An eyeglasses manufacturer can produce eyeglasses according to the following production function: q = SQRT(K L) <--------q = square root of (K L) where K is the number of tiny screwdrivers and tiny screws the firm owns, and L is the number of workers the firm employs. In the short run, the company cannot buy any more tiny screwdrivers or tiny screws (in other words, the capital stock is fixed). 1. What is the short run marginal cost function for the firm if K is fixed at 100, and workers are paid a wage of $w each? [Hint: Figure out how many workers the firm has to hire to make q eyeglasses when it owns 100 tiny screwdrivers and tiny screws. Then use that function to write the total cost function] 2. Now consider the long run. The firm can now buy as many tiny screwdrivers and tiny screws as it wants, at a price of $r each. Solve for the tangency condition that determines the amount of K and L the firm will buy to produce a given amount of eyeglasses at minimum cost. [You should get an equation in terms of K,L,w and r.] Also, explain this condition in words.

Question

An eyeglasses manufacturer can produce eyeglasses according to the following production function:

q = SQRT(K L) <--------q = square root of (K L)

where K is the number of tiny screwdrivers and tiny screws the firm owns, and L is the number of workers the firm employs.

In the short run, the company cannot buy any more tiny screwdrivers or tiny screws (in other words, the capital stock is fixed).

1. What is the short run marginal cost function for the firm if K is fixed at 100, and workers are paid a wage of $w each?

[Hint: Figure out how many workers the firm has to hire to make q eyeglasses when it owns 100 tiny screwdrivers and tiny screws. Then use that function to write the total cost function]

2. Now consider the long run. The firm can now buy as many tiny screwdrivers and tiny screws as it wants, at a price of $r each. Solve for the tangency condition that determines the amount of K and L the firm will buy to produce a given amount of eyeglasses at minimum cost. [You should get an equation in terms of K,L,w and r.] Also, explain this condition in words.