Capital markets

Suppose that there are only 10 individuals in the economy each with the following utility function

over present and future consumption: U(c1; c2) = c1 + 2/3c2, where c1 is consumption today, and

c2 is consumption tomorrow. Consumption tomorrow is less valued because people are impatient

and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today

and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of

$10 dollars today and no income tomorrow (because they will be retired) but they can save at the

market interest rate r 0.

1. What is the price today of one unit of consumption tomorrow? Why?

2. Write an expression for an individual's budget constraint in terms of today's and

tomorrow's consumption expenditure.

3. Draw the indifference curve. How much of their income will an individual consume

and how much will they save given the interest rate of r?

4.How much of his or her income will an individual consume today given that the interest rate is 0.5?

5.How much of his or her income will an individual consume today given that the interest rate is 0.7?

6.Suppose that in this economy all the funds for capital come from savings by the 10 individuals. Firms' demand for capital is given byQD=100100r. What is the market supply for funds if the interest rate is 30%?

7.What is the market supply, QS, for funds if the interest rate is 70%?

8.What is the equilibrium interest rate that clears the capital market?

9.What is aggregate consumption in each period at that interest rate? C1? C2?