Hi! I didn't see an economics section so I decided to post here because my question does have some simple calculus in it. It's more of an economics question though!
I'm having problems with my textbook question (for Labour Economics) and I've completed the majority of this question but I can't seem to find the Marginal Cost.
This question asks you to compare equilibrium wages and employment under monopsony and competitive labour market conditions. Suppose the product market is competitive with product price p = $100. Each firm has the production function f(L) = 1.2L – 0.01 L2. The industry labour supply function is W(L) = 2L. Derive the competitive equilibrium and the monopsony equilibrium, and show these equilibria in a diagram. Briefly explain the reasons for any differences in wages and employment in the two equilibria.
So for the competitive equilibrium, I figured that I would derive the production function to get 1.2 - 0.02L (which is the Marginal Revenue?) and multiply it by 100. Then I equated it with 2L and ended up with:
120 - 2L = 2L
L = 30 and W = 60
However, I can't really figure out the monopsony equilibrium. (I need to equate 1.2 - 0.02L with the Marginal Cost) I understand that in order to figure out the marginal cost, I need to obtain an expression for total cost as a function of labour input L and then differentiate with respect to L. This is where I'm stuck at!