Managerial Economics Elasticity and Demand

1. Managerial Economics Elasticity and Demand The general linear demand for good X is estimated to be Q = 250,000 − 500P − 1.50M − 240PR where P is the price of good X, M is average income of consumers who buy good X, and PR is the price of related good R. The values of P, M, and PR are expected to be $200, $60,000, 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 4 percent increase 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 5 percent decrease in the price of related good R would affect demand for X, all other factors affecting the demand for X remaining the same. Dr. C. Chen

2. Managerial Economics Elasticity and Demand The general linear demand for good X is estimated to be Q = 250,000 − 500P − 1.50M − 240PR where P is the price of good X, M is average income of consumers who buy good X, and PR is the price of related good R. The values of P, M, and PR are expected to be $200, $60,000, 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. Q = 250,000 −500(200) −1.50(60,000) −240(100) = 36,000 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. The point formula E=(Q / P)(P/Q) where (Q / P) = −500 (i.e. the coefficient of P) P/Q = 200/36,000 So, E=(Q / P)(P/Q) = (−500)(200/36,000) = −2.78 (elastic) When the demand is elastic, increasing the price of X will lower the total revenue. Dr. C. Chen

3. Managerial Economics Elasticity and Demand The general linear demand for good X is estimated to be Q = 250,000 − 500P − 1.50M − 240PR where P is the price of good X, M is average income of consumers who buy good X, and PR is the price of related good R. The values of P, M, and PR are expected to be $200, $60,000, and $100, respectively. Use these values at this point on demand to make the following computations. c. Calculate the income elasticity of demand EM. Is good X normal or inferior? Explain how a 4 percent increase in income would affect demand for X, all other factors affecting the demand for X remaining the same. EM=(Q / M)(M/Q) where (Q / M) = −1.50 (i.e. the coefficient of M) and M/Q = 60,000/36,000. So, EM= (−1.50)(60,000/36,000) = −2.50 (< 0, inferior good). %Q = (%M)(EM) = 4%(−2.50) = −10% d. Calculate the cross- price elasticity EXR. Are the goods X and R substitutes or complements? Explain how a 5 percent decrease in the price of related good R would affect demand for X, all other factors affecting the demand for X remaining the same. EXR=(QX / PR)(PR/QX) where (QX / PR) = −240 (i.e. the coefficient of PR) and PR/QX = 100/36,000. So, EXR=(−240)(100/36,000) = − 0.67 (negative, complements) %QX = (%PR)(EXR) = (−5%)(−0.67) = 3.33% Dr. C. Chen