1. Suppose that inverse demand is given by P = 100 − 1/2 Q and each firm’s marginal cost is 10. Assume fixed costs are 0. (a) Solve for equilibrium price and quantity assuming this is a monopoly market. (i.e. Sup- posing there is only one firm, with no threat of entry, find the choice of quantity that maximizes profit, and then compute the corresponding market price.) (b) At this price and quantity, what is the monopolist’s profit? (c) What is consumer surplus?
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1. Suppose that inverse demand is given by P = 100 − 1/2 Q and each firm’s marginal cost is 10. Assume fixed costs are 0.
(a) Solve for
posing there is only one firm, with no threat of entry, find the choice of quantity that
maximizes profit, and then compute the corresponding market price.)
(b) At this price and quantity, what is the monopolist’s profit?
(c) What is consumer surplus?
(d) What would be the
(e) How much is
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- Assume that a firm accepts the following price_demand relationship as being a realistic representation of its market: d=800-10p where p must be between $20 and$70 a. How many units can the firm sell at the $20 per-unit price? At the $70 per-unit price? b. By how many units does a $1 increase decrease demand? c. Which pricing alternative the business is considering maximizes revenue? Group of answer choices $40 $30 $502. Consider a market with 90 firms, each firm has a short-run total cost function as follows: TC(q) = 5q2, and a marginal cost function: MC(q) = 10q. Market demand is given by equation Qd(p) = 200 - p. a. Solve for the short-run equilibrium outcome: P*, Q* and q*. b. What is one firm's economic profit in this market? c. Consider a different market structure, where there is only one firm, interpreted as a monopolist, and then critically discuss the impact on equilibrium price and quantity. Discuss total surplus for these two types of market structures.1) Suppose that market demand is linear, q = 70 - p. Marginal costs are constant and equal to 10. The upstream firm, which is a manufacturer, does not sell directly but through a single downstream firm, which is a retailer. The manufacturer set the wholesale price w at stage 1. At stage 2, the retailer who is assumed not to incur any costs except wholesale price (w), observes the wholesale price and sets the retail price p. Find the optimal wholesale price (w*): Find the optimal retail price (p∗): Find the quantity demanded (q∗) that corresponds to p∗: Find the manufacturer’s profit (π*M) that corresponds to p∗: Find the retailer’s profit (π∗R) that corresponds to p∗: Find the overall channel profit (Π∗ = π*M+ π*R): Next, consider a case that the integrated firm produce the product and sell directly to consumers. Suppose the market demand is q = 70 - p. Marginal costs are constant and equal to 10. Find the optimal retail price (pi): Find the quantity demanded (qi)…
- 1. Suppose that inverse demand is given by P = 100 − 1/2 Q and each firm’s marginal cost is 10. Assume fixed costs are 0. (d) What would be the perfectly competitive price, quantity, and consumer surplus?(e) How much is deadweight loss due to monopoly?Suppose that fixed costs for a firm in the automobile industry (start-up costs of facto-ries, capital equipment, and so on) are $5 billion and that variable costs are equal to$17,000 per finished automobile. Because more firms increase competition in themarket, the market price falls as more firms enter an automobile market, or specifi-cally, P = 17,000 + (150/n), where n represents the number of firms in a market.Assume that the initial size of the U.S, and the European automobile markets are 300million and 533 million people, respectively.a. Calculate the equilibrium number of firms in the U.S. and European automobilemarkets without trade.b. What is the equilibrium price of automobiles in the United States and Europe if theautomobile industry is closed to foreign trade?c. Now suppose that the United States decides on free trade in automobiles withEurope. The trade agreement with the Europeans adds 533 million consumers tothe automobile market, in addition to the 300 million in the…Assume that annual inverse demand for a particular product is P=150-Q. The product is offered by a pair of Bertrand competitors, each with marginal costs of $75. The discount factor is 0.9. What is the current equilibrium price and total surplus? Now, assume though that if R&D is conducted at rate x, it incurs one-off costs of r(x)=10x^2 and reduces the marginal costs to (75-x). Suppose that one firm decides to conduct R&D at rate x=10. This research will be protected by a patent of T years. a) What profit(ignoring the one-off costs of R&D) does the innovating firm make each year during the period of patent protection? b) What is the new equilibrium price and total surplus once patent protection expires? c) Use your answer above to write the total surplus from the innovation
- 5. Suppose that market demand is described by P = 100 – (Q+q), where P is the market price, Q is the output of the incumbent firm and q is the output of a potential entrant to the market. The incumbent firm’s total cost function is TC(Q) = 40Q, whereas the cost function of the entrant is C(q) = 100 + 40q, where 100 is a sunk cost incurred to enter the market. If the entrant observes the incumbent producing Q units of output and expects this output level to be maintained, write down the equation for the residual demand curve that the entrant firm faces. If the entrant firm maximize profit given the residual demand curve in a) what output qe will the entrant produce? [Write qe as a function of Q] How much output would the incumbent firm have to produce to just keep the entrant out of the market? [That is, solve for the limit output QL.] At what price will the incumbent sell the limit output?Profit equals revenue minus cost. We have looked at costs. We now turn to revenue. Let us assume that firm S is a price In other words, it faces a (i) downward-sloping / horizontal (ii) demand curve / supply curve (Delete as appropriate.) Let us assume that it faces a market price of £2 per unit for its product. What is its total revenue from selling: (i) 5 units? ................................ (ii) 8 units? ................................ (c) What shape is its total revenue curve? ....................................................................................... (d) What will be its marginal revenue from selling: (i) the fifth unit? ................................ (ii) the eighth unit?…5. Suppose the demand for crude oil is given by the function: Q = -2000P + 70,000 where Q is quantity of oil in thousands of barrels and P is price per barrel of oil. Suppose there are 1000 identical small crude oil producers each with marginal cost MC = Q + 5 Where Q is the output of the typical firm: a) Derive the market supply curve and the equilibrium price and quantity b) Suppose a practically infinite supply of crude oil is discovered in North- Eastern Province (NEP) by a would-be price-leader and that the oil can be produced at constant average and marginal cost of Kshs.15 per barrel. If the supply behavior of the competitive firm described above is not changed by this discovery, how much should the price leader produce in order to maximize profits? c) What price and quantity will now prevail in the oil market? d) Graph (sketch) the results obtained above and show whether the consumer surplus increases as a result of the North-Eastern Province oil discovery? Indicate how the…
- A price-taking firm in a competitive industry of a good that is continuously divisible (like sand) has a total cost function TC(Q) = 3.5Q^2 + 100Q + 500. The market price for the good is p = $240. a: Carefully write out this firm’s profit maximization problem, using the particulars of thisproblem. b: Give the marginal condition (equation) that characterizes the solution to this problem. Solvethis condition for the firm’s optimal quantity Q*. c: Calculate the firm’s maximized profit. d: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve andmarginal cost curve. Show Q* on your graph. e: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to totalrevenue and variable cost.Question 7 A firm, focusing on producing toothpaste has a demand function 2? = 10 − 0.25?. If fixed cost per unit is -(+ and variable cost per unit function is 2? − 20 + -)), where Q is number of toothpastes produced and P is the price per toothpaste: a) Determine the number of toothpastes that maximizes the company’s profit. b) How much should the firm charge for one toothpaste? c) Find the total profit at the profit maximizing level of output. d) Using the own price elasticity of demand, comment on the firm's pricing policy options.Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. 1.What is the follower’s total revenue function? 2.Determine the equilibrium output level for both the leader and the follower. 3.Determine the equilibrium market price. 4.Determine the profits of the leader and the follower.