(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.
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- Suppose that the price per unit p as a function of the demanda is p = 478.8 -0.9x. (a) Calculate the price elasticity of demand when x = 132. n = -2.44, therefore the demand is elastic (b) Calculate the price elasticity of demand when x = 425. n = -0.202 therefore the demand is inelastic (c) Find the demand that gives unit elasticity. x = 266.0 ✓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).The quantity demanded each week x (in units of a hundred) of the Mikado digital camera is related to the unit price p (in dollars) by the demand equation X = V 400 - 5p (0 sps 80). (a) Is the demand elastic or inelastic when p = 40? elastic O inelastic When p = 70? elastic inelastic (b) When is the demand unitary? p = (c) If the unit price is lowered slightly from $70, will the revenue increase or decrease? increase decrease (d) If the unit price is increased slightly from $40, will the revenue increase or decrease? increase decrease
- In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function p + 69 - 300 at (9, p) = (25, 150). (b) How will a price increase affect total revenue? O Since the demand is elastic, an increase in price will decrease the total revenue. Since the demand is inelastic, an increase in price will decrease the total revenue. O Since the demand is elastic, an increase in price will increase the total revenue. Since the demand is unitary, there will be no change in the revenue with a price increase. Since the demand is inelastic, an increase in price will increase the total revenue. Need Help? Read It Watch It4x+200 A garden shop determines the demand function q = D(x) = 30x+9 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant. (a) Find the elasticity. (b) Find the elasticity when x = 2. (c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity isCurrently, 10,000 people take city buses each day and pay 2 dollars for a ticket. The number of people taking city buses at price p dollars per ticket is given X = 5000 6-p (a) Evaluate the elasticity at 5. E(5) (b) Currently, the price per ticket is 2 dollars. Should the price be raised in order to increase revenue? Enter 1 for Yes or 2 for No. answer = (c) For what value of p, the demand is unitary.p = = (d) What is the maximum revenue? Revenue =
- The demand for wooden chairs can be modeled as D(p) = -0.01p + 4.25 million chairs where p is the price (in dollars) of a chair. (a) Find the point of unit elasticity. The point of elasticity occurs whenp = $ and D(p) = million chairs. (b) For what prices is demand elastic? For what prices is demand inelastic? Demand is inelastic forThe demand for wooden chairs can be modeled as D(p) = -0.01p + 6.75 million chairs where p is the price (in dollars) of a chair. (a) Find the point of unit elasticity. The point of elasticity occurs when p = $ and D(p): = (b) For what prices is demand elastic? For what prices is demand inelastic? Demand is inelastic for < p < ■ Demand is elastic for million chairs.4x + 500 10x +9 the number of plants sold per day when the price is x dollars per plant. A garden shop determines the demand function q = D(x) = (a) Find the elasticity. (b) Find the elasticity when x=3. (c) At $3 per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity is during early summer for tomato plants where q is M IrSuppose that the price per unit p as a function of the demand is p=√1056 - 2x. (a) Calculate the price elasticity of demand when = 305. 305 therefore the demand is elastic 1056 - 2(305) n = (b) Calculate the price elasticity of demand when x = 406. 406 1056 - 2(406) η = therefore the demand is inelastic (c) Find the demand x that gives unit elasticity. x = 528If 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?2x + 500 A garden shop determines the demand function q =| D(x) = during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant. 20x +9 (a) Find the elasticity. (b) Find the elasticity when x=3. (c) At $3 per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity is. (b) When x = 3, the elasticity is| (Simplify your answer. Type an integer or a fraction) (c) Fill in the blank below. At $3 per plant, a small increase in price will cause the total revenue toSEE MORE QUESTIONSRecommended textbooks for you
