•In order to produce output, the firm needs to employ inputs.

•A given level of output can be produced in many ways.

•A firm chooses the combination of inputs which is least expensive.

•Thus the cost function describes the least cost of producing each level of output given prices of factors of production and technology.

•Consider a production function *q *= *x*_{1}^{ a }*x*_{2} ^{b}, where a and b are constants.

•The firm produces *q *amount of output using *x*_{1} amount of factor 1 and *x*_{2} amount of factor 2.

•This is called a Cobb-Douglas production function.

•Let the production function be *q *= *x*_{1}^{ a }*x*_{2} ^{b}

•If we increase both the inputs *t *(*t > *1) times, we get the new output

•*q*_{2} = (t*x*_{1})^{ a }(t*x*_{2}) ^{b}

•*q*_{2} = t^{ a+b }(*q)*

•When a + b = 1, we have *q*_{2 }= *tq*. That is, the output increases *t *times. So the production function exhibits Constant returns to scale (CRS) CRS.

•Similarly, when a + b *> *1, the production function exhibits Increasing returns to scale (IRS).

•When a + b *< *1 the production function exhibits Decreasing returns to scale (DRS).

•In the short run, some of the factors of production cannot be varied, and remain fixed.

•The cost that a firm incurs to employ these fixed inputs is called the total fixed cost (TFC).

•To produce any required level of output, the firm can adjust only variable inputs.

•Accordingly, the cost that a firm incurs to employ these variable inputs is called the total variable cost (TVC).

•It is obtained by adding the fixed and the variable costs.

•The total cost (TC) of a firm *TC *= *TVC *+ *TFC*

•In order to increase the production of output, the firm must employ more of the variable inputs, which will also increase total cost.

•Therefore, as output increases, total variable cost and total cost increase.

•The short run average cost (SAC) incurred by the firm is defined as the total cost per unit of output.

•*SAC *= *TC/q*

•The average variable cost (AVC) is defined as the total variable cost per unit of output.

•*AVC *= *TVC/q*

•Average fixed cost (AFC)

•*AFC *= *TFC/q*

•*Thus SAC *= *AVC *+ *AFC*

•The short run marginal cost (SMC) is defined as the change in total cost per unit of change in output

= âˆ†*TC/* âˆ†*q*

where âˆ† represents the change in the value of the variable

•For any level of output, the sum of marginal costs up to that level gives us the total variable cost at that level.

•Average variable cost at some level of output is the average of all marginal costs up to that level.

Related Articles |

Recent Articles |