(a)
In market 1: P1 = 100 - Q1
In market 2: P2 = 80 - Q2
Profit (Z) = TR1 + TR2 - C(Q) = (P1 x Q1) + (P2 x Q2) - 10 x (Q1 + Q2)
Z = 100Q1 - Q12 + 80Q2 - Q22 - 10Q1 - 10Q2
Z = 90Q1 - Q12 + 70Q2 - Q22
(b)
Profit is maximized when Z/Q1 = 0 and Z/Q2 = 0.
Z/Q1 = 90 - 2Q1 = 0
2Q1 = 90
Q1 = 45
P1 = 100 - 45 = 55
Z/Q2 = 70 - 2Q2 = 0
2Q2 = 70
Q2 = 35
P2 = 80 - 35 = 45
Profit = (55 x 45) + (45 x 35) - [10 x (45 + 35)]
= 2475 + 1575 - (10 x 80)
= 4050 - 800
= 3250
(c)
In this case, P1 = P2 = P
Market demand (Q) = Q1 + Q2 = 100 - P + 80 - P
Q = 180 - 2P
P = (180 - Q)/2 = 90 - 0.5Q
TR = PQ = 90Q - 0.5Q2
MR = dTR/dQ = 90 - Q
MC = dC(Q)/dQ = 10
Setting MR = MC,
90 - Q = 10
Q = 80
P = 90 - 0.5 x 80 = 90 - 40 = 50
Profit = Q x (P - MC) = 80 x (50 - 10) = 80 x 40 = 3200
2. Suppose that a monopoly faces two markets for its product. D: Q1 = 100 -...
2. Suppose a monopoly firm is allowed to price discriminate in 3 markets where the prices for the good in each market are given by: P1 = 63 - 401 P2 = 105 - 502 P3 = 75 - 603 where: Q = Q1 + Q2 + Q3 The cost of the output is (Q) = 20 + 15Q+Q2 a) Give the profit function for the firm. b) Find the FOC's and find the p*'s and Q*'s that maximize profit....
Question 3 Monopoly a) Discuss how monopoly markets discriminate prices by using the concept of market segmentation. b) The market demand curve for a monopoly firm is given as P = 200 – 20. Furthermore, the marginal cost is represented by the equation MC = 20 + 20. The firm's TC can be expressed as TC = 200 + Q2 + 100. Use this information to answer the questions and calculate the following: i) Profit maximizing quantity and price. ii)...
Suppose that a monopoly faces inverse market demand function as P = 70−2Q, and its marginal cost function is MC = 40 – Q. Please answer the following two questions: a. What should be the monopoly’s profit-maximizing output? b. What is the monopoly’s price?
2. Suppose a monopoly firm is allowed to price discriminate in 3 markets where the prices for the good in each market are given by: P1 = 63 - 401 P2 = 105-502 P3 = 75 - 6Q3 The cost of the output is (Q) = 20 + 15Q+Q? where: Q = Q1 + Q2 + Q3 a) Give the profit function for the firm. b) Find the FOC's and find the p*'s and Qo's that maximize profit c) Find...
THIRD-DEGREE PRICE DISCRIMINATION A seller faces two groups of buyers: Pi-16- Q1 and P2-24-Q2. Marginal cost is constant at $4 and fixed costs are zero a. Assuming that resale of the good by consumers is impossible, find profit-maximizing quantities and prices under 3rd-degree price discrimination. No need to calculate profit. Show graphs and math. Suppose someone argues "Under this outcome Pi and P2 differ, so this cannot be profit maximizing since a seller could always transfer a unit from the...
X Text Question 4.3 Question Help Suppose a nonlinear price discriminating monopoly, can set three prices, depending on the quantity a consumer purchases. The firm's profit is T=P1 (Q1) +P2 (Q2-Q1) +P3 (Q3 - Q2) – mQ3, where p, is the high price charged on the first Q, units (first block), P, is a lower price charged on the next Q, -Q, units, P3 is the lowest price charged on the Q3-Q, remaining units, Q, is the total number of...
The inverse demand curve a monopoly faces is p = 100-2Q. The firm's cost curve is C(Q)=30+6Q. What is the profit-maximizing solution? The profit-maximizing quantity is _____. (Round your answer to two decimal places.) The profit-maximizing price is $_____ (round your answer to two decimal places.)
The inverse demand curve a monopoly faces is p equals 100 minus Upper Qp=100−Q. The firm's cost curve is Upper C left parenthesis Upper Q right parenthesis equals 50 plus 5 Upper QC(Q)=50+5Q. What is the profit-maximizing solution? The profit-maximizing quantity is (Round your answer to two decimal places.) The profit-maximizing price is (round your answer to two decimal places.)
4. A monopolist faces a market demand defined by P 20. There are no fixed costs. 100 (1/5)Q. Her marginal cost is given by MC (a) Graph the market demand, the marginal revenue curve and the marginal cost curve, labeling the intercepts. (5 marks) (b) Calculate the monopolist's profit-maximizing price, output and profit. (5 marks) (c) Suppose that this market can now be divided into two separate markets and the supplier can discriminate between them. The demand curves are given...
A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest). Demands for the two markets are: Q1 = 15 - P1 Q2 = 12.5 – 0.5 P2 The monopolist’s total cost is C = 5 + 3(Q1 + Q2 ). What are the prices, outputs, profits in each market if the monopolist can price discriminate? Check that the profit maximizing price and its elasticity of demand have the following relation between markets: P1...