David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

11. 5 The supply of capital services
A firm rents capital up to the point at which its marginal cost - the rental rate - equals its marginal value
product. The firm demands K0 capital services at the rental rate R0.
For given rental rates and quantities of other factors of production, MVPK is the firm's demand curve for
capital services at each rental rate for capital services. The firm's MVPK curve showing its capital demand
curve can be shifted outwards by one of three events: (1) an increase in its output price, which makes the
marginal physical product of capital more valuable, (2) an increase in the level of other factors (chiefly
labour) with which capital works to produce output, making capital more productive, or (3) a technical
advance that makes capital more productive.
The industry demand curve for capital services
As with labour, we can move from the firm's demand for capital services to the industry demand curve for
capital services by horizontally adding the marginal value product of each firm. Again, we must recognize
that, in expanding output, the industry bids down the price of its output.
Thus the industry demand curve for capital services is steeper than the horizontal sum of each firm's
MVPK curves. The industry demand curve recognizes that output prices fall as output rises. The more
inelastic the demand curve for the industry's output, the more inelastic is the industry's derived demand
curve for capital services .
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., The supply of capital services
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Capital services are produced by capital assets. We analyse the market for capital services, then consider
what this implies for the market for capital assets. In so doing, we assume that the flow of capital services
is directly determined by the stock of capital assets, such as machines.
This is a simplification. By working overtime shifts, a firm can alter the effective flow of machine services
it gets from a given machine bolted to the factory floor. It can also leave machines idle.
Even so, in normal times firms have limited ability to vary the flow of capital services from a given capital
stock. We shall grasp the key features of the market for capital if we assume that the flow of capital services
is determined by the stock of capital available. Our analysis must distinguish the long run and the short
run, and examine both the supply of capital services to the economy and to a particular industry.
The short-run supply of capital services
In the short run, the total supply of capital assets (machines, buildings and vehicles), and thus the services
they provide, is fixed to the economy. New factories cannot be built overnight. The supply curve for capital
services is vertical at a quantity determined by the existing stock of capital assets. Some types of capital are
fixed even for an individual industry. The steel industry cannot change overnight its number of blast
furnaces. However, by offering a higher rental rate for delivery vans, the supermarket industry can attract
a larger share of the delivery vans that the economy currently has. For such capital services, an industry
faces an upward-sloping supply curve. It can bid services away from other industries.
The long-run supply of capital services
In the long run, the quantity of capital in the economy can be varied. New machines and factories can be
built. Conversely, without new investment in capital goods the existing capital stock will depreciate and
gradually fall. Similarly, individual industries can adjust their stocks of capital.
At what rental rates will owners of capital assets be willing to buy or build?
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