Madison Gas and Electric (MGE) is a monopoly for electricity in the city. MGE has a cost function of C(Q) = 1/2Q^2 and faces market demand of Q = P^(-u), u > 1. (1) Calculate the price elasticity of demand. (ii) What is the optimal market price as a function u? (iii) What is the markup as a function of u?
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- Madison Gas and Electric (MGE) is a monopoly for electricity in the city. MGE has a cost function of C(Q) = 1/2Q^2 and faces market demand of Q = P^(-u), u > 1. (1) Calculate the price elasticity of demand. (I) What is the optimal market price as a function u? (iii) What is the markup as a function of u?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?Your mom is the monopoly supplier of jokes in (humorless) Ho Hum. She faces a demand curve and a marginal cost curve given by following equations Demand: Q = 100 – 0.19P jokes per day Marginal Cost: MC= 80 dollars per joke Assume that jokes are perfectly divisible.
- Suppose in a monopoly market with linear demand function, the firm produces chocolates with MC = 3.6. The monopolist's profit maximizing price is 13.7. What is the corresponding price elasticity of demand? Round your answer to 2 decimal points. Answer: Chick-Thai is the only store sells chicken sandwiches around Santa Barabar, where the inverse demand function of chicken sandwiches is p(q) 50-5q. The cost function of the chicken sandwiches is C(q) +19g+ 10. After the protest from the angry crowd, the government decides to grant a $2 subsidy for each unit of sandwiches sold. By how much will the price of chicken sandwiches change after the subsidy? Round your answer to 2 decimal points. (f you find the price will increase by 5 dollars, put in '5", if you find the price will decrease by 3.15 dollars, put in -3.15') Answer:You 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?A monopoly firm has estimated the own price elasticity of their market to be Q,P= -14.5at the quantity Q = 30 and price P = $169. If the monopolist cost function is given by: C(Q) = 25 + 11Q + 3Q2 a. How should this firm be managed? b. How much output will be supplied to the market and what price will be charged?
- Let a firm have a cost function C = 100 +5Q2. (a) If the firm can sell as much product as it wants at a price P = 100, how much will it produce and what will her profit be? (b) If the firm is a monopoly and faces a demand function P = 200 – 5Q. Determine the firm's output, price, and profit. (c) At what level of output is the monopolist's revenue maximized and what is the profit in this production?Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q2 + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q+ 30since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equationQd = 60- P/2(alternatively, you can write the demand equation as Qd = 60–0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own pricePm and quantityQm, graphically depictthe monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium pricePm and quantityQm that you depicted graphically.² The monthly demand function for a product sold by a monopoly is p = 2,232 - dollars, and the average cost is = 1,000+ 16x + x² dollars. Production is limited to 1,000 units, and x is in hundreds of units. Find the revenue function, R(x). R(x) = Find the cost function, C(x). C(x) = Find the profit function, P(x). P(x) = (a) Find P'(x). P'(x) = Considering the limitations of production, find the quantity (in hundreds of units) that will give the maximum profit. hundred units (b) Find the maximum profit. (Round your answer to the nearest cent.) $
- A monopolist produces a single good X but sells it in two separate markets. The demand function for each market is?1 = 50 − 4x1 and ?2 = 80 − 3x2where ?1 and x1, ?2 and x2, are the price and quantity in market 1 and 2, respectively. The cost function is ?? = 120 + 8x1 + 8x2.(a) Find the total revenue for the firm in terms of x1 and x2. (b) Find the profit function in terms of x1 and x2. (c) Write down the first and second order partial derivatives, using the function in (b) (d) Solve the system of equationsDerivative of pi/ derivative of x1= 0 and Derivative of pi/ derivative of x2= 0 (e) Show that the point (x1,x2) is a maximum. (f) Find the maximum profit.Don't use pen or paper A monopoly firm faces the following average revenue (demand) curve: P = 360 − 0.04Q where Q denotes the output and P is the price, measured in dollars The firm’s cost function is given by C = 60Q + 5000. Assume that the firm maximizes profits. The marginal cost (MC) of production is $60. question: Can you calculate the deadweight loss (i.e., the efficiency loss) generated in this monopoly market? Group of answer choices $281250 $150000 $252800 $210825If a monopoly faces an inverse demand curve of p=450-Q, has a constant marginal and average cost of $30, and can perfectly price discriminate, what is its profit? What are the consumer surplus, welfare, and deadweight loss? How would these results change if the firm were a single-price monopoly? Profit from perfect price discrimination () is $88200. (Enter your response as a whole number.) Corresponding consumer surplus is (enter your response as whole numbers): welfare is and deadweight loss is Profit from single-price profit-maximization is = $44100. (Enter your response as a whole number.) Corresponding consumer surplus is (enter your response as whole numbers): welfare is and deadweight loss is CS = $0 W = $ 88200 DWL = $0. CS = $ 22050 W = $ 66150 DWL = $ 22050