2. Consider a society consisting with three individuals whose demand curves for a pure public good are Pa = 100-X, P = 110-X, P = 150-X for individual A, B, and C respectively. Marginal costs are constant and equal to $150 for each unit provided. (a) Determine the pareto optimal output rate and calculate the Lindahl prices for each individual.
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- Suppose that over the short run (say the next 5 years), demand for OPEC oil is given by P = 165 – 2.5q. Here q is measured in millions of barrels a day. OPEC marginal cost per barrel is $15. What is OPEC’s optimal level of production? What is the prevailing price of oil at that level? Many experts contend that maximizing short-run profit is counterproductive for OPEC in the long run because high price reduces buyers to conserve energy and spur competition and new exploration that increases the overall supply of oil. Suppose that the demand curve just described will remain unchanged only if oil prices stabilize at $65 per barrel or below. If oil price exceeds this threshold, long run demand (over a second five year-period) will be curtailed to P = 135 – 2.5q. OPEC seeks to maximize its total profit over the next decade. What is the optimum output and price policy? (assume all values are present values)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. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.2. 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.
- 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.I alrready got the first half answered, I need the second half. JointJuice produces a prepackaged joint support supplement for relief of joint pain with 180 tablets per bottle and operates in a perfectly competitive market. Basically, all the firms in this competitive market have technologies (production and cost conditions) that are the same as JointJuice’s. Suppose JointJuice’s total cost function is given by the following where q is JointJuice’s quantity of packages per day: C(q) = 250 + 6q + 0.1q^2 The market demand function for the output in this market is given by: Q = 1848 - 2P If there are 20 identical firms in this industry, find the market equilibrium price for the prepackaged supplements. Calculate JointJuice’s optimal output level and profits given the market price for the product. If JointJuice is typical of the firms in this industry calculate the firm’s long-run equilibrium output, price, and profit level. Suppose the situation changes. JointJuice has its plant in…. (Requires calculus). In the model of a dominant firm, assume that the fringe supply curve is given by Q = -1 + 0.2P, where P is market price and Q is output. Demand is given by Q = 11 – P.What will price and output be if there is no dominant firm? Now assume that there is a dominant firm, whose marginal cost is constant at $6. Derive the residual demand curve that it faces and calculate its profit-maximizing output and price. highest bidder, but both the winning and losing bidders must pay her their bids. So if Jones bids $1 they pay a total of $3, but Jones gets the money, leaving him with a net gain of $98 and Smith with -$1. If both bid the same amount, the $100 is split evenly between them. Assume that each of them has only two $1 bills on hand, leaving three possible bids: $0, $1 or $2. Write out the payoff matrix for this game, and then find its Nash equilibrium.
- It is argued that firms differentiate their products and sustain positive profits while other firms imitate and drive down their profits in the competitive business environments. Would you defend or refute the economic argument above? Explain your position. Do research on a firm’s product innovation to demonstrate the concept of product differentiation (i.e. a real-life example of a firm’s product of which a bundle of characteristics that differs from any existing product).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…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.
- 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…A. Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s chosen price as given (price taker) and chooses output so as to maximise its own profit. Write down the profit function of the follower. Calculate the profit maximising quantity that the follower selects given the leader’s chosen price p (i.e., calculate the follower’s supply curve S(p)). Interpret the solution to the profit maximising problem. B. The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) as defined in (c) above. Calculate the leader’s residual demand curve using the result in (b). Solve for p as a function of the leader’s output y1, i.e. the inverse demand function facing the leader. Write…The market inverse demandfor salt is P(Q) = 1000−10Q. There are n firms producing salt, each with the sameconstant marginal cost c. Show that as n increases, the market gets closer to efficiency.