Returning to the gumball producer in Problem 7.2, let’s look at the possibility that producing these delectable treats does not necessarily experience constant returns to scale.

 a. In Problem 7.2, we showed that the cost function for gumballs was given by TC =  where q is output of gumballs (in thousands), v is the rental rate for gumball presses, and w is the hourly wage. Explain why this cost function illustrates constant returns to scale.

b. Suppose instead that the gumball cost function is given by  Explain why this function illustrates increasing returns to scale. What does the graph of the total cost curve for this function look like? What do the implies average and marginal cost curves look like?

c. Suppose now that the gumball cost function is  Explain why this function exhibits decreasing returns to scale. Illustrate this by graphing the total, average, and marginal cost curves for this function.

d. More generally, suppose  Explain how any desired value for returns to scale can be incorporated into this function by changing the parameter s

Problem 7.2

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 þ w (where v is the hourly rent for gumball presses and w is the hourly wage).

b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be , where q is output of gumballs per hour, measured in thousands of gumballs.

c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)?

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.