Have an exam coming up and was wondering if someone could provide the correct solutions for these problems as a study tool for me to have. Want to work through them and have the solutions handy to ensure that I'm doing them correctly. Thank you!
1.) Let a production function exist such that Q=(K^.33 L^.67)
Let the firm have a total of $5,000 to spend on labor and capital. Let price of labor equal $50 and the price of capital equals $150.(Keep K on the vertical axis and L on the horizontal).
a.) Write out the total cost (isocost) equation, and find the intercepts.
b.) Find the optimal usage of K and L and the optimal output of Q.
c.) Graph the results from part b using the isoquant and isocost (budget) line. (You do not have to calculate the isoquant).
2.) Let total expenditures equal $5,100 in period 2 and $5,200 in period 3.
a.) Calculate the new optimal values of Q, and the new isoquants and plot the LR Expansion path.
b.) Keep K at 25, letting L vary, and plot the SR Expansion Path and the TPL curve.
3.) Let a production function exist such that Q= (K^.35 L^.60).
a.) Does this production function exhibit Increasing, Decreasing or Constant returns to scale? Explain how you know.
b.) What is the effect on Q of a 10% increase in labor hours, keeping K constant?
c.) What is the effect on Q of a 10% increase in capital usage, keeping L constant?
4.) The most efficient production occurs where MC=AC(where AC is minimum). Therefore, a firm with many plants will make sure to have each of them produce at their minimum AC. True, False, explain.
5.) Monopolies are thought of as bad. One reason is that they produce less of an item at a higher price than would be produced under perfect competition.
Let market supply for a product be P= $20 + .50Qs
Let market demand for the product be P= $170 -.75 Qd
a.) Using the D and S equations from above, show the validity of the above statement by finding the output level and price for both a perfectly competitive industry and a monopoly. Carefully explain how you know this. (You should put both points on the same graph, but do it carefully.)
b.) Monopolies can charge whatever they want. True, false, carefully explain.