its capacity constraint so that the collusive equilibrium can si 1? (Hint: The idea here is that, by limiting its own output, Firm 1 have a greater market share. As a result, Firm 1's gain of from the collusive agreement would be smaller.)
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- 4. )In a pure exchange economy with two goods, G and H, the two traders have Cobb- Douglas utility functions. Suppose that Tony's utility function is U, = G.H; and Margaret's utility function is Um= Gm(Hm)³. Between them, they own 100 units of G and 50 units of H. Solve for their contract curve. Continuing with question 4, determine p, the competitive price of G, where the price of H is normalized to equal one.Question 3 Assume we have a market with only two companies in it, Company X and Company Y. Now suppose that both companies have to choose one of two potential strategies for pricing their products: setting a low price or setting a high price. The table below shows the expected profits for each company under each pricing scenario. Assume both companies are in competition with each other and seek to maximize their profits. Under these conditions, how much profit should we expect both companies to earn? Company Y Provide your answer below: High Price Low Price High Price Profit for Company Y: $12, 975,000 Profit for Company X: $12, 975,000 Profit for Company Y: $16, 218,000 Profit for Company X: $1,946, 000 Company X Low Price Profit for Company Y: $1,946, 000 Profit for Company X: $16, 218,000 Profit for Company Y: $6,487,000 Profit for Company X: $6,487,000Two firms, Incumbent & Entrant, can produce the same good. The market demand for the good is given by P = 180 – Q, where P is the market price and Q is the market quantity demanded. The firms must pay w = 45 per unit of output for labour and r = 45 per unit of output for capital (one unit of capital is used per unit of output), but Incumbent may choose capacity KI units of capital before Entrant decides whether to enter the market. Suppose firms each have fixed costs FI =600, FE=500. Incumbent chooses (as a Stackelberg leader) capacity KI equal to the monopoly profit- maximizing quantity. When you answer the following questions, show your work. a. Would Incumbent be able to prevent entry by choosing capacity KI equal to the monopoly profit-maximizing quantity? Explain. b. What is the Incumbent’s equilibrium choice of capacity KI in this Dixit game? c. Does the Incumbent’s choice of capacity KI in part (b) qualify as predatory conduct (here, limit output)? Explain.
- 5. Suppose there is a Chinese firm that could produce a "widget" at a cost of 9qw, where qw is the number of widgets. It can then ship these widgets to a U.S. firm at a transport cost of $1 per unit and for a price of pw. The U.S. firm can then turn one widget into one car at a cost of $10. Cars are then sold on the world market, where inverse demand for cars is given by: P = 500-2Q. (a) If the Chinese firm is a perfect competitor, what is P = TU.S. = Q = qw= Pw= Chinese = (b) If the Chinese firm is a monopolist, what is P = = TU.S. Pw= qw= TChinese =E1 Find Bertrand equilibrium and its outputs for the following asymmetric duopoly:q 1(p1, p2) = 16 - p1 + 0.5 p2, C1(q1) = 4q1;q 2(p1, p2) = 16 + 0.5 p1 - p2, C2(q2) = 6q2.(Note that the average and marginal costs are: AC1=MC1 = c1 = 4, AC2=MC2 = c2 = 6)1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.
- = Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q₂ is the total market quantity, which consists of Q₁ (the quantity produced by Firm 1) and Q₂ (the quantity produced by Firm 2). The firms choose their quantities simultaneously. Firm 1's costs are C₁ = 10- 6Q₁ +Q². Firm 2's costs are C₂ = Q². Which is the best response function for Firm 2? O O O O Q₂ = 15. 1 Q₂ = 30 - ²0₁₁ 3 Q₂ = 42 + ²³² Q₁₁ 2 = 1. 3 Q₂ = 45. What is the equilibrium market quantity Q? O Q = 15.25. O Q = 30. Q = 46.5. O Q = 50. What is the equilibrium market price P? O P = 90. O P = 60. O P = 43.5. O P = 10.3. Consider a simple two-firm case. Suppose both firms produce the same good, but at different marginal costs (with one firm at a lower marginal cost than the other). In this type of situation, compare and contrast the market price, profit, and total output between Cournot and Stackelberg models. Separately consider when 0 the cost-efficient firm is the first-mover vs. when (i) the cost-inefficient firm is the first-mover in the Stackelberg model.Two firms, A and B, are contemplating exporting a local fruit called durian to another country that has strong demand for durian. If both firms export their durians, each firm can earn an export revenue of $25 million. If both firms do not export, each firm can earn a revenue of $12 million from their own domestic market. If one of them exports durians and the other does not export, the firm that exports durians can earn an export revenue of $50 million. But the non-exporting firm will earn a revenue of $18 million. (a)If both firms make a decision simultaneously, construct and analyse a payoff matrix and solve for the Nash equilibrium. Explain whether this is the prisoner’s dilemma game. (b) Suppose Firm A can make a decision before Firm B. Construct and analyse a decision tree model and determine the payoffs to both firms. Does timing matter in this game?
- 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.5. Given that excess demands are continuous and satisfy Walras' law, use Brouwer's Fixed Point Theorem to establish the existence of competitive equilibrium in a simple exchange economy. Suppose that an apple orchard is located next to a bee keeper. If the orchard produces x apples and the bee keeper produces y honey and the cost functions of the two are as follows: C(x) = x² + 10x +9 C(y) = y² - 8x What will be the socially optimal amount of apples that can be produced? How does this compare to privately optimal amount?(Figure: Payoff Matrix for the United States and Canada) Use Figure: Payoff Matrix for the United States and Canada. Suppose that the United States and Canada both produce quinoa, and each country can earn more profit it output is limited and the price of quinca is high. The dominant strategy for the United States is: Canada US Low output High output Low output EU profit $10 million US profit $10 million EU profit $4 million US profit $12 million High output EU profit $12 million US profit $4 million Olow output O The United States does not have a dominant strategy O adopt a fit for tal strategy O high output EU profit $7 million US profit $7 million