2. Suppose that a firm is producing in the short run with output given by:

Q = 200.5L – 2.5L²,

The firm hires labor at a wage of $25 per hour and sells the good in a competitive market at P = $50 per unit. Find the firm’s optimal use of labor and associated level of output. (For extra practice, what is the firm’s associated profit?)

I have already finished and went to check my work on Chegg and got different results. I want to get another opinion, thanks.

3. [Returns to Scale] Determine whether the following production functions are characterized by increasing decreasing or constant returns to scale:
   2. Q = 2 K^.4 L^.6

3. Q = 9 K^.45 L^.75

4. Q = 20 +4K + 2L

4. [Long-Run Production] A firm produces according to the production function:

Q = K^.6L^.4.

where Q denotes units of output, K units of capital, and L units of labor.

2. The price of capital is $15 per unit, and the price of labor is $10 per unit. What is the optimal capital/labor ratio?
4. What happens to the capital/labor ratio if the price of labor increases to $20 per unit?