1) Let a production function exist such that Q = (Kâ€¢251;75).
Let the firm have a total of $1,000 to spend on labor and capital. Let price of labor equal $5 and the price of capital equals $10.

a) Write out the total cost (isocost) equation.
b) Find the optimal usage of K and L and the optimal output of Q. (Keep K on the vertical axis and L on the horizontal).
c) Calculate and plot the isoquant for the optimal Q found in b) given the values for K in the table below. Plot with the isocost. Show the optimal levels of K, and L that go with that optimal level of Q.

K L Q'
20
30
40
50
60
70
80

Let total expenditures equal $1,100 in period 2 and $1,200 in period 3.
d) Calculate the new optimal values of Q, and the new isoquants and plot the LR Expansion Path.
e) Using data from d), keep K at 25, letting L vary, and plot the SR Expansion Path and the TPL curve.

2) Let a production function exist such that Q = (K-25J;75).
a) Does this production function exhibit Increasing, Decreasing or Constant Returns to Scale? Explain what your answer means and how you know. (Each may be answered by one or two sentences at most).
b) Estimate the effect on Q of a 10% increase in Labor hours, keeping K constant.
c) Estimate the effect on Q of a 10% increase in capital usage, keeping L constant.

3) The Halogen Company is a member of the lamp industry. The price of a lamp is $200.
Fixed costs run $1,000
The firm's total cost function is
TC = $1,000 + 20Q + 5Q2
where TC is total cost (in dollars) and Q is hourly output.

a) Is this firm a perfectly competitive firm or not? How can you tell? Explain in detail.
b) What output maximizes profit? Graph results.
c) What is the $ value of the firm's profit at this output level?
d) What is the firm's average cost at this output?
e) Will/should this firm shut down? Why or why not?

1) Let a production function exist such that Q = (Kâ€¢251;75). Let...