Factors of Production

Factors of production are the inputs used to produce goods and services. The two most important factors of production are capital (K) and labor (L). Capital can be tools, machines and structures used in production. Therefore, prices play a big role here (rental rates). Labor can not only be the human body, but also everything related to it, such as the wages (prices), physical and mental efforts of workers.

W = nominal wage
R = nominal rental rate
P = price of output
W /P = real wage (measured in units of output)
R /P = real rental rate

Therefore, the production function represents how much output (Y ) the economy can produce from K units of capital and L units of labor, reflecting the economy’s level of technology and exhibits constant returns to scale.

Production function: Y = F(K, L).

Returns to Scale

Output is determined by the fixed factor supplies and the fixed state of technology:

So, let’s talk  about a firm level here.

The goal of the firm is to Maximize Profit (MPK=R/P). Profit is equal to revenue minus costs.

Revenue equals P ×Y, the selling price of the good P multiplied by the amount of the good the firm produces Y. Costs include both labor costs and capital costs. Labor costs equal W × L, the wage W times the amount of labor L. Capital costs equal R × K, the rental price of capital R times the amount of capital
K. We can write:
Profit = Revenue − Labor Costs − Capital Costs

Profit =      PY      −         WL        −          RK

or

Profit = PF(K, L) −        WL       −           RK

 

The marginal product of labor (MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed:

MPL = F(K, L + 1) − F(K, L) = W/P

MPL

 

 

 

 

 

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:

MPK = F(K + 1, L) − F(K, L) = R/P

The income that remains after the firms have paid the factors of production is the economic profit of the owners of the firms. Real economic profit is:

Economic Profit =Y − (MPL × L) − (MPK × K)

Because we want to examine the distribution of national income, we rearrange the terms as follows:

Y = (MPL × L) + (MPK × K) + Economic Profit

MPL and demand for labour

DIMINISHING MARGINAL RETURNS

As a factor input is increased, its marginal product falls (other things equal). Intuition:
Suppose Labour increase while holding K fixed. We will have fewer machines per worker & lower worker productivity.

Therefore, diminishing returns to capital: MPK falls as K increases.

the equilibrium real wage

 

 

 

 

 

the equilibrium real rental rate

 

The Cobb–Douglas Production Function

The production function would need to have the property that:

Capital Income = MPK × K = aY

and

Labor Income = MPL × L = (1 – a) Y

where alpha is a constant between zero and one that measures capital’s share of income & A represents the level of technology.

Cobb-Douglas Production Function

 The Neoclassical Theory of Distribution:

➢ States that each factor input is paid its marginal product
➢ A good starting point for thinking about income distribution

 

 

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