What is perfect substitutes production function?
Perfect substitutes Such a production function models a technology in which one unit of output can be produced from 1/a units of input 1, or from 1/b units of input 2, or from any combination of z1 and z2 for which az1 + bz2 = 1. That is, one input can be substituted for the other at a constant rate.
What shows the different combinations of capital and labor?
An isoquant represents all possible combinations of labour & capital that can be employed to produce a given level of output.
Are perfect substitutes in production?
Two inputs K and L are perfect substitutes in a production function f if they enter as a sum; that is, f(K, L, x 3, … , xn) = g(K + cL, x 3, … , xn), for a constant c. The marginal product of an input is just the derivative of the production function with respect to that input.
What is the production function of labor L and capital K are perfect substitutes?
Suppose capital and labor are perfect substitutes resulting in a production function of q=K+L q = K + L . That is, the isoquants are straight lines with a slope of −1 . Derive the long-run total cost function TC=C(q) T C = C ( q ) when the wage rate is w and the rental rate on capital is r .
Are labor and capital complements?
In the long run, capital can adjust, and since capital and labor are complements, the higher wage will lead to lower levels of both capital and labor. Thus, labor adjusts (goes down) by more in the long run than in the short run.
Is Cobb-Douglas perfect complements?
The Cobb-Douglas utility results in constant expenditure shares. The utility that gives rise to perfect complements is in the form u(x, y) = min {x, βy} for some constant β (the Greek letter “beta”). First observe that, with perfect complements, consumers will buy in such a way that x = βy.
What is the difference between Isocosts and isoquants?
As nouns the difference between isoquant and isocost is that isoquant is (economics) a line of equal or constant economic production on a graph, chart or map while isocost is (economics) a curve that represents a combination of various inputs that cost the same.
What is a perfect substitute?
A perfect substitute can be used in exactly the same way as the good or service it replaces. This is where the utility of the product or service is pretty much identical. For example, a one-dollar bill is a perfect substitute for another dollar bill.
Which production function implies that that inputs are perfect substitutes?
Linear production function
– The maximum amount of output that can be produced with K units of capital and L units of labor. Linear production function: inputs are perfect substitutes. Leontief production function: inputs are used in fixed proportions.
What is the marginal product of the variable input?
The marginal product for any value of the variable input is the slope of the total product function at that point. In particular, if the total product function is differentiable, the marginal product is the derivative of the total product function.
What is the elasticity of substitution between capital and labor?
According to Equation (2), the elasticity of substitution is defined as the percentage change in the capital–labor ratio due to a 1% change in the ratio of the marginal products of inputs, that is, the marginal rate of technical substitution, along a given production isoquant (Helm, 1987).