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- Question 3 The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has al cost of production of C₁= 15*Q₁ and firm 2 has a cost of production of C₂=20*Q₂. 1) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices? What are the profits of firm 1 and 2? 2) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices? What are the profits of firm 1 and 2? 3) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantity firm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What are the profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 0.5q; the demand function for the firms' output is Q = 1.5 - p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 0.5 (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…Two firms (called firm 1 and firm 2) are the only sellers of a good for which the demand equation is Here, q is the total quantity of the good demanded and p is the price of the good measured in dollars. Neither firm has any fixed costs, and each firm’s marginal cost of producing a unit of goods is $2. Imagine that each firm produces some quantity of goods, and that these goods are sold to consumers at the highest price at which all of the goods can be sold. A Cournot equilibrium in this environment is a pair of outputs (q1, q2) such that, when firm 1 produces q1 units of goods and firm 2 produces q2 units of goods, neither firm can raise its profits by unilaterally changing its output. Find the Cournot equilibrium. Determine whether the price at which the goods are sold exceeds marginal cost.
- Use the orange points (square symbol) to plot the initial short-run industry supply curve when there are 10 firms in the market. (Hint: You can disregard the portion of the supply curve that corresponds to prices where there is no output since this is the industry supply curve.) Next, use the purple points (diamond symbol) to plot the short-run industry supply curve when there are 15 firms. Finally, use the green points (triangle symbol) to plot the short-run industry supply curve when there are 20 firms. PRICE (Dollars per pound) 100 90 80 70 80 50 40 30 20 10 0 0 125 250 375 500 825 750 875 1000 1125 1250 QUANTITY (Thousands of pounds) Demand Because you know that competitive firms earn Supply (10 firms) True Supply (15 firms) If there were 10 firms in this market, the short-run equilibrium price of rhodium would be $ would . Therefore, in the long run, firms would False Supply (20 firms) per pound. From the graph, you can see that this means there will be ? per pound. At that price,…The tables (below) show the willingness to pay by three (competitive) consumers for additional units of some good, and the marginal costs of three (competitive) firms that produce that good. a) Compute the competitive equilibrium quantity and price for this market. Also, compute each consumer's surplus and each firm's profits. b) Now suppose that you have access to the same technology (and competitive input markets) as that of Firm 3. Entering the market (that is, launching a fourth firm) means a fixed (yes, sunk too) cost of $10. Would you decide to enter? (Entry has effects on the market, of course.) c) With the same data, suppose that all three firms merge. That is, now a single corporation controls (and decides on output for) all three firms (now, plants of one single firm). Obtain the output (or, equivalently, the price) that this monopolistic corporation will choose, and evaluate the consequences for the consumers (that is, the effect on the consumer surplus) and for the profits…Consider the Bertrand competition setup with 2 firms producing identical goods. The market demandis given by Q = 100 − P. T C1 = 30q1 and T C2 = 70q2. Derive the Bertrand equilibrium (prices andquantities of both firms) here.
- 3 In a Cournot market with two firms, the inverse market demand curve is P=50-2Q, where Q=q1+q2(Firm 1’s output is ; Firm 2’s output is ). Both firms have a constant marginal cost of 14. If Firm 2 produces 12 units of output, how much should Firm 1 produce? Group of answer choices 3 6 0 12Question 3 Suppose that the cost function of a firm is C(q)=4q. Suppose that this is the only firm in the market, and demand is Q(p)=10-p. What is the amount of the good produced in a competitive equilibrium in this economy? 7 4 6 3 5Using a graph, explain why a firm might not want to spend A on advertising, even though it shifts the firm's demand curve to the right. In the figure to the right, let D¹ and MR¹ be demand and marginal revenue before advertising. Assume the monopoly has a constant marginal cost with no fixed cost such that MR¹ = AC¹. Then, suppose the monopoly advertises and that the advertising shifts demand and marginal revenue to D² and MR². Assume advertising is a marginal cost, such that the new marginal cost after advertising is still a constant and still equals a new average cost. Using the line drawing tool, graph the marginal cost curve, reflecting the cost of the advertising, such that the monopoly breaks even from advertising. Label this curve 'MC².! Carefully follow the instructions above, and only draw the required objects. p, $ per unit 30- 28- 26- 24- 22- 20- 18- 16- 14- 12- 10- 8+ 6- 4- 2+ 0- 0 2 V MC = A ▬▬▬▬▬ AMR MR² D 4 6 8 10 12 14 16 18 20 22 24 26 28 Q, Quantity D²
- PROBLEM (5) In a dominant firm market with demand Q = 30 − p, the dominant firm has MC(Q) = 2Q (that is, with TC(Q) = Q^2) and the fringe is composed of 5 identical firms, each with MC(Q) = 10Q (that is, with TC(Q) = 5Q^2). (a) Calculate the market price in the dominant firm model. Calculate the quantity produced by the fringe. (b) Now assume that the 5 fringe firms form a “union”, and act as 5 “plants” of the union firm and this union firm competes as one single firm against the dominant firm in quantities, as in Cournot competition. What is the Cournot-Nash equilibrium price and quantity in this market organization? (c) Now, the dominant firm convinces the “union” not to compete with it but instead collude (to maximize the sum of profits) to form a cartel. What is the market price and quantity? (d) Back to the problem description. If all the firms (the dominant firm and the 5 fringe firms) acted as price takers, as in the perfect competition, what would be the market equilibrium…Question 2 [Suppose 'Car Today' is the only firm selling cars in a small, rural town. Assume that people in the town do not want to leave the town to buy cars. Also assume that there is a constant marginal cost for 'Car Today'.] a) [What type of market structure do you think 'Car Today' belongs to? Why? Explain in 100 words or less. Market structure identified correctly with logical and sound explanation. b) [Draw a graph for Car Today that shows the firm carrying out perfect price discrimination (first degree). Label the producer surplus, consumer surplus, and deadweight loss in the graph. No explanation required Properly labelled, correct graph. Producer & consumer surplus and dead weight loss correctly identified and labelled on graph. c) [Now suppose the city council hears of Car Today's practices and outlaws price discrimination (and assume they can successfully enforce it). Draw a new graph showing what Car Today will do to maximize profits. Label the producer surplus, consumer…2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; the demand function for the firms' output is Q = 1.5-p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 1 2. (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…