Theory of production

Production Function

Opportunity cost is of two types

1. Explicit -incurred due to factors of production, requires outlay of money
2. Implicit - Does not require outlay of money

An important implicit cost is the cost of capital

Accounting profit = Revenue - explicit cost

Economic profit = Revenue - (Explicit + Implicit cost)

Accounting profit > Economic profit

Sunk costs are costs that have already been incurred and which cannot be recovered to any significant degree

Production function is the correspondence between input and output

The common Cobb-Douglas function used in macroeconomic modeling is

Y = K^αL^{1 − α}

where K is capital and L is labor. When the model coefficients sum to one, as in this example, the production function is first-order homogeneous, which implies constant returns to scale, that is, if all inputs are doubled that output will double.

There is a substitutability between the factors of production. The firm can either use capital-intensive or labor-intensive process.

The relationship between output change and proportionate chnages in both inputs is referred to as returns to scale. This is a long-term phenomenon.

Remember in long run all imputs are variable

In contrast to the concept of returns to scale, when output changes because one input changes while the other remains constant, the changes in the output rates are referred to as returns to a factor.

Remember in short run at least 1 input is fixed.

The production function defines the maximum rate of output per unit time obtained from a given rate of labor and capital input

Total product of labor - is the maximum rate of output forthcoming from combining varying rates of labor input with a fixed capital input

Marginal product of labor - increase in output arising from an additional unit of the variable input, holding all other inputs constant. It is the slope of the total product curve.

Average product of labor - is the total product per unit of the variable input = TPL/L

Inflection point - At this point total product function changes from increasing at an increasing rate to increasing at a decreasing rate.

Remember this

MPL=APL When APL is maximum

MPL>APL when APL is rising

MPL < size="1">L, when APL is falling

Marginal revenue product is defined as marginal revenue times marginal product and represents the value of the extra unit of labor

MRP = MR*MP

Labor will be hired until MRP = W,

We know for a price-taker market MR = P(given)( You can derive this using calculus)

So, P*MP = W (This P*MP is also called value of MP of labor and is denoted by VMPL)

So, MP = W/P

Which stage should a profit-maximizing firm going to operate?

For a production process to be economically feasible profit >=0

i.e; TR>=TC,

PXQ >= wL(w = wage, L =labor)

Q/L >= w/P

APL >= MPL(This is the necessary condition)

The sufficient condition is MPL>=0