functions P₁ = 63-4Q1 P2 = 105-5Q2 Pkets described by the inverse demand P3=75-6Q3, where Q₁ is the quantity sold in market i. The total cost of this firm is given by C = 20 + 15Q, where Q is the total quantity produced (Q=Q₁ + Q2 + Q3). 1. Write down the optimization problem this firms wants to solve, as an optimization problem with three variables, Q1, Q2, and Q3.. 2. Write down the first order conditions. 3. Find the critical values.
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- he Pear Computer Company just developed a totally revolutionary new personal computer. Pear estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be P=2,500−500Q�=2,500−500� where Q� is millions of computers. The marginal (and average variable) cost of producing the computer is $900. Assuming Pear acts as a monopolist in its market, the profit-maximizing price and output levels are per computer and million computers, respectively. The total contribution to profits and fixed costs at this output level is million. Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years: Complete the following table by calculating the contribution to profit and overhead for each of the 10 time periods and prices. Time Period Price Quantity Sold Total Contribution ($) (Million)…Suppose that a monopolist supplies a product in two distinct markets, LA and SF. The demand functions for thetwo markets are PLA = 52 – 4QLA and PSF = 70 – 7QSF. The monopolist has a fixed cost of $20 and a constantmarginal cost of $10 per unit.a. If segmenting is feasible, what are the profit-maximizing prices, quantities, and maximized profit?b. If segmenting is NOT feasible, what is the profit-maximizing price, quantity, and maximized profit?c. How much is the difference in total consumer surplus in the two cases? Which case makes consumers better off?Q48' Assume that Cresco Labs is a monopolist that can sell 15 ounces of marijuana per day at $12.50 for each ounce. To sell 16 ounces of marijuana per day, the price must be cut to $12.20. The marginal revenue of the 16th ounce is Multiple Choice $12. $7.70 . $16. $-0.30. $12.20.
- Discuss in detail the equilibrium of a firm under monopoly.Q. 3. What do you mean by simple linear regression line. Estimate, Y , given thefollowing data:-Demand 3 4 5 6 7 9 8 10 12 14Price 16 13 10 7 7 5 4 3 4 2The Pear Computer Company just developed a totally revolutionary new personal computer. Pear estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be P=2,500-500Q where QQ is millions of computers. The marginal (and average variable) cost of producing the computer is $900. Assuming Pear acts as a monopolist in its market, the profit-maximizing price and output levels are $ per computer and million computers, respectively. The total contribution to profits and fixed costs at this output level is $ million. Time Period Price Units sold Total Contri. 1 2,400 2 2,200 3 2,000 4 1,800 5 1,700 6 1,600 7 1,500 8 1,400 9 1,300 10 1,200 Over the 10 periods, the total contribution to profits and fixed costs from price skimming is $…MARKET SEGMENTATION: Type III Discrimination: Price per customer segmentA company has differentiated its customers into 2 segments between which arbitrage is not possible, arriving at following result: Q1 = 200 - P and Q2 = 180 - 1.5 P. Its MC is constant and equal to 70. Commercial Strategy Manager wants to know:(a) If it is convenient for it to apply type III price discrimination, compared to that which would be obtained with the application of a single price for all units, in terms of extraordinary profit.b) If it applies type III price discrimination, what is market power it has in each segment.c) What is price elasticity of demand in each segment, at respective break-even points.
- A pure monopoly sells 6 units of a product per day at a unit price of $15. If it lowers the price to $14, its total revenue increases by $22. This implies that its sold output increases by _____. rev: 05_15_2018Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is -1.5. The marginal cost of producing the product is constant at $125, while average total cost at current production levels is $190.Determine your optimal per unit price if:Instruction: Enter your responses rounded to two decimal places.a. You are a monopolist.$ b. You compete against one other firm in a Cournot oligopoly.$ c. You compete against 19 other firms in a Cournot oligopoly.$A market analysis employed by the “Sad Student Company” reveals that the number oflots of the game named “Handsome Killer: Revenge of the Teacher” ordered by thewholesalers when the game is offered at a price of dollars per lot is given by the formula:p=1500-2.5qa) Find the company’s total, marginal and average revenues b) Find the price and quantity maximizing the total revenue by first expressing therevenue as a function of price rather than of quantity
- Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural resource. a. How should the analysis of the maximization of the discounted profits from selling this resource (Equation 17.63 be modified to take this fact into account? b. Suppose that the demand for the resource in question had a constant elasticity form q(t)=a[p(t)]b . How would this change the price dynamics shown in Equation 17.67? c. How would the answer to Problem 17.7 be changed if the entire crude oil supply were owned by a single firm?Industry demand and supply for a new soft drink NeuCola is as follows: Qd = 460,000 – 100,000 P + 22,500 Pc + 21 Y + 2,000 T Qs = 40,000 + 80,000 P – 60,000 PL – 5,000 Pk Where P is average price of the drink in $ per pack, Pc is average wholesale price other branded drinks in the market, Y is income in $, T is average daily temperature in degrees, PL is average wage of labor in $ per hour and Pk is the average cost of capital in $. When quantity is expressed as a function of price, what are NeuCola’s demand and supply curves if Pc = $8, Y=$10,000 billion, T=75 degrees, PL=$10 and Pk=$12. Will there be surplus or shortage of NeuCola when P = $5, $7 and $9? Use a table to show values of quantity demanded and quantity supplied at each level of price. (Values of Qd and Qs calculated in millions may be rounded in the table). Calculate the market equilibrium price and equilibrium output. 4. Draw a labelled hypothetical demand and supply model…Industry demand and supply for a new soft drink NeuCola is as follows: Qd = 460,000 – 100,000 P + 22,500 Pc + 21 Y + 2,000 T Qs = 40,000 + 80,000 P – 60,000 PL – 5,000 Pk Where P is average price of the drink in $ per pack, Pc is average wholesale price other branded drinks in the market, Y is income in $, T is average daily temperature in degrees, PL is average wage of labor in $ per hour and Pk is the average cost of capital in $. a. When quantity is expressed as a function of price, what are NeuCola’s demand and supply curves if Pc = $8, Y=$10,000 billion, T=75 degrees, PL=$10 and Pk=$12. b. Will there be surplus or shortage of NeuCola when P = $5, $7 and $9? Use a table to show values of quantity demanded and quantity supplied at each level of price.