14) The demand equation for a monopolist's product is p= 200 -0.98q, where p is the price per unit (in dollars) of producing q units. If the total cost c (in dollars) of producing 8 units is given by c= 0.02q2 + 2q +8000, find the level of production at which profit is maximized.
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- 14) The demand equation for a monopolist's product is p=200 -0.98q, where p is the price per unit (in dollars) of producing q units. If the total cost c (in dollars) of producing 8 units is given by c= 0.02q2 + 2q + 8000, find the level of production at which profit is maximized.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) 4500Suppose you are a monopolist in the market for a specific Q video game. Your demand curve is given by P = 80- - and 2 your marginal cost curve is MC = Q. Your fixed cost is $400. i) Derive the marginal revenue curve. ii) Calculate the equilibrium price and quantity. iii) What is the profit?
- Problem 3 Suppose that a monopolistic seller of flux capacitors faces the inverse demand curve P = 40 - and that the monopolist can produce flux capacitors at a constant marginal and average total cost of $5. (a) How many units will an unregulated monopolist sell? 1 (b) Suppose that the government imposes a price ceiling of $6. Find the firm's marginal revenue of the 10th, the 68th, and the 69th unit. (c) How many units will a profit-maximizing monopolist sell when the price ceiling is in place? At what price? (d) Show in a graph the deadweight loss of unregulated monopoly and the deadweight losses with the price ceiling. Does the price ceiling improve social welfare?19. Firm A is monopolist in x market, and it consumes one unit of y in order to produce one unit of x. It costs 5 + py TL to produce one unit of x. (py is the price of product y.) y is produced by a monopolist, B, and it costs 5 TL to produce one unitf of y. The demand for x is defined by px = 50-qx (px product price, qx quantity demanded). a) Assume that px is set by Firm A and py is set by Firm B. What would be the equilibrium prices for products x and y? Calculate Firm A and B's profits. b) Assume that Firms A and B merge together. What would be the equilibrium prices for products x and y? Calculate the profits of the new firm. c) Would the merger between A and B increase the consumer surplus? Why (not)?The following graph shows the demand (D) for cable services in the imaginary town of Utilityburg. The graph also shows the marginal revenue (MR) curve, the marginal cost (MC) curve, and the average total cost (ATC) curve for the local cable company, a natural monopolist. On the following graph, use the black point (plus symbol) to indicate the profit-maximizing price and quantity for this natural monopolist. (? 100 90 Monopoly Outcome 80 70 60 50 40 ATC 30 MC 20 10 MR D 2 6 8 10 12 14 16 18 20 QUANTITY (Number of subscriptions) Which of the following statements are true about this natural monopoly? Check all that apply. O In order for a monopoly to exist in this case, the government must have intervened and created it. O The cable company is experiencing diseconomies of scale. O The cable company is experiencing economies of scale. O It is more efficient on the cost side for one producer to exist in this market rather than a large number of producers. True or False: Without government…
- 1. A monopolist's marginal cost function is given by: MC = 4q+ 20 where q is the quantity of good the monopolist produces. Fixed costs are 20, and the demand equation for the good produced is p+4q = 40, where p and q are price and quantity, respectively. - Find expressions for total revenue and for profit, as functions of q. Determine the value of q which maximises the profit. 2. Suppose the numbers x, y and z satisfy the following equations, where a is some number: x+y+z= 5-a 2x+y = 7-a x-y-2z = 0. Use a matrix method to determine the values of x, y and z, in terms of a. For what values of a will x, y and z all be positive? 3. Suppose that a is a positive number and that the function f is given by: f(x, y) = y¹ - 8a²y² +11. The inverse demand function for a monopolist's product is given by P=21-2Q. What is the maximum price per unit a monopolist can charge to be able to sell 6 units? What is marginal revenue when Q=6? Show your solution 2. Suppose the inverse demand function for a Meralco's service is given by P= 83 -2Q and the cost function is C=12 + 2Q. Required: Compute the profit-maximizing price, quantity and maximum profits.A monopolist's demand function is given by D(p) = 90 – 2p. This - monopolist is facing a cost function, C(y) = (1/2)y² + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?
- 4. = Assume that a monopolist sells a product with the cost function C F20Q, where C is total cost, F is a fixed cost, and is the level of output. The inverse demand function is P 60-Q, where P is the price in the market. (i) How much profit does the firm earn when it charges the price that maximizes profit? (ii) At what price will the firm earn zero economic profits ?The monopolist faces the demand curve D(p) = 100 – 2p. Its cost function is c(y) = 2y. What is your optimal level of production and prices? Solve mathematically and graphA 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