Inverse elasticity rule
Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual
where
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Check out a sample textbook solution- Refer to the figure below:Use the estimated elasticities to calculate the Rothschild index for each industry.Instruction: Enter your responses rounded to three decimal places for the Rothschild Index column in the table.arrow_forwardAt these levels of output the marginal revenue in the manufactured items market is and the marginal revenue in the semimanufactured raw materials market is . At these prices, the price elasticity of demand in the manufactured items market is and the the price elasticity of demand in the semimanufactured raw materials market is . (Hint: ED=PMR−P��=�MR−�) What are the total profits if the company is effectively able to charge different prices in the two markets? . If the company is required by law to charge the same per-ton rate to all users, the new profit-maximizing level of price and output are per ton and tons respectively. The total profits in this situation is .arrow_forwardSuppose Medic Inc. has a patent for a new pill called Relieve, which alleviates Restless Leg Syndrome (RLS) and is approved to sell its products in two separate markets – USA and Canada. The inverse demand function in USA is given by PU = 24 - QU and the inverse demand function in Canada is given by PC = 12 - 0.5QC. Therefore the total revenue function for USA is given by TRU = 24QU - QU2 and the total revenue function for Canada is given by TRC = 12QC - 0.5QC2 . Relive is sold in strip of 10 pills and the marginal cost of producing each strip is $6.00. PU = Price in USA in US dollars; PC = Price in Canada in US dollars; QU = Quantity sold in USA; QC = Quantity sold in Canada. What will be the profit from the US market? a. $72.00 b. $45.00 c. $81.00 d. $0.00arrow_forward
- Suppose the Bluemont Hotel in Aggieville has a summer demand of: P1 = %3D 100 - 4Q1, where P is the price of a room per night, and Q is rooms sold. Fall demand (football!) is given by P2 = 200 - 2Q2. The hotel's marginal costs are MC = 20 + 2Q, which is increasing in Q due to capacity constraints. Suppose that the hotel engages in peak load pricing. During the summer, the profit-maximizing price is equal to: 56 80 60 68arrow_forwardA fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by 40 p0.6 where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price. Find E(p) E(p) = q= X Find the price elasticity of demand when the price is set at $3.70 per serving. At a price of $3.70, a 1% increase in price leads to a Interpret the result. At a price of $3.70, the demand is elastic They should raise X% decrease in demand. ✓X the price per serving in order to increase revenue.arrow_forwardThe own price elasticity of demand is the most important determinant of pricing strategy by a firm. A firm can charge a high price for its product and earn higher revenue if the demand for its product is relatively inelastic. In other words, demand inelasticity and market power go hand in hand. What strategies should a firm adopt to make the demand for its product inelastic? Explain.arrow_forward
- [Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 Calculate the profit maximizing output levels of each factory?arrow_forward[Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 What is the MR function? What is the MC function of each facility? What is the MC function of the firm? Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?arrow_forward[Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 What is the MR function? What is the MC function of each facility? What is the MC function of the firm?arrow_forward
- [Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?arrow_forwardConsider a market comprised of three firms. Firm 1 produces and sells 23 units per period. Firm produces and sells 19 units per period, while firm 3’s periodic production and sales are 15 units. The (inverse) market demand is estimated to be: P = 100 − Q, where Q = total output = q1+ q2+ q3. Determine the market price and the elasticity of market demand as well as the market share of each firm.arrow_forwarda) A Dutch Brewing company produces Heineken beer, assume further that the marginal cost of producing a six pack of Heineken Beer is $6. Dutch Brewing company sells Heineken in two different Markets namely Africa and Europe whose inverse demand functions are ?? = 24 − ??and ?? = 12 − 0.5?? respectively.Requireda) Calculate the profit maximising Price-Quantity combinations in these two markets Africa and Europe.b) With this Pricing strategy calculate the profit. c) If competitive output (P=MC=6) for Africa is 18 and Europe is 12, Compute the deadweight losses in the two markets. d) Clearly illustrates that the third degree price discrimination is welfare improving over a single price policy. e) Suppose these markets were no longer separated. How would you construct the market demand in this situation? Would the monopolist’s profit-maximizing single price still be 15?arrow_forward