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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

a) The firm will compute the stream of expected MRPs from each unit of capital, and then

purchase all units of capital for which the purchase price is less than or equal to that unit’s

present value of the stream of MRPs. The present value of the stream of future MRPs

depends negatively on the interest rate — that is, a fall in the interest rate raises the present

value of any given stream of MRPs. Thus, for a given purchase price of capital, a decline in

the interest rate raises the PV of capital and leads the firm to purchase more units. The

firm’s quantity of capital demanded is therefore negatively related to the interest rate ─ the

demand curve for capital is downward sloping.

© 2005 Pearson Education Canada Inc.

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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