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- Suppose the European Union (EU) was investigated and proposed a merger between two of the largest distillers of premium Scotch liquor. Based on some economists’ definition of the relevant market, the two firms proposing to merge enjoyed a combined market share of about two-thirds, while another firm essentially controlled the remaining share of the market. Additionally, suppose that the (wholesale) market elasticity of demand for Scotch liquor is −1.4 and that it costs $15.90 to produce and distribute each liter of Scotch. Based only on these data, provide quantitative estimates of the likely pre- and postmerger prices in the wholesale market for premium Scotch liquor. Instructions: Do not round intermediate calculations. Enter your final responses rounded to the nearest penny (two decimal places). Pre-merger price: $ Post-merger price: $arrow_forwardBy how much does the residual elasticity of demand facing a firm increase as the number of firms increases by one firm? The effect of a change in the number of firms on the residual elasticity of demand for a firm as a function of the number of firms (n), the market elasticity of demand (ɛ), and the supply elasticity of the other firms (no) is de; ||: (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. dn E.g., a subscript can be created with the _ character.)arrow_forwardSuppose the European Union (EU) was investigated and proposed a merger between two of the largest distillers of premium Scotch liquor. Based on some economists’ definition of the relevant market, the two firms proposing to merge enjoyed a combined market share of about two-thirds, while another firm essentially controlled the remaining share of the market. Additionally, suppose that the (wholesale) market elasticity of demand for Scotch liquor is −1.3 and that it costs $14.20 to produce and distribute each liter of Scotch.Based only on these data, provide quantitative estimates of the likely pre- and postmerger prices in the wholesale market for premium Scotch liquor.Instructions: Do not round intermediate calculations. Enter your final responses rounded to the nearest penny (two decimal places).Pre-merger price: $ Post-merger price: $arrow_forward
- In a statement to Gillette’s shareholders, its CEO indicated, “Despite several new product launches, Gillette’s advertising-to-sales declined dramatically . . . to 7.5 percent last year. Gillette’s advertising spending, in fact, is one of the lowest in our peer group of consumer product companies.” If the elasticity of demand for Gillette’s consumer products is similar to that of other firms in its peer group (which averages –4), what is Gillette’s advertising elasticity? Is Gillette’s demand more or less responsive to advertising than other firms in its peer group? Explainarrow_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_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_forward
- The 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_forwardSuppose 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_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] 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 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 Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?arrow_forward