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Wire-grid Cobb–Douglas production surface with isoquants A two-input Cobb–Douglas production function with isoquants. In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and ...
In the short run, production can be varied only by changing the variable input. Thus only variable costs change as output increases: ∆C = ∆VC = ∆(wL). Marginal cost is ∆(Lw)/∆Q. Now, ∆L/∆Q is the reciprocal of the marginal product of labor (∆Q/∆L).
In the short run, production function at least one of the 's (inputs) is fixed. In the long run, all factor inputs are variable at the discretion of management. Moysan and Senouci (2016) provide an analytical formula for all 2-input, neoclassical production functions. [4]
This formula is important to relate back to diminishing rates of return. It finds the change in total product divided by change in labour. The marginal product formula suggests that MP should increase in the short run with increased labour. In the long run, this increase in workers will either have no effect or a negative effect on the output.
The principal difference between short run and long run profit maximization is that in the long run the quantities of all inputs, including physical capital, are choice variables, while in the short run the amount of capital is predetermined by past investment decisions. In either case, there are inputs of labor and raw materials.
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. [1] 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.
The variable cost curve is the constant price of the variable input times the inverted short-run production function or total product curve, and its behavior and properties are determined by the production function. [3]: 209 [nb 1] Because the production function determines the variable cost function it necessarily determines the shape and ...
The equation below (in Cobb–Douglas form) is often used to represent total output (Y) as a function of total-factor productivity (A), capital input (K), labour input (L), and the two inputs' respective shares of output (α and β are the share of contribution for K and L respectively). As usual for equations of this form, an increase in ...