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?
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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
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- Acme is a monopolist for a good with inverse demand P = 4000 – 6Q, where P is the price in dollars and Q is the amount sold. Acme's variable costs are TVC(Q) = 4Q². With these functions, the marginal revenue is MR(Q) = 4000 – 12Q and marginal cost is MC(Q) = 8Q. a) If Acme has no fixed costs, what is its profit maximizing price? b) If Acme has non-sunk fixed costs of $700,000, is it worth operating or should they shut down?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.<Consider 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 1A 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.The demand a monopoly faces is p = 400 - Q+A 0.5 where Q is its quantity, p is its price, and A is the level of advertising. Its marginal cost of production is $40, and its cost of a unit of advertising is $1. What is the firm's profit equation? The monopoly's profit equation (л) as a function of Q and A is π= (400-Q+A05) Q-40Q-A. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) The monopoly's profit-maximizing price is p = $270, quantity is Q = 260, and advertising is A = 16900. (Enter numeric responses using real numbers rounded to two decimal places.)
- A monopolist has a demand curve given by P = 90 - 2Q and a total cost curve given by TC = 72 + Q2. The associated marginal cost curve is MC = 2Q, %3D and the associated marginal revenue curve is MR = 90 – 4Q. What is the profit-maximizing quantity and price. How much economic profit does the monopolist earn? Suppose this monopolist could engage in an advertising campaign that would increase demand to P = 108 – 2Q (and MR = 108 – 4Q). What would be the maximum amount this company would be willing to pay for this advertising campaign?Consider a monopoly market in which the market demand curve is given by P = 240 – 2Q, the marginal revenue curve is MR = 240 – 4Q, the marginal cost curve is MC = 2Q, and there are zero fixed costs. Suppose the government intervenes and turns the market into a competitive market, and all the firms in the market have the same marginal cost curve as the monopolist, MC = 2Q, and zero fixed costs. How much is the resulting gain in total surplus?[12:17]800 600 300 400A monopolist's inverse demand function is estimated as P=100-2Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC₁(Q)=4Q₁, and the marginal cost of producing at facility 2 is MC₂(0₂)=202. a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q+Q₂ = Q.) MR(Q)=-91-9₂ b. Determine the profit-maximizing level of output for each facility. Instructions: Round your response to two decimal places. Output for facility 1:[ Output for facility 2:[ c. Determine the profit-maximizing price. Instructions: Round your response to the nearest penny (two decimal places).
- 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 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 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