Returning to the gumball producer in Problem, let us look at the possibility that producing these delectable treats does not necessarily experience constant returns to scale.
a. In Problem, we showed that the cost function for gumballs was given by TC = q (2v + w), 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 TC = (2v + w) √q. 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 TC = (2v + w)q2. 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 TC = (2v + w)qs. Explain how any desired value for returns to scale can be incorporated into this function by changing the parameter s.