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- 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?The price elasticity of demand for air travel differs radically from first-class (1.3) to unrestricted coach (1.4) to restricted discount coach (1.9). What do these elasticities mean for optimal prices (fares) on a cross-country trip with incremental variable costs (marginal costs) equal to $120?(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?
- Using regression analysis on data from a field experiment, the demand curve for a product is estimated to be QXd = 1,200 − 3PX − 0.1PZ where Pz = $300. a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price below $140?Enter your response rounded to two decimal places. Own price elasticity: Demand is: . If the firm prices below $140, revenue will:What price should you set for a product? This week we’re learning a useful numerical rule. You’re brought in to consult for a business that currently has a Marginal Cost of $5 for its product. It sells its product to customers for $9 per unit and the estimated price elasticity of demand is -1.5. Is the current price optimal? Should it be raised or lowered? To what? Support your answer using the markup pricing equations from the text. (MR = P*(1+(1/elasticity)) combined with the MR=MC rule).Using regression analysis on data from a field experiment, the demand curve for a product is estimated to be QXd = 1,200 − 3PX − 0.1PZ where Pz = $300. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240? Enter your response rounded to one decimal place. Own price elasticity: Demand is: . If the firm prices above $240, revenue will:
- Using regression analysis on data from a field experiment, the demand curve for a product is estimated to be QXd = 1,200 − 3PX − 0.1PZ where Pz = $300. a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price below $140?Instruction: Enter your response rounded to two decimal places. Own price elasticity: Demand is: . If the firm prices below $140, revenue will: . b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240? Instruction: Enter your response rounded to one decimal place. Own price elasticity: Demand is: . If the firm prices above $240, revenue will: . c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z…The demand curve for product a is given as Q = 2000 - 20P. How many units will be sold at $10? At what price would 2,000 units be sold? 0 units? 1,500? Write equations for total revenue and marginal revenue (in terms of Q). What will be the total revenue at a price of $70? What will be the marginal revenue? What is the point elasticity at a price of $70? If price were to decrease to $60, what would total revenue, marginal revenue, and point elasticity be now? At what price would elasticity be unitary?2. After a careful statistical analysis, the Chidester Company concludes the demand function for its product is Q = 500 - 3P + 2Pr + 0.1Iwhere Q is the quantity demanded of its product, P is the price of its product, Pr is the price of its rival’s product, and I is per capita disposable income (in dollars). At present, P = $10, Pr = $20 and I = $6,000.a. What is the price elasticity of demand for the firm’s product?b. What is the income elasticity of demand for the firm’s product?c. What is the cross-price elasticity of demand between its product and its rival’s product?d. What is the implicit assumption regarding the population in the market?
- The demand curve for product a is given as Q = 2000 - 20P. a. How many units will be sold at $10? b. At what price would 2,000 units be sold? 0 units? 1,500? c. Write equations for total revenue and marginal revenue (in terms of Q). d. What will be the total revenue at a price of $70? What will be the marginal revenue? e. What is the point elasticity at a price of $70? f. If price were to decrease to $60, what would total revenue, marginal revenue, and point elasticity be now? g. At what price would elasticity be unitary?The Potomac Range Corporation manufactures a line of microwave ovens costing $500 each. Its sales have averaged about 6,000 units per month during the past year. In August, Potomac’s closest competitor, Spring City Stove Works, cut its price for a closely competitive model from $600 to $450. Potomac noticed that its sales volume declined to 4,500 units per month after Spring City announced its price cut. a. What is the arc cross elasticity of demand between Potomac’s oven and the competitive Spring City model? b. Would you say that these two firms are very close competitors? What other factors could have influenced the observed relationship? c. If Potomac knows that the arc price elasticity of demand for its ovens is −3.0, what price would Potomac have to charge to sell the same number of units it did before the Spring City price cut?The demand for Amazon 's Kindle e-reader can be approximated by q(p)=21e−0.01pmillionunitsperyear(50≤p≤400), where p is the price charged by Amazon. Obtain a formula for price elasticity of demand E, and calculate its value at the two endpoints of the given range of prices. Is the price that would maximize annual revenue within the range of prices shown? How would you know this without calculating that price?