Question

Nadine sells user-friendly software. Her firm’s production function is         f(x1, x2) = x1 + 2x2, where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs

a) If Nadine faces factor prices (1, 1), what is the cheapest way for her to produce 20 units of output? 

b) If Nadine faces factor prices (1, 3), what is the cheapest way for her to produce 20 units of output?

c) If Nadine uses only unskilled labor, how much unskilled labor would she need in order to produce y units of output? 

d) If Nadine uses only skilled labor to produce output, how much skilled labor would she need in order to produce y units of output?

Answer 1

a and b) To find which one of the inputs she must use in order to minimize the cost we need to find the marginal product.

If marginal product of x1 < marginal product of x2: she must use only x2 

If marginal product of x2 < marginal product of x1 she must use only x1

 

c and d) output = y: f(x1,x2) = y

 

The complete solution is down below: 

 

a) x2 = 2 and x1 = 0

 

b) x1 = 20 and x2 = 0

 

c) x1 = y

 

d) x2 = y/2