I.

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. Consumptionj 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.

What is the price today of one unit of consumption tomorrow?

To verify that you have the correct answer, calculate the price today of one unit of consumption tomorrow if r = 0.05.

P =

0.95

II.

1 point possible (graded)

Write an expression for an individual's budget constraint in terms of today's and tomorrow's consumption expenditure.

To verify that you have the correct answer, calculate the maximum you can consume today if you consume today 6.24 tomorrow and the interest rate is 0.07.

C1 =

III.

3 points possible (graded)

Draw the indifference curve. (This is for your understanding. Your drawing will not be graded.....

How much of his or her income will an individual consume today given that the interest rate

oLess than half of it

oExactly half of it

oThe individual is indifferent between consuming today and saving

oMore than half of it

oAll of it

oNone of it

How much of his or her income will an individual consume today given that the interest rate

oLess than half of it

oThe individual is indifferent between consuming today and saving

oNone of it

oAll of it

oMore than half of it

oExactly half of it

How much of his or her income will an individual consume today given that the interest rate

oLess than half of it

oAll of it

oNone of it

oMore than half of it

oExactly half of it

oThe individual is indifferent between consuming today and saving

IV.

5 points possible (graded)

Suppose that in this economy all the funds for capital come from saving by the 10 individuals. Firm demand for capital is given by Q_D = 100 - 100r.

What is the market supply for funds if the interest rate is 30%?

Q_S =

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

Q_S =

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

r =

what is aggregate consumption in each period at that interest rate?

C₁ =

C₂ =