微观经济学作业3

Central University of Finance and Economics

School of Economics

Intermediate Microeconomics, Spring 2011

Homework 3

（Due Date: Friday, April 1, 2011）

1. (25 points)

A worker is considering how many hours to work, how many hours to enjoy life and how many dollars to consume. Let h represent the number of hours he works, l ( the lowercase of L) represent the hours of leisure, and c represent his consumption of

stuff in dollars. His preferences are represented by the utility function U=l*c. He has 24 hours in a day that he can allocate to working or leisure. Let w denote the hourly wage.

a. Given that he only has 24 hours in a day, how are l and c related? Given w , how are c and h related?

b. If w is equal to 1 ( the number), what are the combinations of leisure and consumption that he can achieve? Find the formula for his budget line. Graph the budget line in the graph (leisure in the horizontal axis).

c. Calculate the optimal choice? Draw his optimal choice in the previous graph. How many hours will he work?

d. Assume that now the wage decrease to 1/2, Write down the equation for her budget line and graph it.

e. Calculate the optimal choice? Draw his optimal choice in the previous graph. How many hours will he work?

f. How did his supply of labor change? What does this tell us about the magnitudes of the income and substitution effects from the change in wages?

2. (25 points)

A consumer is considering how much money to allocate to consumption when young and to consumption when old. Let c11represent her consumption in dollars when young, and let c2 represent her consumption in dollars when old. The consumer preferences are represented by the utility function U =c1c2. She earns 100 dollars when young and 100 dollars when old. Assume that the interest rate is 25% and that there is no inflation. She can either saver or borrow at the market interest rate and must pay back loans with interest.

a. What is the present value of the income flow for the person? What is the future value of the income flow for the person?

b. Write down the equation for her budget constraint and graph it.

c. Calculate the consumer’s optimal consumption bundle? Does she save or borrow? How much? Draw the optimal consumption bundle in the graph in point c.

d. Assume that now the interest rate increases to 100%. Write down the equation for her budget constraint and graph it. Be sure to graph the point where she neither saves nor borrow.

e. Calculate the consumer’s optimal consumption bundle? Do savings increase? How much? Draw the optimal consumption bundle in the graph in point d.