2. Derive the monopoly equilibrium, i.e., the profit maximizing price and quantity, as well as the firm's profit, for each of the demand functions given below, assuming the firm's total cost of q units of output is given by C(q) = 4q a) c) 9=e-²p+16 q= 20000 q=400 - 8p
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- 2. Derive the monopoly equilibrium, i.e., the profit maximizing price and quantity, as well as the firm's profit, for each of the demand functions given below, assuming the firm's total cost of q units of output is given by C(q) = 4q a) b) c) q=e q= -2p+ 16 20000 2 q=400 - 8pYou are the manager of a monopoly, and your analysts have estimated your demand and cost functionsas P = 300 − 3Q and C(Q) = 2, 000 + 2Q2, respectively.(a) What price-quantity combination maximizes your firm’s profits?(b) Calculate the maximum profits.(c) Is demand elastic, inelastic, or unit elastic at the profit maximizing price-quantity combination?(d) What price-quantity combination maximizes revenue?(e) Calculate the maximum revenues.(f) Is demand elastic, inelastic, or unit elastic at the revenue maximizing price-quantity combination?Assume that Gas & Minerals is the only copper mining firm in Chile. The national demand for copper in thousands of tonnes per month is: q^d(p) = 15 - pThe total costs in millions of dollars are: c(q) = 5q(a) What would be the profit-maximising level of production for this firm? Determine the monopoly price and quantify the profits. Graph the demand, marginal revenue and marginal cost, identifying their values along with determining the social loss generated and identifying it in the graph above. Assume now that due to a bad internal restructuring, the operations manager was fired and a professional with little mining experience was hired. The new manager does not know environmental protocol and mining waste (tailings) has gotten out of control and has been dumped into a river. This generated a negative externality on copper production. The estimated damage is US$5 million per 1,000 tonnes.(b) Obtain the social marginal cost of this mining activity.(c) What level of production will…
- Question 2 Alice is the monopoly producer for DrinkMeTM, a magical potion that makes you shrink in size. Market demand for this potion is given by p = 60 - 3Q and Alice's costs of production are C(q) = 12g. Please calculate the following quantities. %3D %3D a) Monopoly price, quantity and profits b) The fair market price in perfect competition c) The welfare loss which occurs due to the monopolyAssume that we are in a monopoly and demand curve is given by following expression:p(q) = 45 - q2And further it is known that marginal cost (MC) is given by:MC(q) = 6 + (q2/4)Under assumption that utility is maximized, answer:(a) Calculate marginal revenue (MR) and equilibrium point of monopoly. Graphb) Calculate consumer surplus (CS). Show it on the graphNOTE: remember that functions ARE NOT LINEAR. Consumer surplus is calculated as (see attached image)A monopoly function for a firm given ? = 20 − 0.2? where ? is price and ? is output. Find (a) Total revenue function (b) Average revenue function (c) Marginal revenue function (d) ? = dq/dp , p/q at ? = 50 and show that at this ∈ value, ?$(?) = 0.
- The demand and total cost functions for a monopoly firm are:Q(P) = 39.5 – 0.5PTC(Q) = 60 – Q + 0.5 Q2a) Plot the demand, marginal revenue, marginal cost, and average total cost curves, including the intersections with the horizontal and vertical axes. b) What are the profit maximising QM and PM for this firm? c) What is the firm’s profit πM? d) What are the firm's fixed and variable costs? e) What would be the socially optimal Q* and P* (round to 1 decimal place if needed)?You are a consultant who is advising a monopoly on the optimal pricing strategy. Your analysis has yielded the following information. • The marginal cost (MC) is $3. • The demand equation is P = 90 - 3Q . The total cost (TC) is given by 35+ 3Q The marginal revenue (MR) is given by 90 - 6Q Based on this information, answer the following questions. Show FULL calculations! (a) Following the concepts of profit maximization, what is the profit maximizing quantity for this monopoly? (b) Following the concepts of profit maximization, what is the profit maximizing price for this monopoly? (c) Following the concepts of profit maximization, what is the monopoly's profit at the profit maximization point?A firm has three factories for which costs are given by: C (Q1) = 10Q, C2 (Q2) = 40Q, C (Qs) = 80Q; The firm faces the following demand curve: P= 2,000 - 20 where Q is total output, i.e. Q - Q + Q, + Q3 What would be the Lerner index of monopoly power for this monopolist?[Please choose the closest-answer O 0.175 O 0.245 O 0.137 0.108 0.142 0.121 O 0.215 Nest
- The names of the compagny is H20 A compagny of water production and distribution company is in a monopoly situation. it's total cost function is given by: CT (q) = q² + 10q where q represents the quantities produced in millions of m ^ 3 of water. She is faced with the following request p = 50-4q with p the price in cents. Please answer the following question a) Calculate the price, quantity and monopoly profit of H20 b) Represent the demand curves of average cost, marginal cost and marginal revenue of H20 c) H20 learns from the news that a potential entrant wants to enter the market by selling 5 units at a unit cost of 20. Determine the price level below which H20 can set a limit price Then check whether the monopoly price calculated in question 1 can be considered a limited price d) Would H20 remain profitable if the entrant were to enter the market anyway ? (for this you have to calculate the market price that will rise as a result of the entry of the competitor) e) The entrant…1.-Dayna’s Doorstops, INC. (DD) is a monopolist in the doorstop industry. Its total cost function C(⋅) is given by the quadratic function of output C(Q) =100 – 5Q + Q2 . The inverse demand function for doorstops P(⋅) is given by the linear function P(Q) = 55 – 2Q . Note that the marginal cost C′(Q) is not constant. (Also, it happens to be negative for 0 ≤ Q < 2.5.) (a) Write down the profit-maximizing problem for DD, and determine its optimal output, QM. (b) Find the profit-maximizing price set by DD, PM and its marginal cost at the output level QM. From these two pieces of information, can you compute the elasticity of demand at that same level of output without taking any derivative? (c) How much consumer surplus CSM and producer surplus PSM and total surplus does DD generate by its profit-maximizing plan? (d) Find the profit-maximizing output, Qc, if DD acted like a price-taker (i.e., a perfect competitor). (e) Find the profit-maximizing price set by DD, Pc, as well as its…A monopoly company has a demand curve that can be shown as P = 3 000 - 100Q. It has fixed costs of R1 000 and additional cost per unit produced of R200. 1. a) What is the total cost equation? [2] 2. b) What is the marginal cost equation? [2] 3. c) What is the total revenue equation? [2]
