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ECN 104 Final: Econ Exam review.docx

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Ryerson University
Department
Economics
Course
ECN 104
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Questions 1-15: consider a cournot duopoly with two firms 1 and 2. Let q1 and q2 be quantity produced by firms 1,2 and let the inverse demand given by p = 20 q1 q2 where p = price of the good. Both firms have an identical constant unit cost 4. Assume each firm can produce only one of the following levels of quantity: 2, 3, 4, 5 or 6. Table 3: profit and best response of firm 1. Table 4: profit and best response of firm 2. Table 5: profits and best responses of both firms. Questions 16-30: consider a bertrand duopoly with two firms 1 and 2. Let p1 and p2 be price set by firms 1,2. The demand q is given by q = 21 p. Assume both firms have identical constant unit cost 3. Assume each firm can set only one of the following levels of price: 1, 3, 4, 5 or 6.

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Related Questions

Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q1 and q2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q1 and q2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reaction functions to find q1 and q2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.

Consider the following game. Firm 1, the leader, selects an output q1, after which firm 2, the follower, observes the choice of q1 and then selects its own output q2. The resulting price is one satisfying the industry demand curve P = 200 - q1 - q2. Both firms have zero fixed costs and a constant marginal cost of 10.

A. Derive the equation for the follower firm's best response function. Draw this equation on a graph with q2 on the vertical axis and q1 on the horizontal axis. Indicate the vertical intercept, horizontal intercept, and slope of the best response function.

B. Determine the equilibrium output of each firm in the leader-follower game. What are each firm's profits in the equilibrium?

C. Now let the two firms choose their outputs simultaneously. Compute the Cournot equilibrium outputs and industry price. Who loses and who gains when the firms play a Cournot game instead of the Stackelberg one?

Please show the steps with the correct answer for me to follow. Thanks for the help!

Pricing and Advertising

2. A monopoly sells in two countries, and resale between the countries is impossible. The demand curves in the two countries are P1=100-Q1 and P2=120-2Q2. The monopoly’s marginal cost is m=30. Solve for the equilibrium price in each country.

3. Suppose that the nonlinear price discriminating monopoly in panel a of figure 12.4 can set three prices, depending on the quantity a consumer purchases. The firm’s profit is

Î =P1Q1+P2(Q2-Q1)+P3(Q3-Q2)-mQ3

Where P1 is the high price charged on the first Q1 units (first block), p2 is a lower price charged on the next Q2-Q1 units, p3 is the lowest price charged on the Q3-Q2 remaining units, Q3 is the total number of units actually purchased, and m=$30 is the firm’s constant marginal and average cost. Use calculus to determine the profit maximizing p1,p2, and p3.

4. The demand a monopoly faces is p=100-Q+A^0.5

Where Q is its quantity, p is its price, and A is its level of advertising. Its marginal cost of production is 10, and its cost of a unit of advertising is 1. What is the firm’s profit equation? Solve for the firm’s profit maximizing price, quantity, and level of advertising.