CALCULATING ELASTICITY FROM THE DEMAND FUNCTION
Q1. The general linear demand for good X is estimated to be
Q = 18,000 - 175P + 0.35 M - 16P
whereP is the price of good X, M is average income of consumers who buy good X, and PRis the price of related good R. The values of P, M, and PRare expected to be $65, $52,000, and $100, respectively. Use these values at this point on demand to make the following computations.
a. Compute the quantity of good X demanded for the given values of P, M, and PR.
b. Calculate the price elasticity of demand E. At this point on the demand for X, is demand elastic, inelastic, or unitary elastic? How would increasing the price of X affect total revenue? Explain.
c. Calculate the income elasticity of demand EM. Is good X normal or inferior? Explain how a 1.75 percent decrease in income would affect demand for X, all other factors affecting the demand for X remaining the same.
d. Calculate the cross-price elasticity EXR. Are the goods X and R substitutes or complements? Explain how a 2.5 percent increase in the price of related good R would affect demand for X, all other factors affecting the demand for X remaining the same.
Q2. Using the following equation for the demand for a good or service, calculate the price elasticity of demand, cross elasticity with good x, and income elasticity.
Q = 8-2P+0.10I+Px
where Q is quantity demanded, P is the price of the product, I is income, and Px is the price of a related good. Assume that P=$10, I=100, and Px=20.
Q3. A firm has estimated the following demand function for its product:
Q = 10-2P+.20I+2A where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P=$5, I=50, and A=10. Based on this information, select the correct values for: quantity demanded; price elasticity of demand; income elasticity of demand; and advertising elasticity.
Q4. The demand curve for a product is given by Qdx = 1200 - 3Px - 0.1Pz, where Pz = $300.
a. What is the own price elasticity of demand when Px = $140? Is the demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $140?
b. What is the own price elasticity of demand when Px = $240? Is the demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above $240?
c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?
Q5. Suppose the demand function for a firm's product is given by
Qdx = 7 - 1.5Px + 2Py - 0.5M + A
where
Px = $15
Py = $6
M = $40,000
A = $350
a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic.
b. Determine the cross price elasticity of demand between good X and good Y, and state whether these goods are substitutes or complements.
c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good.
d. Determine the own advertising elasticity of demand.
Q6. Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if:
a. The price of good X decreases by 5%.
b. The price of good Y increases by 8%.
c. Advertising decreases by 4%.
d. Income increases by 4%.
Q7. Suppose the cross price elasticity of demand between goods X and Y is 4. How much would the price of good Y have to change in order to increase the consumption of good X by 20%?
Q8. You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross price elasticity of demand between product Y and X is -1.8. How much will your firm's total revenues (from both products) change if you increase the price of good X by 2%.