Question

Suppose that a firm has only one variable input, labor, and firm output is zero when labor is zero. When the firm hires 6 workers it produces 90 units of output. Fixed cost of production are $6 and the variable cost per unit of labor is $10. The marginal product of the seventh unit of labor is 4. Given this information, what is the total cost of production when the firm hires 7 workers?

Answer 1

Answer:

Case 1:

When, Labor = 6 ;

Output = 90

Fixed Cost = $6

Variable cost per unit of labor = $10

∴ Total Variable Cost = $10 × 6 = $60

Total cost = Fixed Cost + Total Variable Cost

= $60 + $6

= $66

Case 2:

When, Labor = 7 ;

Let us assume the total output be 'x' , when firm hires 7 workers.

Marginal product( $MP_{L}$) of the seventh unit of labor = 4

i.e. $MP_{L}$= $\frac{\delta TP}{\delta Q}$ = 4

$\frac{\delta TP}{\delta Q}$ = 4

$\frac{(x- 90)}{(7-6)}$ = 4

x = 94

Fixed Cost will remain the same , i.e. $6

Variable cost per unit of labor = $10

∴ Total Variable Cost = $10 × 7 = $70

Total cost = Fixed Cost + Total Variable Cost

= $70 + $6

= $76