Question

A firm manufactures at home, and faces input prices for labor and capital produces q units of output using L units of labor and K units of capital. Abroad, the wage and cost of capital are half as much as at home. If the firm manufactures abroad, will it change the amount of labor and capital it uses to produce q? What happens to its cost of producing quantity q? The manager would also like you to explain the Cobb Douglas Production Function and how she would be able to use it to determine that production is efficient.

Answer 1

Cobb Douglas production function:

Y = ALK

Where A is the technology parameter and alpha and beta are output elasticity.

Production will be efficient when the Marginal rate technical Substitution(MRTS) between L and K equals price ratio of L and K

MRTS = Marginal Product of Labor/Marginal Product of Capital

Marginal Product of Labor = dY/dL = AL^-1K

Marginal Product of Capital = dY/dK = ALK^-1

MRTS = K/ L

Let the price of Labor =w and price of capital = r

Thus for production to be efficient

K/ L = w/r

If the w and r are halved, the condition for production function to be efficient still holds as,

K/ L = w/2/r/2

K/ L = w/r

Thus the ratio of L and K will remain same. With the reduction in w and r the firm will employ more L and K but in the same ratio as before.

If the firm produces the same output as before, the cost of production will also be halved.