Answer to Question #288827 in Microeconomics for ALI

Question

Catalina Films produces video shorts using digital editing equipment (K) and editors (L).

The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage.

The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units

of output at the lowest possible cost.

a) Find the marginal product of each input.(4 marks)

b) Determine whether the production function exhibits diminishing marginal product to

each input.(4 marks)

c) Find the marginal rate of technical substitution(MRTSLK) (4 marks)

d) How does MRTSLK change as more L, is used holding output constant.(3 marks)

e) Find the least costly combination of labor and capital to produce 3000 units (5 marks).

Answer 1

a)

$MPL=(K\times L)'=K$

$MPK=(K\times L)'=L$

b)As the resources used increase, the production function becomes more and more flat, as the marginal product decreases.

c)$MRTSLK=\frac{MPL}{MPK}=\frac{K}{L}$

d)

When capital is replaced by labor, MRTSLK shows the amount of capital that can be replaced by one additional unit of labor while maintaining a constant output volume

e)25L+50K=3000

K=60, L=120