Suppose a monopoly supplied its market from two plants, with cost functions: C₁-18 q₁ and C₂ (92) — 392. The monopolist faces a linear demand p = 238 - 5 Q, where is the amount sold in this market, which is the total amount produced by both plants. Find the quantities produced at each plant to maximize the monopolist's profit. 91 · 92 Number Number Now check the second order conditions:
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- Given the industry demand function X(p) = 100 - 2p, consider the following scenarios: a) The market is a perfectly competitive market. Assume there are identical firms with marginal cost of 12 in this perfectly competitive market. b) The market is dominated by one monopolist with a marginal cost of 12. This monopolist is able to achieve first degree pricing. c) The market is dominated by one monopolist with a marginal cost of 12, but the monopolist is able to achieve only second degree pricing. Assume the menu offers only 2 choices:(Q1= 30; P1= 35), and (Q2= 60; P2= 20). d) The market is dominated by one monopolist with a marginal cost of 12, but the monopolist now uses third degree pricing. Assume the firm can distinguish between low-demand consumers on the weekday and high-demand consumers on the weekend such that Qh = 55 - (1/2)Ph andQl= 45 - (3/2)Pl. The monopolist charges a difference price, Pl and Ph, in each distinct market. e) The market is dominated by one monopolist that is…Suppose that a monopolist sells its product in two countries; Japan and Canada. The monopolist’s marginal cost is $60 and total fixed cost is $100. The direct market demand equations in the two countries are as follows:QJ = 200 − 2PJ and QC = 100 − 0.5PC;where the subscript J denotes Japan and the subscript C denotes Canada. Suppose that the monopolist cannot prevent resale, i.e, the monopolist must charge a single price for both countries.a) Derive the direct total market demand equation, QD = f(P).b) What would be the profit-maximizing quantity (Q*), price (P*), and profit (π*)? Please answer both a) and b). Thank you.A monopolist knows there are two customers with different demand curves for two differently sized bags of potato chips. Customer S would only buy the small bag and has a willingness-to-pay given by P=160-2q (where P denotes the price and q denotes the quantity). Customer L would buy the large bag and has a willingness-to-pay given by P=200-q. The monopolist does not know who is customer S and who is customer L. Marginal cost of production is zero. AFTER second degree price discrimination, how large are the bags?
- A monopolist knows there are two customers with different demand curves for two differently sized bags of potato chips. Customer S would only buy the small bag and has a willingness-to-pay given by P=160-2q (where P denotes the price and q denotes the quantity). Customer L would buy the large bag and has a willingness-to-pay given by P=200-q. The monopolist does not know who is customer S and who is customer L. Marginal cost of production is zero. BEFORE second degree price discrimination, and if the monopolist perfectly price discriminated the small bag, what is the price of the small bag?Based on the best available econometric estimates, the market elasticity of demand for your firm's product is -3. The marginal cost of producing the product is constant at $225, while average total cost at current production levels is $315. Determine your optimal per unit price if: a. You are monopolist b. You compete against one other firm in a Cournot oligopoly c. You compete against 19 other firms in a Cournot oligopoly. A monopolist sells two products Q1 and Q2 for which the demand functions are: Q1 = 100 – 3P1 + 2P2 , Q2 = 75+0.5P1 - P2 and the joint cost function is TC = Q1 2 + 2Q1Q2 + Q2 2 . a. Use Cramer’s rule method to find the prices. Solve for the profit maximizing level of output and the maximum profit. b. Use the Hessian to check the second-order condition.
- A monopolist in a given market faces inverse demand function P = 90 – 2 Q. Its cost structure is given by C(Q) = 10 Q + F, where F represents a set-up cost that the firm only pays if it decides to produce and sell in this market. Solve this firm’s profit maximization problem and determine the following: The deadweight loss in the market as a proportion of profits, assuming that F = 300 instead: 0.25 0.8 1 0.75Assume a monopoly has two groups of customers, and each group of customers has different demand for the firm's product. Group A's demand is: Pa = 90 - .1qa where qa is group A's quantity demanded and Pa is the commodity's price in dollars for group A customers. Group B's demand is: Pb = 170 - .2qb where qb is group B's quantity demanded and Pb is the commodity's price in dollars for group B customers. The firm's total cost curve is: TC = 30,000 + .05q2 where TC is the firm's total cost in dollars and q is the total quantity of output produced by the firm. Based upon the above equations, answer the following questions: a. What quantity of the commodity would the firm sell to customers in group B? What price would the firm establish for customers in group B? b. What quantity of the commodity would the firm sell to customers in group A? What price would the firm establish for customers in group A?Consider a monopolist who is selling his blockbuster drug in two markets where one market is much larger than the other. Suppose the demand in the two markets is given by q1 = 30 − p1 and q2 = 3 − p2 (quantity is measured in millions of complete dosages and price is in your favorite currency) and the marginal cost of production and distribution is roughly the same and equal to 1 per unit (c=1). This problem asks you to compare equilibrium outcomes (prices, quantities, profits, consumer surplus, and consumer surplus per unit of output) when the monopolist can price discriminate across the two markets versus when it must set a uniform price. It then asks you to comment on some recent policy proposals. For each market separately, set up and solve the monopolist’s profit-maximizing problem. Specifically, write down/compute the following. Inverse demand and the profit functions. Equilibrium prices (), quantities () and profits () Consumer surplus () and consumer surplus per unit of…
- A firm is a profit-maximizing monopolist in the market of a patented computer software. As an economic analyst,you observe the following data:a) The monopoly’s price is set at $50 per copy.b) The monopoly’s total revenue is $300,000.c) The monopoly’s marginal cost at the profit-maximizing quantity is at $30 per copy.Based on the observed data, please determine the linear inverse demand function.Fill in the blanks. Suppose the inverse demand function is of the formwhere a, b are both positive constants, determine the value for a: 1 and b: 2 .Hint: a should be an integer, the answer for b should round to four decimal places.Curse Purge Plus is a monopolist in the curse removal market They face an inverse demand curve given by P=200-4Q, where Q is the number of curse removals they sell. Their cost function is C(Q)=10+8Q. Find the first-order condition for profit maximization.You are considering entering a market serviced by a monopolist You are considering entering a market serviced by a monopolist. You currently earn $0 economic profits, while the monopolist earns $5. If you enter the market and the monopolist engages in a price war, you will lose $5 and the monopolist will earn $1. If the monopolist doesn’t engage in a price war, you will each earn profits of $2.There are two possible solutions or equilibria. What are they? You are considering entering a market serviced by a monopolist