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Problem Set 3 - due 2/2/17 ECN 312 - Intermediate Microeconomic Theory Spring 2017 Please make sure that your problem set is legible and stapled....


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Hello, I need help with number one. Im not quite sure if im doing the graphs correctly.


Problem Set 3 - due 2/2/17 ECN 312 - Intermediate Microeconomic Theory

 

Spring 2017

 

Please make sure that your problem set is legible and stapled. Please write your name

 

and section number on your problem set. On your graphs, please label axes, curves,

 

intercepts, and all points relevant to the question. Explain your work thoroughly in

 

order to receive full credit. Possible points are given in parentheses.

 

1. (15) Cheri is given $600 on the first day of this month and $600 on the first day of next month.

 

Cheri has a credit card that charges 20% interest per month. She can use the credit card this

 

month, but must pay the balance in full (plus interest) next month. She cannot use the credit

 

card next month. In addition, Cheri is able to put money under her mattress this month for

 

next month.

 

(a) (2) Plot and label Cheri’s endowment (the bundle she starts off with) in the space of

 

consumption this month (C1 ) and consumption next month (C2 ). Put C1 on the horizontal

 

axis.

 

(b) (3) Plot and label the point indicating the maximum amount of consumption that Cheri

 

can get this month. Plot and label the maximum amount of consumption that Cheri can

 

get next month. Use these points, along with the endowment from (a), to draw Cheri’s

 

budget line and label its slope.

 

(c) (3) Suppose that Cheri’s preferences are given by the following utility function:

 

U (C1 , C2 ) = 2C1 + C2

 

Draw and label three indifference curves associated with these preferences.

 

(d) (2) What is Cheri’s optimal consumption bundle given the preferences in (c)? Does she use

 

her credit card? If so, how much does she charge?

 

(e) (3) Suppose that Cheri’s preferences are instead given by the following utility function:

 

U (C1 , C2 ) = min{2C1 , C2 }

 

Draw and label three indifference curves associated with these preferences.

 

(f) (2) With the preferences in (e), does she use her credit card to consume at her optimal

 

bundle? Describe in two sentences or less.

 

2. (20) Suppose that David (an automobile enthusiast) has Cobb-Douglas preferences over vans (V)

 

and sports cars (S):

 

3

 

1

 

U (V, S) = 4V 4 S 4

 

When David goes to the car dealership, he finds that the price of vans is $25, 000 and the price

 

of sports cars is $100, 000. David has $850, 000 to spend on new automobiles. (a) (5) What is the marginal utility of V? What is the marginal utility of S? What is the

 

marginal rate of substitution of vans for sports cars (M RSV,S )?

 

(b) (5) In what ratio will David purchase V and S at the optimum (solve for tangency condition

 

and express S as a function of V)?

 

(c) (5) How many vans will David buy? How many sports cars will David buy?

 

(d) (5) Show this solution graphically (label V ∗ and S ∗ , the IC at the optimum (does not need

 

to be exact - make sure that you get the correct shape and the correct tangency), the budget

 

line, and all axes and other relevant points). Put vans on the horizontal axis.

 

3. (15) In answering this question, please refer to the attached graph. For part (e) of this question,

 

add to the existing graph by using a ruler to draw budget constraints. Attach the graph to your

 

write-up when you turn in your work.

 

Suppose that a typical poor family chooses to allocate its income between food (F) and other

 

consumption (C) in such a way that it picks point A on budget line 1 in the graph on the following

 

page. At this point, the family spends $1, 000 of its $5, 000 income on food. The price of other

 

consumption is $1 per unit.

 

In an effort to win votes from this segment of Americans, the government decides to lift the

 

typical poor family’s level of utility from that implied by indifference curve I to that implied by

 

indifference curve II.

 

(Please note that when I solve this question, I get relatively easy numbers to work with....)

 

(a) (3) Suppose the government does this by subsidizing the family’s consumption of food (i.e,

 

by paying part of the price of food). What is the initial price of food? To what does the

 

government need to lower the price of food to get the family to indifference curve II?

 

(b) (3) What is the cost to the government (per poor family) of this price subsidy?

 

(c) (3) How could the government achieve the same result by way of a simple income subsidy?

 

What would be the cost to the government per poor family?

 

(d) (3) Suppose that the government’s objective is to both increase the utility of poor families

 

to indifference curve II and to raise their quantity of food as much as possible. Cost is not

 

a concern. Which policy (price subsidy or income subsidy) would the government choose?

 

(e) (3) Describe the two policies graphically. 2 3

 


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