# Microeconomic theory part 2

1. Mar 5, 2008

### MM79992

1. The problem statement, all variables and given/known data
A firm produces a single output (q) using Labor (L), and Capital (K). Its technology is described by the cobb-douglas production function Q= 10K and L is in a square root.
a. Does this technology exhibit increasing,decreasing, or constant returns to scale? Does it exhibit a diminishing marginal productivity of labor?
b. What can you say about the shape of this firm's short-run marginal cost curve? Is it positively sloped, negatively sloped, flat or u-shaped? What can you say about the shape of the long-run averagce cost curve?

2. Relevant equations
A relative equation is the Cobb-Douglas is relevant. Q= AK^B(beta) times L^a(alpha)

3. The attempt at a solution
What I did since L is in a square root, I raised L(labor) to the 1/2. I then concluded 1/2 was alpha, and if alpha is less that 1 then its MPL was decreasing. But if alpha = 1 then its a constant, and if its greater than 1, than its increasing. But I cant figure how the graphs would look or if I calculated it right. If someone can help I would appreciate it, thanks.