Consider a simplified version of the model of the public agency captured in eg. (11.2) suppose inverse demand for Q is given by D(Q)= 10-Q. Suppose the price of labor (w) is 1 and production of Q is in direct proportion to the amount of labor used: Q=L.
a. Write an expresion for the budget (consumer surplus) as a function of Q.
b. In a plot of Q versus P, plot the budget constraint and sketch indifference curves for the agency head.
c. On the same figure, sketch the objective function for profit maximizing monopolist.
d. How do the results differ in terms of choice of Q between the profit maximizing monopolist and the public agency?
e. For a given Q, how would the choice of l differ between a profit maximizing monopolists and the public agency?