Question 1:

In a market, demand for a consumer product is Qd = 70 - P. In this industry, firms' total cost is TC(q) = 300 + 10q.

One firm, GoSolo, is the sole monopolist in this market. The firm cannot prevent rehsales and charges one price to all buyers.

a) Find the monopolist's profit maximizing quantity and price.
b) Find the consumer surplus and the monopolist's profit in this market.

A second firm, HereICome, enters the market and sells an identical product. After the second firm enters the market, both GoSolo and HereICome must charge a price of Pd = 70 - (qG + qH) where qG is the quantity sold by GoSolo and qH is the quantity sold by HereICome.-

c) For each firm, write the profit function in terms of the quantities qG and qH and compute the best response function.
d) Find the Cournot equilibrium quantities qG* and qR* and the market quantity and market price at the Cournot equilibrium.
e) Does the entry of the second firm increase consumer surplus? Does it increase the sum of consumer surplus and profit?

Question 2:

In a small town, two restaurants, Xavier's and Yvonne's, compete for customers. The two restaurants sell different food and at Xavier's, demand depends on the prices charged by both restaurant according to Qx = 44 - 2Px +Py, while at Yvonne's, demand depends on the prices charged by the two restaurants according to Qy = 44 - 2Py +Px.

The two restaurants have the same total cost of TC(q) = $8q (at both restaurants the marginal cost of serving one more customer is $8). The restaurants compete a la Bertrand (by choosing prices).

a) For each restaurant, write profit as a function of Px and Py.
b) Find the best response functions of the two restaurants.
c) Find the Bertrand equilibrium prices and the total quantity produced in the market when in equilibrium.