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?
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- 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 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 the demand curve Q(P ) = 50 − P 2 . The firm can produce output with marginal costs MC(Q) = Q and no fixed costs. Hint for the following questions: if revenue is of the form R(Q) = (a − bQ)Q, then the derivative of revenue is a − 2bQ. (a) What is the profit maximizing price for the monopolist in this market? (b) What is the deadweight loss from monopoly in this market, compared to the efficient output that sets price equal to marginal cost? *Please fully explain out any math
- A monopolist has a single customer with the demand curve P=20-Q. (So this customer will buy different quantities at different prices.) Suppose the monopolist’s marginal cost is MC=0. (And assume FC=0 to keep things simple.) The monopolist uses “standard” pricing, i.e., it sets a single price for all units that the customer buys. The graph below shows the demand curve and MC curve. Solve graphically for the price & quantity that will maximize profit for the monopolist. Shade the areas on your graph that represent consumer surplus and the monopolist’s profit.A monopolist has a cost function of c(y) = y so that its marginal costs are constant at $1 per unit. It faces the following demand curve: D(p) = {100/p if ps 20. 0, if p> 20%3; (a) What is the profit-maximizing choice of output? (b) If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should they set? (c) What output would the monopolist produce if forced to behave as a competitor?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?
- Suppose inverse demand is given by the following equation: P(Q) = 600 - 20Q Suppose further that you are a monopolist with constant marginal cost equal to 40. How much profit do you earn at the optimal price and quantity? A) 3920 B) 1120 C) 0 D) 4500Consider a market with a demand curve P = 500 − 5Q which is being supplied by a monopolist. The cost of production of the monopolist is given by C(Q) = 5Q2 2 . P and Q are the price and quantity of the entire market. (a) Find the expression of total and marginal revenue, and marginal cost. Draw the demand, MR and MC curves in a clearly labelled diagram. (b) Find out how much output will be sold by the monopolist in equilibrium? What price she will charge? How much profit will be earned by her. (c) What would be the equilibrium price and quantity if the market were served by a perfectly competitive firms instead? (d) Find the consumer and producer surplus in competitive and monopoly markets? Find and explain the dead-weight loss due to monopoly operation.A monopolist has a constant marginal cost of 12. Consumers' inverse demand is P = 32 - 4Q. The monopolist runs a persuasive advertising campaign that costs 26 and increases consumer demand to P = 37 - 4Q. (a) What is the gain (or loss) in the firms profits caused by the advertising campaign? b) When consumers' pre-advertising preferences are used to calculate welfare, what is the welfare gain (or loss) caused by the advertising campaign? Answer 2 Question 1 (c) When consumers' post-advertising preferences are used to calculate welfare, what is the welfare gain (or loss) caused by the advertising campaign? Answer 3 Question 1
- A monopolist has a cost function of c(y)=yso that its marginal costs are constant at $1 per unit. it faces the following demand curve: 0 if p> 20 or 100/y if p is less than or equal to 20 find (1) What is the profit-maximizing choice of output? (2) If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should the government set? 3) What output would the monopolist produce if he is forced to behave as a competitor?A monopolist faces a demand curve P = 100 – 4Q and initially faces total costTC = 12Q. (a) Calculate the profit-maximizing monopoly quantity and price, and compute the monopolist's total revenue and profits at the optimal price. (b) Suppose that the monopolist's total increases to TC = 44Q. Verify that the monopolist's total revenue goes down. c) Suppose that all firms in a perfectly competitive equilibrium had a combined total cost T C = 12Q. Find the long-run perfectly competitive industry price and quantity. Also what are the combined industry profits and revenue. (Hint: the supply curve is just the marginal cost) (d) Suppose that all firms' total costs increased to T C = 44Q. Verify that the increase in marginal cost causes total industry revenue to go up.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.