(This problem is somewhat advanced.) Using symbols, we can write that the margin

Question

(This problem is somewhat advanced.) Using symbols, we can write that the marginal product of labor is equal to Q/L. Marginal cost is equal to TC/Q. Because fixed costs by definition don’t change, marginal cost is also equal to VC/Q. If Jill Johnsons’s only variable cost (VC) is labor cost, then her variable cost is just the wage multiplied by the quantity of workers hired, or wL. a. If the wage Jill pays is constant, then what is VC in terms of w and L? b. Use your answer to question a and the expressions given above for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, TC/Q, in terms of the wage, w, and the marginal product of labor, Q/L.

a. If the wage Jill pays is constant, then what is VC in terms of w and L? b. Use your answer to question a and the expressions given above for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, TC/Q, in terms of the wage, w, and the marginal product of labor, Q/L

b. Use your answer to question a and the expressions given above for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, TC/Q, in terms of the wage, w, and the marginal product of labor, Q/L.

c. Use your answer to part (b) to determine Jill’s marginal cost of producing pizzas if the wage is $750 per week and the marginal product of labor is 150 pizzas. If the wage falls to $600 per week and the marginal product of labor is unchanged, what happens to Jill’s marginal cost? If the wage is unchanged at $750 per week and the marginal product of labor rises to 250 pizzas, what happens to Jill’s marginal cost?

Explanation / Answer

(a) VC = w*L

It is provided that wage Jill pays is constant. So, wage bill of Jill changes only when it changes number of workers hired.

Since, VC = w*L, and w is constant, any change in VC is due to change in L.

So,

VC = w * L

Thus, VC in terms of w and L is

VC = w * L

(b) VC = w * L [From part (a)]

MPL = Q/L

Or,

Q = MPL * L

MC = VC/Q          ---equation (i)

Putting value of VC and Q in equation (i) –

MC = (w * L)/(MPL * L)

MC = w/MPL

So, expression for marginal cost in terms of wage and the marginal product of labor is as follows –

MC = w/MPL

(c) MC = w/MPL               [From part (b)]

(i) w = $750 per week

MPL = 150 pizzas

MC = w/MPL = $750/150 = $5 per pizza

Thus, Jill’s marginal cost of producing pizzas if the wage is $750 per week and the marginal product of labor is 150 pizzas is $5 per pizza.

(ii) w = $600 per week

MPL = 150 pizzas

MC = w/MPL = $600/150 = $4 per pizza

If the wage falls to $600 per week and the marginal product of labor is unchanged then Jill's marginal cost falls from $5 per pizza to $4 per pizza.

(iii) w = $750 per week

MPL = 250 pizzas

MC = w/MPL = $750/250 = $3 per pizza

If the wage is unchanged at $750 per week and the marginal product of labor rises to 250 pizzas then Jill's marginal cost falls from $5 per pizza to $3 per pizza.

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