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Assignment 1 University of Calgary Department of Economics ECON357 2013 Winter Dr. Wen Assignment 1 is due on February 4, 2013 at the beginning of...

This question was answered on Jan 26, 2013. View the Answer
2. (20 marks) Jack has preferences over consumption in period 1 and 2 of the form

ux1, x2   2 x1

3/ 4
2

. The price of consumption is $1 in both periods. He has $6,000 in

the bank now and is trying to decide between two different investment opportunities, A
and B.
A: invest $5,000 in period 1 and receive $12,000 in period 2. B: invest $1,000 in period 1 and receive $3,000 in period 2.

a. If Jack can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Jack cannot invest more than $5000 if he chooses A, or $1000 if he chooses B.) Show your analysis
b. Given your answer in (a), how much will he consume in each period?
Assignment 1 University of Calgary Department of Economics ECON357 2013 Winter Dr. J.-F. Wen Assignment 1 is due on February 4, 2013 at the beginning of class on that day. Your answers should be submitted on paper, and may be handwritten or printed. Photocopies will not be accepted. You are encouraged to work with a classmate as a team. However, you have to submit answers individually. Please do not write more than is required in the question; show your work; and check your spelling. No Late Assignments will be accepted. All questions should be answered, with the answers in order. Maximum score is 90 marks A2-01 (20 marks) Company X has a demand for its services given by q q p 5 . 0 80 ) ( = . Its cost function is given by 2 125 . 0 ) ( q q c = . In the past it was not taxed, but now it must pay a tax of 10 dollars per unit of output. a. Calculate the monopolist’s profit-maximizing output and price and verify that the second- order derivative condition holds at your solution. b. By how much will the monopolist increase its price when the tax is imposed? c. What is the effect of the tax on the monopolist’s profits? A2-02 (20 marks) Tim has preferences over consumption in period 1 and 2 of the form 4 / 3 2 4 / 1 1 2 1 2 ) , ( x x x x u = . The price of consumption is $1 in both periods. He has $6,000 in the bank now and is trying to decide between two different investment opportunities, A and B. A: invest $5,000 in period 1 and receive $12,000 in period 2. B: invest $1,000 in period 1 and receive $3,000 in period 2.
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a. If Tim can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $5000 if he chooses A, or $1000 if he chooses B.) Show your analysis. b. Given your answer in (a), how much will he consume in each period? A2-03 (10 marks) Daddy Warbucks has given his niece the following choice. She can choose between two different inheritance bundles. Bundle F consists of $100 tomorrow and $10 today. Bundle P consists of $30 tomorrow and $60 today. His niece can borrow and lend money at an interest rate of 15%. Consumption goods cost $1 per unit today and there is no inflation. a. What is the present value of each of the two bundles? The future values? b. Which bundle do you think the niece of Daddy Warbucks should choose? Explain why in terms of a diagram that illustrates combinations of c 1 (consumption today) and c 2 (consumption tomorrow) which are affordable for each inheritance bundle. c. Bankers recognize that perfect capital markets make it hard to make money by lending money. Thus they will now pay the niece 15% for any monies that she lends them and they will charge her 50% interest on any monies that she borrows. Which bundle will the niece choose? Why? Again answer using a diagram illustrating combinations of c 1 and c 2 which are affordable for each inheritance bundle. A2-04 (10 marks) Nelly’s preferences between consumption this year, 0 c , and consumption next year, 1 c , are given by the utility function 3 / 2 1 3 / 1 0 1 0 ) , ( c c c c u = . She is endowed with income of $4,000 in period 0 and $11,000 in period 1. a. If she can borrow and lend at an interest rate of 10 percent, how much will she consume in period 0 and in period 1? b. Suppose she can lend at the interest rate of 8 percent, but due to a bad credit history Nelly can only borrow from a loan shark, who charges her an interest rate of 40 percent. How much will she consume in each period? [Hint: draw a diagram of her inter-temporal budget constraint and sketch her indifference curves.]
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OPTION
A
B c1
1000
5000 investment in pd 1
5000
1000 c2
12000
3000 As per above table utility is higher from option A
So he will consume 1000 in period 1 and 12000 in period 2 Utility(from given...

This question was asked on Jan 21, 2013 and answered on Jan 26, 2013.

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