Economic question

Consider a market for an electronic component used in airport radar systems. Two firms hold a patent on the component and only they can sell the product. The market demand function is given by:

P = 100 – 1/2Q

Where Q = Q1+ Q2, is the industry output and P the price. Q1and Q2are the outputs of the two firms respectively.

The total cost functions for the two firms are given by:

(a) Assume that the two firms behave as Cournot Duopolists. Explaining the concept of “best response” or “reaction function”, determine the best response function for each firm. Calculate the profit maximizing output of each firm and the market price. Calculate optimal profit of each firm.

Assume that the two firms collude and form a cartel to maximize their joint profit. Calculate the optimal output and profit for each firm and the market price. Also, calculate the resulting profit of cartel. Determine whether firm 1 has any incentive to “cheat” the cartel by overproducing.

Suppose that firm 1 acts as a “Stackelberg” leader and sets its quantity first to maximize its own profit. Firm 2 acts as a follower and sets its own quantity in response to the output set by firm 1. Calculate optimal outputs price and profits

2.

A competitive firm’s short run total cost function is given by

Determine the range of prices for which the firm incurs a loss but continues to produce. Also determine the range of prices for which the firm earns a profit.

Calculate the profit maximizing output and the resulting profit when price is $100.

Propylene is used to make plastic. The propylene industry is perfectly competitive and each producer has a long run total cost function given by

Where Q denotes the output of the individual firm.

The market demand for propylene is

Where X and P denote the market output and price respectively.

(a) Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).

(b) Calculate the market price and market output at the LRCE.

(c) Calculate the number of firms at the LRCE.

(d) Suppose the demand curve shifts to

Where A is a positive number.

Calculate how large A would have to be so that in the new LRCE, the number of firms is twice what it was in the initial equilibrium.

Suppose that Saudi Arabia lets other members of OPEC sell all the oil they want at the existing price which the Saudis set and other members accept. The daily world demand for OPEC oil is given by:

P = 88 – 2Q

where P is the price per barrel of oil and Q the total quantity of OPEC oil (in millions of barrels per day). The supply function for other members of OPEC who behave like a “competitive fringe” is given by:

Qr= .6P

The Saudis’ cost of production of oil is given by:

TCs= 15Qs+20

where Qsis the daily output of oil produced by the Saudis.

Calculate the price that Saudi Arabia will set to maximize its own profit. Also calculate the optimal output and profit of the Saudis. Determine the output produced by other members of the OPEC as well as the total market output.

3.

A monopolist faces the following demand and total cost functions:

Calculate the profit maximizing output and price of the monopolist.

Calculate the resulting profit.

Suppose the government imposes an excise tax of $30 on the production

and sale of the product. Calculate the resulting optimal profit maximizing

output and price for the monopolist. Also determine the level of profit

If the government’s objective is to generate the maximum possible tax

revenue from the monopolist, what excise tax rate should the government

impose on the monopolist? Calculate the resulting optimal output, and

price of the monopolist as well as government’s tax revenue

ii

Two firms produce differentiated products and set prices to maximize

their individual profits. Demand functions for the firms are given by

,