Problem Set 3: Sec C

NAME:

Problem Set 3: Sec C

DUE DATE:Tuesday, 17thNovember

NO LATE PROBLEM SETS WILL BE ACCEPTED.

1. Suppose a Pakistani consumer is very uncertain about future increase in price level and hence, prefers consuming today rather than saving. Whereas, Japanese consumer prefers saving over consumption in the current time period.

1. Draw appropriate Intertemporal Choice models for the two consumers. Assume there are only two time periods. Also, assume that prevailing deposit and lending rates are 10%

1. Now assume that in Pakistan, the lending rate is 13% while deposit rate is 7%. How would the budget constraint change? Reflect the change in Japanese consumer budget constraint if the lending and deposit rates are 8% and 20% respectively.

1. Is the Pakistani consumer worse off or better off as a result of interest rate change. What about the Japanese consumer? Use both the graphs and the equation while explaining your answer.

1. Jennifer lives two periods. In the first period, her income is fixed at $10000; in the second, it is $20000. She can borrow and lend at the market rate of 7%

1. Sketch her intertemporal budget constraint

1. The ‘r’ increases to 9%. Sketch the new budget constraint. What effect do you expect this change to have on her saving?

1. Suppose that Jennifer is unable to borrow at any interest rate, although she can still lend at 9%. Sketch her intertemporal budget constraint.

1. A student entering college has been given $15000 by his parents. This is to be the student’s pocket money during all four years of college. Suppose further that he can borrow and lend freely at a market rate of 5%

1. Firstly, write down the equation of his intertemporal budget constraint

1. If the interest rate were higher than 5%, would the student be better or worse off? (Make sure you use your answer in part 1 to explain)

4. The production function of pizzas for One Guy's Pizza shop is K represents the number of ovens One Guy's Pizza uses and is fixed in the short-run at 4 ovens. L represents the number of labor hours One Guy's Pizza employees and is variable in the short and long-run. Fill in the empty columns in the table below.

5. Tad's Baitshop currently uses no computers in determining inventory. The number of items that can be inventoried in a day is given by where L is the number of labor hours used. If Tad purchases a computer to be used for inventory purposes, the number of items that can be inventoried in a day becomes Use the information in the table below to sketch Tad's marginal product of labor curves before and after the use of the computer for inventory purposes.

6. Fill in the following table with equations for the MPL, MPK, and MRTS for each of the production functions. YOU MUST SHOW YOUR WORK

7. For each production function, put an I, C, or D in the second column if the production function has increasing, constant, or decreasing returns to scale. Put an I, C, or Din the third column if the MPK is increasing, constant, or decreasing as K is increased. Put an I, C, or Din the fourth column if the MPL is increasing, constant, or decreasing as L is increased. YOU MUST SHOW YOUR WORK

8. The production function for high quality glassware is Q = K/2 + L1/2.

a. Are there constant, increasing, or decreasing returns to scale?

b. As the amount of capital is increased, is the marginal product of capital constant, increasing, or decreasing?

c. In the short run, labor is fixed at 4 units, since skilled labor for producing these high quality goods is difficult to find. Capital is variable. i) On the graph below, draw output as a function of capital input in the short run. ii)Draw the marginal product of capital as a function of capital input in the short run. The average product of capital is defined as the total output divided by the amount of capital input. iii) Draw the average product of capital input in the short run.

9. Omaira has an income of $2000 this year and expects next year’s income to be $1100. She can borrow and lend money at an interest rate of 10%.

1. What is the present value of Omaira’s endowment? What is the future value of her endowment? Draw intertemporal budget constraint. Label appropriately.

1. Suppose that Omaira has the utility function U = c1 c2. Write the general formula for her MRS between consumption this year and consumption next year.

1. What is the slope of Omaira’a Budget line? Write the equation for the present value budget constraint” and the “future value budget constraint”.

1. Solve for the optimal level of consumption in period 1 and period 2.

1. Will she borrow or save in the first period? How much?

1. Suppose the interest rate increases to 20%. Draw the new budget constraint.

1. Solve for the new optimal consumption in each period

1. Based on your answer to part g, does she save or borrow in the first period? How has her first and second period consumption changed compared to when the interest rate was 10%?