In economics, the marginal product of capital (MPK) is the additional production that a firm experiences when it adds an extra unit of input. [1] It is a feature of the production function, alongside the labour input.
The marginal product of capital (MPK) is the additional output resulting, ceteris paribus ("all things being equal"), from the use of an additional unit of physical capital, such as machines or buildings used by businesses.
The marginal product of capital (MPK) is the amount of extra output the firm gets from an extra unit of capital, holding the amount of labor constant:
Thus, the marginal product of capital is the difference between the amount of output produced with K + 1 units of capital and that produced with only K units of capital. [2]
Determining marginal product of capital is essential when a firm is debating on whether or not to invest on the additional unit of capital. The decision of increasing the production is only beneficial if the MPK is higher than the cost of capital of each additional unit. Otherwise, if the cost of capital is higher, the firm will be losing profit when adding extra units of physical capital. [3] This concept equals the reciprocal of the incremental capital-output ratio. Mathematically, it is the partial derivative of the production function with respect to capital. If production output , then
One of the key assumptions in economics is diminishing returns, that is the marginal product of capital is positive but decreasing in the level of capital stock, or mathematically
Graphically, this evidence can be observed by the curve shown on the graphic, which represents the effect of capital, K, on the output, Y. If the quantity of labor input, L, is hold fixed, the slope of the curve at any point resemble the marginal product of capital. In a low quantity of capital, such as point A, the slope is steeper than in point B, due to diminishing returns of capital. By other words, the additional unit of capital has diminishing productivity, once the increase on production becomes less and less significant, as K rises. [4]
Consider a furniture firm, in which labour input, that is, the number of employees is given as fixed, and capital input is translated in the number of machines of one of its factories. If the firm has no machines, it would produce zero furnitures. If there is one machine in the factory, sixteen furnitures would be produced. When there are two machines, twenty eight furnitures are built. However, as the number of machines available increase, the change in the output turns out to be less significant compared to the previous number. That fact can be observed in the marginal product which begins to decrease: diminishing marginal returns. This is justified by the fact that there is not enough employees to work with the extra machines, so the value that these additional units bring to the company, in terms of output generated, starts to decrease.
Number of machines | Output (Furnitures produced per day) | Marginal Product of Capital |
---|---|---|
0 | 0 | 0 |
1 | 16 | 16 |
2 | 28 | 12 |
3 | 39 | 11 |
4 | 46 | 7 |
5 | 49 | 3 |
6 | 50 | 1 |
In a perfectly competitive market, a firm will continue to add capital until the point where MPK is equal to the rental rate of capital, which is called equilibrium point. This fact justifies why in perfectly competitive capital markets, the price of capital can be seen as the rental rate. [5] The price of capital is determined in the capital market by the respective capital demand and supply.
The marginal product of capital determines the real rental price of capital. The real interest rate, the depreciation rate, and the relative price of capital goods determine the cost of capital. According to the neoclassical model, firms invest if the rental price is greater than the cost of capital, and they disinvest if the rental price is less than the cost of capital. [2]
It is only profitable for a firm to keep adding capital when the marginal revenue product of capital, MRPK (the change in total revenue, when there is a unit change of capital input, ∆TR/∆K) is higher than the marginal cost of capital, MCK (marginal cost of obtaining and utilizing a machine, for example). Thus, the profit of the firm will reach its maximum point when MRPK = MCK.
Growth accounting is a procedure used in economics to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy. Growth accounting decomposes the growth rate of an economy's total output into that which is due to increases in the contributing amount of the factors used—usually the increase in the amount of capital and labor—and that which cannot be accounted for by observable changes in factor utilization. The unexplained part of growth in GDP is then taken to represent increases in productivity or a measure of broadly defined technological progress.
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In economics, the marginal cost is the change in the total cost that arises when the quantity produced is increased, i.e. the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output. Marginal cost is different from average cost, which is the total cost divided by the number of units produced.
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In economics, average cost (AC) or unit cost is equal to total cost (TC) divided by the number of units of a good produced :
In economics and in particular neoclassical economics, the marginal product or marginal physical productivity of an input is the change in output resulting from employing one more unit of a particular input, assuming that the quantities of other inputs are kept constant.
In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal. The law of diminishing returns states that in productive processes, increasing a factor of production by one unit, while holding all other production factors constant, will at some point return a lower unit of output per incremental unit of input. The law of diminishing returns does not cause a decrease in overall production capabilities, rather it defines a point on a production curve whereby producing an additional unit of output will result in a loss and is known as negative returns. Under diminishing returns, output remains positive, but productivity and efficiency decrease.
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