Take a situation with 100 of the same persons where each them have the following demand qd = 10 p. Production of the good is done by a single firm at a marginal cost of $1.

a) Show that, given p, an expression for the consumer surplus (CS) of a particular consumer is given by (10020p+p^2)/2 . Illustrate with a graph.

b) Similarly, show that the profit () of the firm is given by 100(11pp 210).

c) Assume that the utility a specific consumer obtains from participation in this market is given by the sum of CS and their share of the firm profit (The ownership share is noted ). Write down an expression that represents the consumers utility as a function of p.

d) Assuming equal ownership of the firm and hence an equal claim to the firm profit, point out (on the same graph) what area corresponds to a typical consumers utility, for some p. What is the price level that maximizes the utility of any consumer? Explain.

e) Suppose, instead, that the firm ownership is concentrated in the hands of two individuals. That is = 1/2 for two individuals and = 0 for all of the 98 others. What value of p would the two owners like to set now?

f) Compare the effect of unequal ownership, comparing your answers to d) and e), focusing on the following elements: markup, market efficiency (deadweight loss) and inequality.