Question

Joe owns a small coffee shop, and his production function is q = 3K^1/2L^1/2 where q is total output in cups per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). Joe's capital is currently fixed at K=64 machines, the price of K is $5 and the price of L is $2. What is the marginal cost?

a. MC=q/12

b. MC=2L+320

c. MC=q/6

d. MC=q/12+320

e. none of the above are correct

Answer 1

Answer

A)

12×L^-1/2
Q=3×K^0.5×L^0.5
K=64 (given)
So,

Q= 3×8×L^0.5

Q= 24×L^0.5
Marginal product of labor= partial derivative of Q with respect to L

MPL=( 24÷2) L^(0.5-1)

So MPL= 12 L^(-0.5)

Marginal product of labor refers to the change in output due to an additional unit of labor input or it is the change in output when an additional unit of labor is employed .

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