Price Discrimination

Suppose Rialto is the only movie cinema in a small college town, so it is essentially a monopoly for the local movie market. They charge a certain price P for a monthly pass. There is an overall demand curve for movie passes, given by

P=9004Q

However, demand in the town has two distinct consumer groups: adults (A) and students (S). The demand for the whole group of adults is given by

P=12008QA

and the inverse demand for students is given by

P=4002QS

Assume for simplicity that the constant marginal costMC(Q)of showing a movie is 20 and there are no additional fixed costs.

(a)Suppose everybody can easily get a fake student ID and there is no way for UMovie to differentiate one group of consumers from another. As a result, the cinema is forced to charge a single price for both groups. Depict this in a figure.

(b)Compute the optimal quantity and price charged by UMovie, as well as total costs and profits. Under this price, who will go to movies?Remember the firm's production rule. Show these values in the figure.

(c)Suppose UMovie has spent $M > 0 to install a machine that can detect very accurately whether a student ID is fake. As a result, the cinema is able to charge each group a different price. Compute the optimal prices for the two groups of consumers.

(d)Depict the demand curve of each group of consumers in a diagram (the same or two different).

(e)Calculate the profit-maximizing quantities and prices for students and adults.

(f)Calculate total costs, revenues, and profits resulting from these values.

(g)Show this in your figures graphically, as well

(h)Compare total profits in (b) with (f). Which is greater. Under what circumstances would the ID machine be worth it (that is, for what values of $M)?