# equilibrium interest rate

See the attached file.

1. Given that Y=900 and desired consumption and investment are given by:

Fill in as many entries as you need to answer the questions.

Assume that this is a closed economy (NX=0).

R C I G S C+I+G

0 925 80 15

0.01 900 75 15

0.02 875 70 15

0.03 850 65 15

0.04 825 60 15

0.05 800 55 15

a) Find the interest rate that is consistent with equilibrium in the goods market.

b) what is national savings in equilibrium?

c) what is total desired spending in equilibrium?

d) what is desired investment in equilibrium?

4. Suppose the economy-wide expected future marginal product of capital is MPK=30.1-0.01K

where K is the future capital stock. The depreciation of the capital stock is 5% (0.05) per period.

In parts a and b we will suppose that r=0.05 we find the equilibrium r in part d. It is unlikely to be 0.05.

The price of a unit of capital is one.

The current capital stock is 1900 units of capital. The price of one unit of capital is one unit of output.

Firms do not pay any taxes.

a) what is the optimal value of capital? Supposing that the interest rate is 0.05

b) what is the optimal value of investment? Supposing that the interest rate is 0.05

c) write the optimal investment as a function of the interest rate.

d) Let the consumption function is C=4000+0.8Y-100r where C is consumption and Y is output.

Government consumption is 1005 and full employment output is 30,000.

What is the equilibrium interest rate?

See attached file for full problem description.

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#### Solution Preview

Please see the attached file.

1. Given that Y=900 and desired consumption and investment are given by:

Fill in as many entries as you need to answer the questions.

Assume that this is a closed economy (NX=0).

Sd = Y-Cd-G =900-Cd-15=885-Cd

R C I G S C+I+G

0 925 80 15 -40 1020

0.01 900 75 15 -15 990

0.02 875 70 15 10 960

0.03 850 65 15 35 930

0.04 825 60 15 60 900

0.05 800 55 15 85 870

a)Find the interest rate that is consistent with equilibrium in the goods market.

Equilibrium in the goods market is achieved when demand for goods is equal to the output

Y=Cd+Id+G

From table we have r=0.04

b) what is national savings in ...

#### Solution Summary

Demand for goods is calculated and discussed in the solution.