(a) Output of the home firm is y = d(q, p, I). Use the fact that d(q, p, I) is homogeneous of degree zero in (q, p, I) to show that dqq+dpp+dII = 0. Then use the assumption that the income elasticity of demand is unity to show that dpp/d = (η–1). (b) Using (a), compute the total change in home output y = d(q, p, I) as p increases along the home reaction curve. Show that output increases if 0 2.
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(a) Output of the home firm is y = d(q, p, I). Use the fact that d(q, p, I) is homogeneous of degree zero in (q, p, I) to show that dqq+dpp+dII = 0. Then use the assumption that the income
(b) Using (a), compute the total change in home output y = d(q, p, I) as p increases along the home reaction curve. Show that output increases if 0 2.
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- Consider the following demand equation for a good:p =(200) / (q + a)^2 where a is a constant. (a) Find dq/dp . (b) Find the expression for elasticity, η, such that only q and a appear. (Hint: Use the original function for demand to get rid of p). (c) Find a. such that at q = 20 demand is unitary elastic. (d) Classify the demand at q < 20 and q > 20 as elastic and inelastic for the a value found in the previouspart. Explain what happens to revenue as price increases for both q < 20 and q > 20.(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.In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function 2p + 3q = 180 at the price p = 18. (b) How will a price increase affect total revenue? Since the demand is inelastic, an increase in price will decrease the total revenue.Since the demand is elastic, an increase in price will decrease 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.Since the demand is elastic, an increase in price will increase the total revenue.
- In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function p2 + 2p + q = 36 at p = 5. (b) How will a price increase affect total revenue? Since the demand is unitary, there will be no change in the revenue with a price increase. 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. Since the demand is elastic, an increase in price will increase the total revenue. Since the demand is inelastic, an increase in price will increase the total revenue.In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function 2p + 3q = 270 at the price p = 15. (b) How will a price increase affect total revenue? 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.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.The demand function for a product is modeled by p = 400 − 2x, 0 ≤ x ≤ 200, where p is the price per unit (in dollars) and x is the number of units. Determine when the demand is elastic and inelastic. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Determine when the demand is of unit elasticity.
- Use the price-demand equation below to find the revenue function. Sketch a graph of the revenue function, and indicate the regions of inelastic and elastic demand. x-f(p)%3D108-12p R(p) =]In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function p +6g = 180 at (q, p) = (15,90). 90 (b) How will a price increase affect total revenue? 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. 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. O Since the demand is inelastic, an increase in price will increase the total revenue. XConsider 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).
- Suppose Government of Pakistan wants to put a curb on public smoking. Studies indicate that the price elasticity of demand for cigarettes is about 0.4. If a pack of cigarettes currently costs Rs.175 and the government wants to reduce smoking by 30 percent, by how much should it increase the price? Kindly type only percentage change in the box given below. Do not use percentage sign in the box. Also, do not use any plus or minus sign in the box.Suppose 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 = 528Elasticity of demand for a company is e d -2 for P = 2 and Q = 5. (a) Derive the linear inverse demand function (b) Would demand be more or less responsive for P = 1? Explain =