If D (p) = 100/p and c(y) = y² a) What is the optimal level of output of the monopolist? b) What is the optimal level of output if there is a tax of $0.10 per unit paid by the monopolist? c) What is the optimal level of output if there is a tax of $0.10 per unit paid by the consumer? That is, the consumer pays Sp +0.10.
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- All 20 consumers are alike and each has a demand curve for a monopolist's product of p=15 -3q. The cost of production C(Q) =2Q. Let the monopolist charge a price of $PM for qM unit purchased. Find the menu prices that maximize profits? (The buyer pays menu price PM for quantity qM) What is the maximum profit the monopolist can earn in this market? (pi)?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 an inverse demand curve P(q) = 28 – 3q. The cost curve is C(q) = 10q. What is deadweight loss in this market? (a) DWL = 3 (b) DWL = 27/2 (c) DWL = 19 (d) DWL = 27 (e) None of the above.
- A monopolist faces linear demandp = a - Bq and has cost C = cq + F, where all parameters are positive, a > c, and (a – c)? > 4BF. (a) Solve for the monopolist's output, price, and profits. (b) Calculate the deadweight loss. Assume now the government requires this firm to set the price that maximizes the sum of consumer surplus and producer surplus, and to serve all buyers at that price. (c) What is the price the firm must charge? (d) Calculate the firm's profit (or loss) under this regulation. Is this form of regulation sustainable in the long run?Question 4. Consider a monopolist facing a demand curve of the form D(p) = 100 – 2p where p is the - unit price. Suppose the monopolist has a constant marginal cost of production of $2 a unit. Bunter was asked to determine the price which would maximize consumer surplus. Here is his solution: Total surplus as a function of price is 50(100 – 2x)dx. The derivative of this with respect to p is -(100-2p). This is maximized by making p as large as possible, i.e., p = 50. Is Bunter correct? If not, what is the error that Bunter has made?Only answer BOLD and ITALIC part of the question. 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 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=1,200-200P2. - Calculate the profit maximising output produced and price charged in each country by the price-discriminating monopolist and comment in which country the price charged is higher and by how much.…
- Let a firm have a cost function C = 100 +5Q2. (a) If the firm can sell as much product as it wants at a price P = 100, how much will it produce and what will her profit be? (b) If the firm is a monopoly and faces a demand function P = 200 – 5Q. Determine the firm's output, price, and profit. (c) At what level of output is the monopolist's revenue maximized and what is the profit in this production?The demand function facing the monopolist is given by D(p) 10/p, and the monopolist has positive marginsl cost of c. What is the profit maximising level of outputA 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 monopolist has a cost function given by C(y)=y2 and faces a demand curve given by P(y) = 120-y. a) What is the profit maximising level of output and the price that the monopolist will charge? Show your calculations. b) If you impose a lump sum tax of £100 on this monopolist, what will be the impact on output? Explain your calculations and the intuition behind your result. c) If you wanted to choose a price ceiling for this monopolist so as to maximise consumer plus producer surplus, what price ceiling should you choose? How much output will the monopolist produce at this price ceiling? Explain your calculations.A monopolist faces a market demand curve given by: Q = 80 - pa) Assume that the monopolist has a cost structure where total costs are described by: C(Q) = 0.25Q2 - 5Q + 1000.What price-quantity combination will a profit maximising monopolist choose? What will profits be? b) What output level would be socially optimal? What is the price at this output level, if all units are sold at the same price? What is the profit? What would the social welfare gain be from this output level compared to the outcome in (a)?c) If government regulation forces the firm to set its price equal to its average cost of production, what will the output level be? What is the price at this output level, if all units are sold at the same price? What is the profit? What would the social welfare gain or loss be from this output level compared to the outcomes in (a) and (b)?A monopolist faces a market demand curve given by Q(p) = 70 – p. Its total costs are described by TC(Q) = 3ố0 Q³ – 5Q + 250. 1 a) Derive the monopoly price, quantity, and profits. b) Calculate Lerner Index under the monopoly equilibrium. c) Now suppose the government sets the maximum price at $40. What output level and price level will the monopolist choose to maximize profits? What is the deadweight loss? d) Suppose the government sets the maximum price at $30. What output level and price level will the monopolist choose to maximize profits? What is the deadweight loss?