 ][ ]  I (Q1 Q2 ) / 2

w MPL  r MPK MU F P  F MU C PC

1

1) (10) Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior. To help explain Jennifer’s behavior, we need to look at the reference point from which she is making the decision. In the first instance, she does not own the shirt so she is not willing to pay the $50 to buy the shirt. In the second instance, she will not accept $50 for the shirt from her friend because her reference point has changed. Once she owns the shirt, the value she attaches to it increases. Individuals often value goods more when they own them than when they do not. This is called the endowment effect.

2

2) (10) Explain the difference between a positive and a negative network externality and give an example of each. A positive network externality exists if one individual’s demand increases in response to the purchase of the good by other consumers. Fads are an example of a positive network externality. For example, each individual’s demand for baggy pants increases as more other individuals begin to wear baggy pants. This is also called a bandwagon effect. Another example of a positive network externality occurs with communications equipment such as telephones. A telephone is more desirable when there are a large number of other phone owners to whom one can talk. A negative network externality exists if the quantity demanded by one individual decreases in response to the purchase of the good by other consumers. In this case the individual prefers to be different from other individuals. As more people adopt a particular style or purchase a particular type of good, this individual will reduce his demand for the good. Goods like designer clothing can have negative network externalities, as some people would not want to wear the same clothes that many other people are wearing. This is also known as the snob effect. Another example of a negative network externality is road congestion. As more people use a road, the more congested it becomes, and the less valuable it is to each driver. Some people will drive on the road less often (i.e., demand less road services) when it becomes overly congested.

3

3) (10) Describe the indifference curves associated with two goods that are perfect substitutes. What if they are perfect complements? Two goods are perfect substitutes if the MRS of one for the other is a constant number. In this case, the slopes of the indifference curves are constant, and the indifference curves are therefore linear. If two goods are perfect complements, the indifference curves are L-shaped. In this case the consumer wants to consume the two goods in a fixed proportion, say one unit of good 1 for every one unit of good 2. If she has more of one good but not more of the other then she does not get any extra satisfaction.

4

4) (20) Consider a person with a current wealth of $10,000 who faces the prospect of a 25 percent chance of losing her $1,900 automobile through theft during the next year. Suppose also that this person’s utility index is, U(W) = Sqrt(W), where W is her wealth. a. If this person faces next year without insurance, what would her expected utility be? b. What is the maximum amount (insurance premium) that this person would pay for insurance protection? c. If the insurance company were to charge an actuarially fair insurance premium (situation in which an insurance premium is equal to the expected payout by the insurance company), what would that insurance premium be? (assume that the insurance company has only claim costs and that administrative costs are $0) a. If this person faces next year without insurance, expected utility will be Expected utility = .75U(10,000) + .25U(8,100) = 97.5 b. The maximum amount that might be paid for the insurance protection (x) Expected utility = U(100,000 – x) 97.5 = sqrt (10,000 – x) x = 10,000 – 9,506.25 Therefore the maximum premium is x = 493.75 c.In this situation a fair insurance premium would be $475 (25 percent of $1,900, assuming that the insurance company has only claim costs and that administrative costs are $0). This person would be willing to pay up to $18.75 ($493.75-$475) in administrative costs to an insurance company (in addition to the $475 premium to cover the expected value of the loss). Even when these costs are paid, this person is as well off as he or she would be if forced to face the world uninsured.

5) (20) Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is -1.0. Suppose also that Felicia spends $10,000 a year on food, the price of food is $2, and that her income is $25,000. a. If a sales tax on food caused the price of food to increase to $2.5, what would happen to her consumption of food? (Hint: Because a large price

5

change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity.) b. Suppose that Felicia gets a tax rebate of $2,500 to ease the effect of the sales tax. What would her consumption of food be now? c. Is she better or worse off when given a rebate equal to the sales tax payments? Explain. (Hint: You can explain using an indifference curve graph.)

6

7

8

6) (10) For the following utility functions, determine whether they have convex indifference curves (that is, whether the MRS declines as x increases). a. b.

U(x,y) = 3x + y U(x,y) = x. y

9

7) (20) David get $3 per week as an allowance to spend any way he pleases. Because he likes only peanut butter and jelly sandwiches, he spends the entire amount on peanut butter (at $0.05 per ounce) and jelly (at $0.10 per ounce). Bread is provided free of charge by a concerned neighbor. David is a particular eater and makes his sandwiches with exactly 1 ounce of jelly and 2 ounces of peanut butter. He is set in his ways and will never change these proportions. a. How much peanut butter and jelly will David buy with his $3 allowance in a week? b. Suppose the price of jelly were to rise to $0.15 an ounce. How much of each commodity would be bought? c. By how much should David’s allowance be increased to compensate for the rise in the price of jelly in part (b)? d. Graph your results in parts (a) to (c). e. In what sense does this problem involve only a single commodity, peanut butter and jelly sandwiches? Graph the demand curve for this single commodity. f. Discuss the results of this problem in terms of the income and substitution effects involved in the demand for jelly.

10

11...