Marginal Revenue Product Capital Quiz

The marginal revenue product of capital equals the additional output from one more unit of capital, which is the marginal product of capital, multiplied by the price at which that output is sold. MRPk = MPk times output price. It measures the monetary value of the additional output generated by the last unit of capital employed, serving as the benchmark against which the cost of acquiring that capital is compared in investment decisions.

The optimal capital employment rule states that a firm maximizes profit by using capital up to the point where MRPk equals the rental rate of capital. Below this point, each unit of capital generates more revenue than it costs, so adding more capital increases profit. Beyond this point, each unit costs more than it generates, reducing profit. The equality of MRPk and the rental rate is therefore the profit-maximizing condition for capital employment.

As more capital is added while labor remains fixed, the law of diminishing marginal returns applies. Each additional unit of capital has less labor to work with per machine, reducing its marginal contribution to output. Since MRPk equals marginal product of capital times output price, falling marginal product directly reduces MRPk. This declining MRPk produces the downward-sloping demand curve for capital and explains why firms do not demand unlimited quantities of capital even at low prices.

Since MRPk equals marginal product of capital multiplied by output price, any increase in the price of the output good directly raises MRPk at every quantity of capital. The same physical output generated by each unit of capital is now worth more in the market. This higher MRPk increases the marginal benefit of capital investment, causing firms to demand more capital at every given rental rate and shifting the capital demand curve to the right.

The MRPk curve is the demand curve for capital in a factor market. At each quantity of capital, MRPk tells the firm the revenue value of the last unit. A profit-maximizing firm will pay up to MRPk for a unit of capital. Therefore, the MRPk curve directly maps the firm's willingness to pay for each additional unit, forming the downward-sloping demand curve for capital that shows quantity demanded at each possible rental rate.

When MRPk exceeds the rental rate, the firm earns more from the last unit of capital than it pays. Each additional unit hired increases profit. The firm should continue acquiring capital until diminishing marginal returns lower MRPk to equal the rental rate. At that point, no further capital acquisition adds to profit. Operating below this point leaves profitable units of capital undeployed, sacrificing revenue that could be earned at no net cost to the firm.

The downward slope of the capital demand curve reflects the declining MRPk as capital increases. As more capital is employed with fixed labor, the marginal product of capital falls due to diminishing returns. Since MRPk equals marginal product times output price, a falling marginal product reduces MRPk. A profit-maximizing firm will only pay up to the MRPk for each unit, so as MRPk falls, lower rental rates are required to induce the firm to employ additional capital, tracing out the downward-sloping demand curve.

When technology improves the marginal product of capital, each unit of capital generates more additional output. Since MRPk equals MPk times output price, a higher marginal product directly raises MRPk at every quantity of capital. The higher MRPk means firms are willing to pay more for each unit, or equivalently demand more capital at every given rental rate. The demand curve for capital shifts rightward, increasing capital investment and productive capacity.

MRPk equals marginal product times output price: 50 times 8 equals 400 dollars. The rental rate is 500 dollars. Since MRPk of 400 is less than the rental rate of 500, the last unit of capital costs 100 dollars more than the revenue it generates. The firm is overemploying capital and should reduce it. Reducing capital raises MRPk due to diminishing marginal returns working in reverse, until MRPk rises to equal the 500 dollar rental rate at the profit-maximizing employment level.

Factor market equilibrium for capital occurs when the rental rate equals MRPk for all firms. If MRPk exceeds the rental rate anywhere, firms profit from acquiring more capital, raising demand and the rental rate until equality is restored. If MRPk is below the rental rate, firms reduce capital, lowering demand and the rate until equality is re-established. This equilibrating process ensures capital flows to its highest-value uses, achieving allocative efficiency across the capital market.

MRPk equals MPk times output price, declines due to diminishing marginal product, and serves as the capital demand curve. MRPk does not rise continuously; it declines as more capital is added due to diminishing returns. A rising MRPk would produce an upward-sloping capital demand curve, which contradicts the standard theory. The declining nature of MRPk is the fundamental reason the demand for capital is a downward-sloping relationship between rental rate and quantity demanded.

A rational firm will not pay more for a unit of capital than the additional revenue it brings in. MRPk is therefore the maximum price the firm is willing to pay per unit of capital. If the rental rate exceeds MRPk, the unit costs more than it earns, and a profit-maximizing firm will not hire it. The firm hires capital up to the point where MRPk just equals the rental rate, making MRPk the precise determinant of willingness to pay in the capital factor market.

This is true. In a competitive output market, MRPk equals MPk times price. Setting MRPk equal to the rental rate r gives MPk times P equals r, which rearranges to MPk equals r divided by P. This condition states that the marginal physical product of capital must equal the real cost of capital in terms of output units. It is the profit-maximizing condition for capital employment in a competitive market, directly linking physical productivity to market prices.

In imperfect competition, the firm faces a downward-sloping demand curve and must lower its price to sell additional output. Marginal revenue falls below price. MRPk equals marginal product times marginal revenue, which is less than price. This makes MRPk lower at any given quantity of capital than in a competitive market where MR equals price. Consequently, an imperfectly competitive firm employs less capital than a competitive firm would at the same marginal physical product.

The MRPk framework gives firms a practical decision rule: employ capital as long as each unit generates more revenue than it costs. This rule ties together the physical productivity of capital, the price of output, and the cost of capital into a single comparison. It explains why firms invest more when output prices rise or when technology improves productivity, and less when borrowing costs rise or productivity falls. The framework is central to understanding factor demand and investment across all market conditions.