Suppose that demand for cruise ship vacations is given by P =1200 − 5Q, where Q is the total number of passengers when the market price is P. a) The market initially consists of only three sellers, Alpha Travel, Beta Worldwide, and Chi Cruiseline. Each seller has the same marginal cost of $300 per passenger. Find the symmetric Cournot equilibrium price and output for each seller
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Suppose that
Q is the total number of passengers when the market price is P.
a) The market initially consists of only three sellers, Alpha Travel, Beta Worldwide, and Chi
Cruiseline. Each seller has the same marginal cost of $300 per passenger. Find the symmetric
Cournot
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- Consider a market structure comprising two identical firms (A and B), each with the cost function given by: Ci = 30Qi , where Qi for i = {A, B} is output produced by each firm. Market demand is given by: P = 210 − 1.5Q, where Q = QA + QB (i) Find Cournot equilibrium. (ii) What will be the outcome if the firms decide to collude? Compare it with the results under the Cournot equilibrium.Suppose two brothers own identical skydiving companies but have decided to experiment with different pricing structures. The older brother’s company, Air Adventures, charges everyone the same price, while the younger brother’s company, Sky Warriors, sets its prices using a twotiered, price-discrimination model. Assuming that both companies face the same market demand curves, marginal costs, and costs of production, and wield significant market power for their service area, which of the following is most likely to occur? a. Air Adventures will generate a similar net revenue to Sky Warriors. b. Sky Warriors will generate a higher net revenue than Air Adventures. c. Sky Warriors will generate a lower net revenue than Air Adventures. d. Air Adventures will generate a higher net revenue than Sky Warriors. e. Sky Warriors will eventually switch to the Air Adventures model.Suppose that there are two firms in the market. The market demand is given by P=220 - 2Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=8Qi, i=1, 2. Consider the collusion, in which they decide the output level together to maximize the joint profit. If they divide the production into half, then each firm should produce Qi= _______ units in order to maximize the joint profit.
- Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants. Consumers of type B will pay $75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. If the firm can identify each consumer type and can price discriminate, what is the optimal price for a pair of pants? Multiple Choice Charge type A consumers $50 and type B consumers $75. Charge both types $150. Charge both types $75. Charge type A consumers $50 and type B consumers $50.Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.
- Consider Cournot competition with n identical firms. Suppose that the inverse demand function is linear with P(X) = a - bX, where X is total industry output, a; b > 0. Each firm has a linear cost function of the form C(x) = cx, where x stands for per firm output. It is assumed that a > c. a. At the symmetric equilibrium, what are the industry output and price levels? What are the equilibrium per firm output and profit levels? What is the equilibrium social welfare (defined as the difference between the area under the demand function and total cost)? b. Now let m out of n firms merge. Show that the merger is profitable for the m merged firms if and only if it involves a pre-merger market share of 80 percent. c. Show that each of the (n – m) non merged firms is better off after the merger. d. Show that the m-firm merger increases industry price and also lowers consumer welfare.suppose there are two firms that compete in prices, say firms 1 and 2, but that the firms produce differentiated products. Suppose that the demand for firm 1 is q1(p1,p2)=10-2p1+p2 and the demand for firm 2 is q2(p2,p1)=10-2p2+p1. Also, assume that firm 1 has a constant marginal cost of c1 = 2 and firm 2 has a constant marginal cost of c2 = 3. i. Solve for the Bertrand equilibrium in prices. ii. Now, suppose firms 1 and 2 merge and firm 1 will operate both firms and they will split the resulting profits equally. Will both firms agree to this merger or do they prefer the Bertrand outcome?Suppose the inverse market demand for manufactures is P(Q) = A – Q, where P and Q denote price and total goods produced and the parameter A denotes the size of the domestic market. Suppose any firm has a cost function, c(q) = cq, where A > c. Suppose there are two firm in the market which produce q1 and q2, where Q = q1 + q 2 a. Solve for the Cournot equilibrium levels of output (Q*), price (P*) and markups. b. What is the impact of an increase in market size, A, on Q*, P* and markups when there are two firms? Provide some intuition for these predictions. c.…
- Assume the inverse demand function in a market is given by P ( Q ) = 500 − Q where Q is the total industry output, that is the sum of the output of all firms in the market. There are two firms (indexed by i = 1,2) who both have a cost of producing the good given by c ( q i ) = 10 ∗ q i The two firms are competing in the Cournot manner, that is they choose their quantities simultaneously in order to maximize profits. What is the best response of firm 1 if firm 2 chooses an output level of 200? (input a whole number:) The best response function of firm 1 with respect to firm 2's quantity choice takes the form: q 1 ( q 2 ) = w ∗ ( x − y ∗ q 2 − z ) where (w,x,y,z) are parameters of the problem. Solve for this best response function and provide the product (w*x*y*z) in the next blank: What is the Nash Equilibrium quantity produced by firm 1? (round to the nearest whole number)Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model we imagine that the two firms simultaneously choose their production or quantity, and that demand (market clearing) determines the price given each firms’ quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts like a monopolist and sets output where MR = MC)? Hint: The first…Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model, we imagine that the two firms simultaneously choose their production or quantity and that demand (market clearing) determines the price given each firms’ quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts as a monopolist and sets output where MR = MC)? Hint: The first…