Using symbols, we can write that the marginal product of labor is equal to Q/L. Marginal cost

Question:

Using symbols, we can write that the marginal product of labor is equal to ΔQ/ΔL. Marginal cost is equal to ΔC/ΔQ. Because fixed costs by definition don't change, marginal cost is also equal to ΔC/ΔQ. If Jill Johnson's only variable cost (ΔC) is labor cost, then her variable cost equals the wage multiplied by the quantity of workers hired, or wL.

a. If the wage Jill pays is constant, then what is ΔC in terms of w and L?

b. Use your answer to part (a) and the expressions given for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, ΔC/ΔQ, in terms of the wage, w, and the marginal product of labor, ΔQ/ΔL.

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?