7) The market demand curve for a homogeneous product is given by p=70-Q where Q is the total quantity demanded at a price p. Suppose that there are two firms in the market. Each firm has a constant marginal cost of 10, and there are no fixed costs. What price and firm output levels does the Bertrand model of competition predict? How much profit does each firm make in equilibrium?
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- Consider a market where the inverse demand function is P = 400 – 20Q, where Q is the aggregate output. Assume there are three firms which compete à la Bertrand. a)What is the equilibrium price and the corresponding aggregate output if all firms have a constant marginal cost equal to 40? b)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 100? c)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 260?You are the manager of the local movie theatre in a small town. Running a movie has a fixed cost of $2,000, but selling an extra ticket (i.e. accommodating an extra viewer) has zero marginal cost. Below are the demand schedules for your two types of customers: Price $ Adults Teens and Seniors 10 50 9 100 8 200 7 200 50 6 300 100 5 350 150 4 400 200 3 400 300 400 300 1 400 300 If you are to charge a single price (i.e., if price discrimination is prohibited), what price would you set for a ticket to maximize profit? How much profit do you make? Price = $ Profit = $ If you were allowed to price-discriminate, what price would you charge for an adult ticket? For senior/teen ticket? How much profit do you make? Price for adults = $ Price for seniors/teens= $ Profit = $There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?
- Consider the weekly market for gyros in a popular neighborhood close to campus. Suppose this market is operating in long-run competitive equilibrium with many gyro vendors in the neighborhood, each offering basically the same gyros. Due to the structure of the market, the vendors act as price takers and each individual vendor has no market power. The following graph displays the supply (S = MC) and demand (D) curves in the weekly market for gyros. Place the black point (plus symbol) on the graph to indicate the market price and quantity that will result from competition. PRICE (Dollars per gyro) 5.0 PRICE (Dollars per gyro) 4.5 4.0 3.5 1.0 0.5 5.0 4.5 4.0 0.5 0 0 10 20 0 10 30 Now assume that one of the gyro vendors successfully petitions the neighborhood development board to obtain exclusive rights to sell gyros in the neighborhood. This firm buys up all the rest of the gyro food trucks in the area and begins to operate as a monopoly. Assume that this change does not affect demand and…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.Question 3 Suppose a market demand function is given by QD(P) = 1,000 - 10P. The product can be produced with a cost function C(Q) = 10,000 + 20Q. (a) Determine Q and P and the firm's profit if there is a single firm. (b) Determine total output Q, the equilibrium price, and the profit of each firm if there are two firms (i.e., a Cournot oligopoly). (c) Determine Q. the equilibrium price, and the profit of each firm if there are 10 firms.
- Suppose there are many identical competitive firms with constant marginal cost MC = 7 and inverse market demand p = 100 q. Now one of the firms made an innovation and lowers its marginal cost to MCi = 5, what’s the largest profit this innovating firm make? What if the innovator lowers its marginal cost to MCi = 3?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,…Consider a competitive industry with a market demand curve of P = 121 – Q, where P is market price and Q is the quantity demanded in the market. In the short run there are 4 firms in the industry, and each firm has a total cost function of TC = 25 + 6q + q2, where q is output of the individual firm. In the long-run market equilibrium what is the number of firms in the industry? Group of answer choices 26 15 5 110 21
- In competitive markets, there are many small firms with each firm unable to influence the market price. Suppose company ABX operates in the wheat market. The company produces and markets wheats at a Price = $20 per container. The firm’s total costs are given as: TC = 50 +2Q + 3Q2 Find the Firm’s marginal cost? Show your steps, including graphs. Review additional resources? Hint: See the rules for differentiationA friend has just started up her own business. Her firm asks you how much to charge for her product to maximize profits. The demand schedule for it is given by the first two columns in the table below; its total costs are given in the third column. For each level of output, you can calculate total revenue, marginal revenue, average cost, and marginal cost. The profit-maximizing level of output can be found at the point where TR - TC is greatest, or where MR = MC, (or the last quantity where MR is still greater than MC.) What is the profit-maximizing level of output for her product? 40 How much will she earn in profits? 80 Price Quantity TC TR? MR? MC? $25.00 0 $130 $24.00 10 $275 $23.00 20 $435 $22.50 30 $610 $22.00 40 $800 $21.60 50 $1,005 $21.20 60 $1,2254. A vertically integrated automobile company has an upstream engine division and a downstream assembly division. The demand for the company's cars is given by Q = 20-P. Each car requires one engine. The downstream division's total cost of assembling cars is TCD(Q) = 4Q. The upstream division's total cost of producing engines is TCv (Q) = Q². (a) Suppose that there is no outside market for engines. What is the price and quantity of cars produced by the company? (b) Suppose that there is no outside market for engines. What should be the transfer price for engines? [Hint: the transfer price of an engine should equal the marginal cost of engine production at the optimal quantity.] (c) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the price and quantity of cars produced by the company? (d) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the quantity of engines that the company buys or…