An oil-producing country estimates that the demand for oil (in millions of barrels per day) is D(p) = 9.5e-0.01p, where p is the price of a barrel of oil. (a) Determine the elasticity of demand function, E(p), for the oil.
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- 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?Consider the demand function for bicycles in South Florida: Q = 24 + 3Y – 1.2P where: Q is quantity demanded, Y is monthly income, and P is the price per unit. If/when P = $54, and Y = $2,300, (a) Find the quantity of bicycles that would be sold. (b) Calculate the amount of the seller's total revenue. (c) Compute the price-elasticity of demand (Ep) for bicycles. (d) Interpret your result in (c). (e) Compute the income-elasticity of demand (Ey) for bicycles. (f) Interpret your result in (e).
- Worldwide annual sales of smartphones over two year period were approximately q=-5p+3040 million phones at a selling price of $p per phone. (a) Obtain a formula for the price elasticity of demand E. E=_______ (b) in one of the years the actual selling price was $375 per phone. What was the corresponding price elasticity of demand? E=_______ The demand was going down by about _____% per 1% increase in price at that price level. (c) Use your formula for E to determine the selling price that would’ve resulted in the largest annual revenue. $_______ What would’ve been the resulting annual revenue? (Round your answer to two decimal places) $_____billionWorldwide annual sales on smart phones over a two year period were approximately q=-5p+3090 million phones at the selling price of $p per phone. (a) obtain a formula for the price elasticity of demand E. E=______ (b) in one of the years the actual selling price was $355 per phone. What was the corresponding price elasticity of demand? E=______ The demand is going (up/down) by about _____% per 1% increase in that price level.Worldwide annual sales of smartphones over a two year period were approximately q=-4p+3020 million phones at a selling price of $p per phone. (a) obtain a formula for the price elasticity of demand E E=_____ (b) in one of the years the actual selling price was $305 per phone. What was the corresponding price elasticity of demand? E=_____ (c) The demand was going down by about _____% per 1% increase in the price at that price level. (d) use your formula for E to determine the selling price that would have resulted in the largest annual revenue. $____ What would’ve been the resulting annual revenue? $____ billion
- Worldwide annual sales on smartphones over a two year period were approximately q=-4p+3,020 million phones at a selling price of $p per phone. (a)obtain a formula for the price elasticity of demanding e. E=_____ (b) in one of the years the actual selling price was $305 per phone. What was the corresponding price elasticity of demand? E=_____ What would’ve been the resulting annual Revenue? $_____billionTutorial Exercise Worldwide annual sales of smartphones in over a 5 year period were projected to be approximately q = −10p + 4,540 million phones at a selling price of $p per phone. (a) Obtain a formula for the price elasticity of demand E. (b) In one particular year the actual selling price was $277 per phone. What was the corresponding price elasticity of demand? Interpret your answer. (c) Use your formula for E to determine the selling price that would have resulted in the largest annual revenue. What, to the nearest $10 million, would have been the resulting annual revenue? Step 1 (a)Obtain a formula for the price elasticity of demand E. Recall that the price elasticity of demand E is the percentage rate of decrease of demand divided by the percentage increase of price, given by the formula. E = − dq dp · p q We are already given the formula q = −10p + 4,540 for the demand of smartphones (in millions). First, we find the derivative…If the demand, q , is q = V 1600 – 4 p² , (a) Find the Elasticity, E , in terms of p. (b) If the price is p = 10 , find the elasticity, E. (C) Which best describes the situation at this price?
- The demand for a product can be approximated by q = D(p) = 90e-0.01P, where p represents the price of the product, in dollars, and q %3D is the quantity demanded. (a) Find the elasticity function: E(p) = (b) Evaluate the elasticity at 6. E(6) = (c) Should the unit price be raised slightly from 6 in order to increase revenue? ? (d) Use the elasticity of demand to find the price p which maximizes revenue for this product. p = Round to three decimal places as needed.(a) Show that the function Q = a/P* , where a and c are constants, has a constant elasticity of demand: ɛg = -c. (b) (i) Determine the elasticity of demand for train journeys on a given route when the demand function is Q = 1200/P|.2, where Q is the number of fares in thousands. (ii) If the fare increases by 5%, use elasticity to calculate the percentage change in demand. (iii) If the fare decreases by 5%, use elasticity to calculate the percentage change in demand.Worldwide annual sales of smartphones over a two year period were approximately g = -6p + 3,060 million phones at a selling price of $p per phone. (a) Obtain a formula for the price elasticity of demand E. E = (b) In one of the years the actual selling price was $355 per phone. What was the corresponding price elasticity of demand? (Round your answer to two decimal places.) E = Interpret your answer. The demand was going ---Select-- v by about |% per 1% increase in price at that price level. (c) Use your formula for E to determine the selling price that would have resulted in the largest annual revenue. $ What would have been the resulting annual revenue? (Round your answer to two decimal places.) 2$ billion