Firm’s Demand for the Desired Capital Stock (With Diagram)

The demand for capital comes from the business in form of machines and the households in form of houses.

Desired capital stock is the amount of capital goods that a firm would like to have to maximize its profit.

Therefore, firms before investing will compare the cost, that is, rental cost of capital (r_c) and benefit of capital, that is, the Marginal product of capital (MP_k) or (VMP_k)

MP_k → It is an increase in the output by using an additional unit of capital.

VMP_k → Value of marginal physical product

VMP_k = MP _k.P_x where : P_x → Price of output

Rental cost of capital is the cost incurred by firm for using capital.

They are:

1. Real interest rate

2. Depreciation

3. Taxes

Reason:

1. If the firm finances the purchase of capital by borrowed funds then it pays interest rate (i) If inflation occurs then nominal value of capital increases. As interest rate is known but inflation rate is not known, therefore, expected inflation rate (π^e) is taken.

.^.. Real interest rate (r) = i – π^e

2. Over a period of time capital wears out. Therefore, cost of depreciation is added to the rental cost of capital (r_c)

3. as regards taxes:

(a) In case of corporate income tax, which is a proportional tax on profit, a higher tax will lead to an increase in r_c. .^.. desired capital stock decreases

(b) In case of investment tax credit, where the firms are allowed to deduct from their taxes a fraction of their investment expenditure, a higher credit will lead to a fall in r_c.

Reason:

Investment tax credit reduces price of capital goods.

.^.. Demand for desired capital stock increases

MP_k curve is negatively sloped showing, as we increase the use of capital, the MP_k falls because of law of diminishing returns (Fig. 20.2).

Fig. (20.2) shows : lower the r_c, higher is the demand for capital and vice versa.

(a) When demand for desired capital stock increases from K₁ to K₂, VMP_k falls from AK₁ to BK₂

Therefore, when VMP_k falls, people will invest more only when user cost of capital falls from rc₁ to rc₂

This implies that the cost of using capital falls. Therefore, demand for capital increase from K₁ to K₂ (inspite of the fact that MP_k is falling).

Thus, when r_c falls from rc₁ to rc₂ demand for capital increases from K₁ to K₂ Firms’ decision to invest will depend on the profitability from the investment.

Profit = Revenue – Cost

= MP_k – r_c

= MP_k – (i – π^e + d) …(iv)

The equation (iv) shows that the Business Fixed Investment depends on:

(1) MP_k

(2) Cost of capital

(3) Depreciation.

(i) If : MP_k > r_c : Firm will invest more,

e.g. at rc₂ → MP_k = AK₁

rc = rc₂

.^.. Investment will increase from K₁ to K₂

(ii) Similarly, if MP_k < r_c : Firm will invest less because it will incur loss

Thus the firm will invest till the point where MP_k = r_c ← Steady state level