# Capital and the Interest Rate Discussion

Capital and the Interest Rate Discussion
Capital and the Interest Rate Discussion
Question 2
a) reduce; increase; increase
b) increase; rightward shift
c) increase; reduction; reduction; leftward shift
Question 4
a) The present value of each asset is equal to the discounted stream of payments
(discounted back to the present period). We assume for this question that the first payment
takes place one year from now, the second payment two years from now, and the third
payment three years from now. In this case, the PV of the four assets are:
A: PV = \$1000/(1.08) 0 0 = \$925.93
B: PV = 0 0 \$5000/(1.07)3
= \$5000/1.225 = \$4081.49
C: PV = \$200/(1.09) 0 \$200/(1.09)3
= \$183.49 \$154.44 = \$337.93
D: PV = \$50/(1.10) \$40/(1.10)2
\$60/(1.10)3
Capital and the Interest Rate Discussion
= \$45.45 \$33.06 \$45.08 = \$123.59
b) In each case, the most the firm would be willing to pay to purchase the asset is the
asset’s present value. At any higher price, the firm is better off lending its money at the
interest rate.
c) If the asset’s listed selling price is less than its present value, all firms would want to
purchase it. There will be an excess demand for the asset that will cause its price to rise.
From the argument in (b), at any price above PV there will be an excess supply that will
cause the asset’s price to fall. Thus the competitive equilibrium asset price is the asset’s
present value.
Question 6
b) An “especially good market” for its product in the future means that the future MRP
from any unit of capital increases (because the firm’s product price increases). This
increase in MRPs is shown by a rightward shift in the firm’s demand curve for capital. At
any given real interest rate, the firm will purchase more units of capital.
c) The technical problem reduces the stream of future MRPs (because the future marginal
product of capital declines) and thus leads to a leftward shift in the firm’s demand curve for
capital. At any given interest rate, the firm purchases fewer units of capital.
Question 8
a) The tax credit makes investment more profitable and shifts the DK curve to the right.
The result is a higher real interest rate and a larger capital stock.
b) There is no contradiction. The increase in the demand for capital led to the increase in
the interest rate. The capital stock increased only because the higher interest rate induced
households to increase their saving, thus “financing” the firms’ increase in capital stock.
The DK curve is still downward sloping, showing a negative relationship between interest
rates and the quantity of capital demanded (along any given DK curve).
c) The tax credit makes saving more attractive and shifts the SK curve to the right. The
real interest rate falls and the capital stock rises.
d) There is no contradiction. The interest rate fell because of the increase in the supply of
capital. The capital stock increased only because the lower interest rate induced firms to
increase their investment, thus “using” the greater supply of capital. The SK curve is still
upward sloping, slowing a positive relationship between real interest rates and the
quantity of capital supplied (along any given SK curve).
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