The demand function for a monopolist is given by P1 = 1,450 - 3.5Q and the cost function is C(Q)= 1,200 + 2.8Q^2. However, the new market price is p = $400 Produce a comparative table of P, Q, and profits before and after the new price
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The demand function for a monopolist is given by P1 = 1,450 - 3.5Q and the cost function is C(Q)= 1,200 + 2.8Q^2. However, the new market price is p = $400
Produce a comparative table of P, Q, and profits before and after the new price
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- Consider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is C(Q) = 6Q - Q^2/400 . (a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints).(b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.Total costs for a monopolist are defined as: C(q) = q3 + 1 Hence, marginal costs are: MC(q) = 3q2 If market demand is: P(q)=100 - 10q. a) How much is the monopolist going to produce? b) Provide a graphical representation of your results. c) If the monopolist could discriminate prices perfectly, how would your answers to a) and b) change.A monopolist with cost function C(q) = ;q? faces 2 consumers with the following demands: p(q1) = 10 - q1 and p(q2) = 20 – 2q2. Determine prices, quantities to be produced and sold and the monopolist's profits in the following cases: (a) The good can be resold at zero cost among consumers and it is technologically impossible to sell it in bundles of more than 1 unit. b) There is resale at zero cost and bundling in packages of arbitrary size. c) Resale is possible at a cost of "t" per unit. d) The good is a personal and non-transferable service. e) Repeat the above analysis, but this time assuming that costs are C(q) = q with q < 8.
- A monopolist has a cost function c(q) = 5q+800 and faces aggregate demand q=3000 - 120p. Suppose first that monopolist sells q=400 units. The monopolist's revenue would be The monopolist profit would be The absolute value of the price elasticity of demand would be The consumer surplus would be Now suppose that the monopolist chooses q to maximize its profit. The monopolist's revenue would be The monopolist profit would be The absolute value of the price elasticity of demand would be The consumer surplus would be(a) A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula. (b) A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…The demand function faced by a monopolist is D(p)= a-p and the cost function is C(q)=cq. 02 and it increases 2 The monopolist advertises to increase demand. The cost of advertising 0 is the demand by 0. The profit of the monopolist is (a-c) (a) 4 (a-c) (b) 2 (a-0) (c) 2 (a-0) (d) 4
- A monopolist faces two geographically distinct markets, say market 1 is New York and market2 is California. The inverse demand curves in each market are P1 = 300 – Q1 and P2 = 200 – Q2. Themonopolist’s total cost function is C(Q) = 0.5Q^2 + 50Q and marginal cost function is MC(Q) = Q + 50,where Q = Q1 + Q2 is the total quantity that it produces. Your job is to find out how much quantity to sellin each market in order to maximize profit.a) Carefully express this monopolist’s profit maximization problem.b) State the two equations that characterize the profit-maximizing amounts of Q1 and Q2, given an interiorsolution with positive quantities sold in each market.c) Solve these two equations for Q1* and Q2*.d) Find the prices P1* and P2* that the monopolist should charge in each market.A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. A. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula. B. A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…Suppose the inverse demand function is linear: p(q) = a - Bq. The monopolist's cost function is c(q) = 6q2 . Assume the monopolist must charge a uniform price. (a) Find the optimum monopoly price and quantity. Also calculate the deadweight loss. (b) Suppose the government can levy a lump-sum tax T (i.e., a fixed amount independent of production) and an excise tax t per unit of production on the monopolist. These taxes can be negative, in which case they are subsidies. The proceeds of these taxes can be transferred to consumers. The monopolist is always free to quit the market, in which case she does not have to pay any taxes. The government wants to maximize the consumer welfare. Find the optimum values of t and T.
- A monopolist faces a market demand curve given by: Q= 70−p. a) If the monopolist can produce at constant average and marginal costs of: AC = MC = 6. what output level will the monopolist choose to maximize profits? What is the price at this output level? What are the monopolist’s profits? b)Assume instead that the monopolist has a cost structure where total costs are described by: C(Q) = 0.25Q^2 - 5Q + 300.With the monopolist facing the same market demand and marginal revenue, what price- quantity combination will be chosen now? What will profits be? c)Assume instead that the monopolist has a cost structure where total costs are described by: C(Q) = 0.0133Q^3 -5Q + 250.With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now? What will profits be? d) Graph the market demand curve, the MR curve, and the three marginal cost curves from (a), (b), and (c).A monopolist faces two geographically distinct markets, say market 1 is New York and market2 is California. The inverse demand curves in these markets are P1 = 400 – Q1 and P2 = 200 – Q2. Themonopolist’s total cost function is C(Q) = 0.25Q^2 and marginal cost function is MC(Q) = 0.5Q, where Q =Q1 + Q2 is the total quantity that it produces. Your job is to find out how much quantity to sell in eachmarket in order to maximize the monopolist’s profit.a) Carefully express this monopolist’s profit maximization problem.b) State the two equations that characterize the profit-maximizing amounts of Q1 and Q2, given an interiorsolution with positive quantities sold in each market.c) Solve these two equations for Q1* and Q2*.d) Find the prices P1* and P2* that the monopolist should charge in each market.e) Calculate the monopolist’s (maximized) profit.If the demand of a Monopolist is as follows: Qd = 5500-12P And the TC function is equivalent to the following function: Total Cost = 8000 + Q2 a) Determine the level of production where profit is highest. b) Graph situation of the monopolist
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