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[Short-Run Production] Suppose that a firm is producing in the short run with output given by:...

  1. [Short-Run Production] 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.

  1. [Returns to Scale] Determine whether the following production functions are characterized by increasing decreasing or constant returns to scale:
    1. Q = 2 K.4 L.6
  1. Q = 9 K.45 L.75
  1. Q = 20 +4K + 2L

  1. [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.

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