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+(2/3)c2 , wherec1is consumption today, andc2is 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 rater0 .

1). 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 .

a. What is the market supply, QS, for funds if the interest rate is 30%?

b.What is the market supply for funds if the interest rate is 70%?

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

d.What is aggregate consumption in each period, c1 and c2, at that interest rate?