What is the average and marginal cost of gumball production ?Write the equation for the firm’s short-run supply curve and indicate it in the above graph.

A firm uses capital and labor to produce output according to the production function q = 4√KL, for which MPL = 2√K/L and MPK = 2√L/K.
a. If the wage w = $1/labor-hr. and the rental rate of capital r = $4/machine-hr., what is the least expensive way to produce 16 units of output?
b. What is the minimum cost of producing 16 units?
c. Show that for any level of output q, the minimum cost of producing q is $q.
d. Explain how a 10% wage tax would affect the way in which the firm choose to produce any given amount of output.
5. Suppose that the Acme Gumball Company has a fixed proportions production function that requires
it to use two gumball presses and one worker to produce 1000 gumballs per hour.
a. Explain why the cost per hour of producing 1000 gumballs is 2v + w .
b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v + w), where q is output of gumballs per hour, measured in thousands of gumballs.
c. What is the average and marginal cost of gumball production ?
d. Graph the average and marginal cost curves for gumballs assuming v = 3, w = 5.
e. Now graph these curves for v = 6, w = 5. Explain why these curves have shifted.
6. For each of the following total cost curves, determine if the technology exhibits increasing, decreasing, or constant returns to scale.
a. TC(q) = q2
b. TC(q) = √q
c. TC(q) = 2q
d. TC(q) = 2q + 4
7. A competitive firm has a short-run total cost curve STC(q) = 0.1q2 + 10q + 40.
a. Identify SVC and SFC.
b. Find and plot the SAC and SAVC curves.
c. For this function, the SMC curve is given by SMC(q) = 0.2q + 10. Include this curve in your diagram for part b.
d. Write the equation for the firm’s short-run supply curve and indicate it in the above graph.
e. Find the firm’s break-even price pe and its shut-down price ps