3- Faced with two distinct demand functions Q_{1} = 24 - 0.2P Q_{2} = 10 - 0.05P_{2} Where TC = 35 + 40Q what price will the firm charge (a) with discrimination (b) without discrimination
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3- Faced with two distinct
Where TC = 35 + 40Q what
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- Q. Total consumers can be divided into Group A and Group B, and it is assumed that a monopoly company makes third-degree price discrimination. The demand function of each group and the cost function of the company are as follows. QA = 10-PA, QB = 12-2 PB, C(Q) = Q2 (1) Find the third-order price discrimination price that maximizes the profit of the company. (2) Assume that price discrimination between groups is prohibited by law. Find the maximum profit price.A monopolist in a given market faces inverse demand function P = 90 – 2 Q. Its cost structure is given by C(Q) = 10 Q + F, where F represents a set-up cost that the firm only pays if it decides to produce and sell in this market. Solve this firm’s profit maximization problem and determine the following: The deadweight loss in the market as a proportion of profits, assuming that F = 300 instead: 0.25 0.8 1 0.75. Suppose you are a manager of a County government project that is meant to provide rent-regulated housing units in low-income settlements. Using your knowledge of equilibrium, advice the Governor whether this policy will be a success. b. A Monopolist producing and supplying cooking gas to Mombasa city faces the demand function. Q = 8800 – 20P. Its cost function is given by TC = 20Q + 0.05Q2. i. Determine the quantity of cooking gas she will produce and the price she will charge to maximize profits and determine her profit. ii. Explain how her profits she will affected if regulators forced her to operate like a perfectly competitive firm. iii. Illustrate and compute dead-weight loss and lost consumer surplus associated with her Monopoly operations.
- Assume a monopoly has two groups of customers, and each group of customers has different demand for the firm's product. Group A's demand is: Pa = 90 - .1qa where qa is group A's quantity demanded and Pa is the commodity's price in dollars for group A customers. Group B's demand is: Pb = 170 - .2qb where qb is group B's quantity demanded and Pb is the commodity's price in dollars for group B customers. The firm's total cost curve is: TC = 30,000 + .05q2 where TC is the firm's total cost in dollars and q is the total quantity of output produced by the firm. Based upon the above equations, answer the following questions: a. What quantity of the commodity would the firm sell to customers in group B? What price would the firm establish for customers in group B? b. What quantity of the commodity would the firm sell to customers in group A? What price would the firm establish for customers in group A?Imagine that there are two types of consumers indexed by θi with i = H, L. Let the inverse demand curve for each be: P = θi(1 − qi) with θH > θL. Let the shares of the total population of N for each type be λ and 1 − λ, for groups θH and θL respectively. (a) Show that the aggregate demand is Q(P) =( N 1 − P ˜θ ) where ˜θ = λ/θH + 1−λ/θL , assuming that both groups are induced to buy. (b) Find the profit-maximizing menu-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c.Suppose the market demand function (expressed in dollars) for a normal product is P= 90-q, and the marginal cost (in dollars) of producing it is MC = 1q, where P is the price of the product and q is the quantity demanded and/or supplied 1. Compute the consumer surplus and the producer surplus assuming this same product was supplied by a monopolist. Note that the monopolist’s marginal revenue curve has twice the slope of the demand curve. 2. Compare and contrast economic surpluses under monopoly market vs competitive market. 3.
- 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 that the monopolist from Question 4 is now forced to charge the same price in both markets. Using thedemand functions and cost function from Question 4, what is the total inverse demand in this case? What is theprofit-maximizing price? What is the monopolist’s profit? (Question 4 = A monopolist is operating in two separate markets. The inverse demand functions for the two markets are P1 = 35 – 2.5Q_1 and P2 = 30 – 2Q_2. The monopolist’s total cost function is TC(Q) = 8 + 5(Q_1 + Q_2). Q_1 means Q subscript 1Consider a monopolist who is selling his blockbuster drug in two markets where one market is much larger than the other. Suppose the demand in the two markets is given by q1 = 30 − p1 and q2 = 3 − p2 (quantity is measured in millions of complete dosages and price is in your favorite currency) and the marginal cost of production and distribution is roughly the same and equal to 1 per unit (c=1). This problem asks you to compare equilibrium outcomes (prices, quantities, profits, consumer surplus, and consumer surplus per unit of output) when the monopolist can price discriminate across the two markets versus when it must set a uniform price. It then asks you to comment on some recent policy proposals. For each market separately, set up and solve the monopolist’s profit-maximizing problem. Specifically, write down/compute the following. Inverse demand and the profit functions. Equilibrium prices (), quantities () and profits () Consumer surplus () and consumer surplus per unit of…
- Faced with two distinct demand functions Q1=16-0,4P1 and Q2=20-0,1P2 where TC=100+20Q with Q=Q1+Q2.What price will the firm charge without discrimination? A)P= 16 B)P=36 C)P=26 D)P=46Suppose a monopoly firm has an annual demand function of Qd = 20,000 - 250P, annual variable costs of VC = 16Q + 0.002Q2 and marginal cost of MC = 16 + 0.004Q, where Q is the annual quantity of output. In addition, the firm has an avoidable fixed cost of $25,000 per year. If this firm maximizes its profit, what is the value of the consumer surplus in the market?Suppose a monopolist faces two groups of consumers. Group 1 has a demand given by P1=50−2Q1�1=50−2�1 and MR1=50−4Q1��1=50−4�1. Group 2 has a demand given by P2=40−Q2�2=40−�2 and MR2=40−2Q2��2=40−2�2. The monopolist faces a constant marginal cost equal to MC=10��=10.If the monopolist is allowed to engage in 3rd degree price discrimination, how many units of output will the monopolist sell? Question 12Answer a. 25 b. 10 c. 15 d. 20
