The demand of a monopolist is given by P(Q, A) = 74-40+2√A, where P is the price, Q is the quantity and A is the advertising expenditure. The total cost function is given by TC(Q) = Q2 + 10Q. What is the optimal quantity produced? Answer:
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- 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…A monopolist faces a demand curve given by Qd = 270 – P and faces a short run total cost function given by TC = 30 + 3q2. (i) What is the output level that maximizes the firm's revenue?A monopolist has a cost function given by c(y) = y2 and faces a demand curve given by P(y) = 120 - y. What is the profit maximizing level?
- 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?The demand function for a monopolist is given by: P1= 1,250 - 3.5 Q and the cost function if given by C(Q) = 1,200 + 2.8Q^2. Graph this case and show optimal P, Q, and profits.A monopolist has a cost function given by c(y)=y2 and faces a demand curve given by P(y)=120-y. What is the profit maximizing level of output?
- 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.Suppose a monopolist has the following cost function C(Q) = 40Q (with marginal cost MC = 40). Suppose it faces market demand of P = 100 - Q.< (a) Sketch market demand, marginal revenues, and marginal costs. Be neat.< (b) What is the monopolist's optimal level of output, price, and profits? Show your work.< (c) What is the deadweight loss (DWL) associated with the monopoly output? Show your work and explain why the DWL arises.< (d) (Cournot Competition) Now suppose we added a second firm that has identical costs to the monopolist. Show that the resulting Cournot Equilibrium has each firm producing output of 60 units. That is, show that, if the other firm sells 60 units, then the best a firm can do is also sell 60 units. (e) What are total profits under Cournot Competition compared to the Monopoly case? Why do they differ? (f) What happens to the deadweight loss under Cournot Competition relative to the Monopoly case? Explain why this happens.<Economics Consider the following cost function faced by the monopolist: TC(q)= 2q2+20q+10. The demand faced by the monopolist is the following: p(q)=200-10q, where q denotes quantity and p denotes price. Find the price and quantity that maximizes profit of the monopolist. If the monopolist becomes a perfectly price discriminating monopolist, calculate the Consumer Surplus and Producer Surplus.
- Consider a market for cars with just one firm. The firm has a linear cost functionC(q) = 2q. The market inverse demand function is P(Q) = 9 − Q, where Q is thetotal quantity produced. Since initially there is just one firm, q = Q.(a) Set up the maximisation problem for the monopolist and determine the optimalprice and quantity of cars produced. How much profit does the firm make?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 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.
