A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 10Q, +Q,Q2+10Q, where O, and Q, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pı and P2 denote the corresponding prices then the demand equations are R = 50-Q+Q2 P = 30+20, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.
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- Question 10A monopolistic producer of two goods, G1 and G2, has a joint total cost function TC = 5Q1 + Q1Q2 + 5Q2Where Q1 and Q2 denote the quantities of G1 and G2 respectivel. If P1 and P2 denote the corresponding prices then the demand equations areP1 = 40 − Q1 + Q2P2 = 20 + 2Q1 − Q2a) Find the total revenue function for each goodb) Find the profit function for the firmc) Find the maximum profit if the firm is contracted to produce a total of 12 goods of either typed) Find the price that the firm is supposed to charge for each good.e) Estimate the new optimal profit if the production quota increases by 2 unitsConsider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the profit of each of the oligopolists? b) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will remain very close to what they are today and its profits will not increase"Suppose you are employed at a monopolistic company as a research (pricing) economist and you are deriving the behavior of two markets based on demand curves given by: Di(P1) 3 50 — Pі D:(p>) — 50 — 2р2 Assume that the marginal cost is constant at $8 a unit. (a) If it can price discriminate, what price should it charge in each market in order to maximize profits? (b) If it can't price discriminate, what price should it charge?
- Question 10 A monopolistic producer of two goods, G, and Gz, has a joint total cost function TC = 5Q, + Q,02 + 5Q2 Where Q1 and Q2 denote the quantities of G, and Gz respectively. If P, and Pz denote the corresponding prices then the demand equations are P = 40 - Q, + Q2 P, = 20 + 20, - Q2 a) Find the total revenue function for each good b) Find the profit function for the firm e) Find the maximum profit if the firm is contracted to produce a total of 12 goods of either type d) Find the price that the firm is supposed to charge for each good. e) Estimate the new optimal profit if the production quota increases by 2 units9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC =10Q, +Q,Q, +10Q, where Q, and Q, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pi and P2 denote the corresponding prices then the demand equations are P = 50 - Q, +Q; P, = 30+2Q, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.If a monopolistic firm has an increasing marginal cost (MC) curve, it is not in its interest to apply a two-part tariff. Comment on statement by arguing CONCEPTUALLY, GRAPHICALLY and ALGEBRAICALLY.
- 9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 100, + QQ, +100, where 9 and O; denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 – Q, + Q, P, = 30 + 20, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 100, + 00, +100, where 9 and denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 – Q, + Q, P, = 30 + 2Q, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.The market for dark chocolate us characterized by Cournot duopolists - Honeydukes and Wonka industries. The market demand for dark chocolate is: P = 8 - 0.005Qd where P is the price per bar in dollars and Qd is dark chocolate's daily quantity demanded in bars (use qh to represent the quantity of dark chocolate sold by Honeydukes and qw to represent the quantity of dark chocolate sold by Wonka Industries). Honeydukes has a constant marginal cost of $2.50 per bar, while Wonka Industries has a constant marginal cost of $3.00 per bar. The firms move simultaneously in choosing their profit-maximizing quantity of output. a. Given the firms move simultaneously, what is the equation for Honeydukes' reaction function with qh expressed as a function of qw? b. Given the firms move simultaneously, what is the equation for Wonka's reaction function with qw expressed as a function of qh? c. What quantity of dark chocolate will each firm produce in equilibrium and what price will be established for a…
- The price elasticity of demand for a monopolistic firm's product is given by 0.3 p 8-0.6 p najp == (a) If the firm raises their price from po = $64.00 to p₁= $65.00, then the demand for their good will... [Select] (b) The firm's marginal revenue is maximized when they set their price to... [Select]9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 100, + Q,0, +10Q, where 9 and 2: denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 -Q +Q. P, = 30 + 20, -Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.3. a) Maximise utility u = x0.6 y0.5 subject to the budget constraint 5x+6y=120. Use the Hessian %3D to test the second-order condition b) A monopolistic producer of two related goods faces the demand functions x=50–2 P,+ Py y=55+4p,-8p, His total cost function is TC = 0.2x² +2xy+0.4 y² . Find the profit maximising level of output if a production quota requires 2x+ 6 y= 300. Use the Bordered Hessian to test the second-order condition