Technical Problem 10 Chapter 6
10. Use the figure below to answer the following questions:
a. Calculate price elasticity at point S using the method E=ΔQ × P
E=ΔQ P+ 90 100
ΔP × Q= −300× 60 =−0.5
b. Calculate price elasticity at point S using the method E=P P−A
E=P × 100 = 100 =−0.5
P−A 100−300 −200
c. Compare the elasticities in parts a and b. Are they equal? Should they be equal? The values of E in parts a and b are equal, as they should be, because the two methods are mathematically equivalent formulas for computing price elasticity.
d. Calculate price elasticity at point R.
E= P × 400 = 400 = −1. 33
P−A 400−700 −300
e. Which method did you use to compute E in part d, E=ΔQ × P or E= P ? Why?
At point R, Q is not given, and ΔQ/ΔP cannot be computed. Thus E = P is the only method to use at point R.
Technical Problem 2 Chapter 7
2. The estimated market demand for good X is
Qˆ = 70 – 3.5P – 0.6M + 4PZ
where Qˆ is the estimated number of units of good X demanded, P is the price of the good, M is income, and PZ is the price of related good Z. (All parameter estimates are statistically significant at the 1 percent level.) a. Is X a normal or an inferior good? Explain.
X is an inferior good. A negative parameter estimate for income (–0.6) means the quantity of X demanded decreases (increases) when income increases (decreases). b. Are X and Z substitutes or complements? Explain.
X and Z are substitutes. A positive parameter estimate for the price of Z (4) means that the quantity of X demanded increases (decreases) when the price of Z increases (decreases). c. At P = 10, M = 30, and PZ = 6, compute estimates for the price (Ê), income (ÊM), and cross- price elasticities (ÊXZ). Qˆ = 70 – 3.5(10) – 0.6(30) 1 4(6) = 41.0
Eˆ = bˆ (P/Q) = –3.5(10/41) = –0.85
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