A profit seeking monopolist has three choice variables: output level q, marketing intensity m, and newequipment e.
The cost of producing q units of output is cqe, where c > 0 is a constant. Equipment is purchased in a competitive market at the price r. The cost of marketing intensity level m is h(m, θ), where θ is parameter and h is increasing in both of its arguments. The maximum price at which q units of outputcan be sold with marketing intensity m is P(q, m), where Pq 0. (Subscripts denote partialderivatives.)
a. Assume here and below that hmθ > 0. Interpret this condition and give a possible economic interpretationfor the parameter θ.
b. Under what condition on P does higher marketing intensity increase marginal revenue? From now on, assume that this condition holds.
c. Suppose that in the short run, the amount of new equipment, e > 0 is fixed. How do the firm's short run choices of output level and marketing vary depending on the parameter θ? depending on e? Be asspecific as possible and interpret your conclusions.
d. In the long run, the firm is free to choose any nonnegative levels of q, m and e. How does the firm'slong run choice of e vary depending on θ? Interpret your conclusion.
e. Compare the short and long run responses of q to a change in θ. Interpret the comparison.
f. Show how the firm's long run profit changes in response to changes in r. Does the answer depend on θ?If so, in what way. Interpret the results. This answer requires very little computation (why?).