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Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006 William M. Boal
MIDTERM EXAMINATION #2 ANSWER KEY
VERSION A
I. MULTIPLE CHOICE
(1)c. (2)c. (3)b. (4)a. (5)d. (6)c. (7)c. (8)a. (9)d. (10)d. (11)a. (12)c. (13)e. (14)b. (15)e. (16)a. (17)d. (18)a. (19)a. (20)c. (21)d. (22)c. (23)b. (24)a. (25)e. (26)a. (27)b. (28)b. (29)a. (30)b. II. PROBLEMS (1) a. 200 = 10 q 1 + 5 q 2. b. MRSC = MU 2 /MU 1 = (q 1 -2) / q 2. c. q 1 * = 11, q 2 * = 18. (2) a. MRSC = q 1 / (2q 2 ). b. q 1 * = (2I) / (3p 1 ). c. q 2 * = I / (3p 2 ). (3) a. The function is indeed homogeneous of degree zero in income and prices. Justification:
1 2 1 2 1 1 2
p
I p
p
I p
q p p I
b. Own-price elasticity =
1 2 1 2 1 2 1 1 1
p I p p p I p q p p q
. An alternative derivation rewrites the demand function as. 6 18 1 *^2 1 ^1 p I p q Holding I and p 2 constant, this can be viewed as a power function in p 1. For all power functions, the exponent is the elasticity, so the own-price elasticity = -1. c. Good #1 is an ordinary good because the own-price elasticity is negative. d. Income elasticity = (^2) 1 (^112) 1 18 6
I p
I
p I p
I
q p
I
I
q
e. Good #1 is a normal good because the income elasticity is positive. f. Cross-price elasticity of demand for good #1 with respect the price of good #2 = 2 2 1 2 2 1 1 2 2 1 18
I p p p I p p q p p p q
g. Goods #1 and #2 are substitutes because the cross-price elasticity is positive.
III. CRITICAL THINKING
(1) A decrease in income of $50 would hurt the consumer more than an increase in the price of electricity to $0.15 per kilowatt-hour, because the loss of consumer surplus from the price increase would be less than $50 (assuming only that demand slopes down). In the diagram below, the loss of consumer surplus is shown as the area of the shaded trapezoid, which is clearly less than the area of the dotted rectangle. The area of the dotted rectangle is ($0.15-$0.10)x1000 = $50. (2) A decrease in the price of electricity to $0.05 per kilowatt-hour would benefit the consumer more than an increase in income of $50, because the gain of consumer surplus from the price decrease would be more than $50 (assuming only that demand slopes down). In the diagram below, the gain of consumer surplus is shown as the area of the shaded trapezoid, which is clearly more than the area of the dotted rectangle. The area of the dotted rectangle is ($0.10-$0.05)x1000 = $50. VERSION B I. MULTIPLE CHOICE (1)e. (2)b. (3)d. (4)c. (5)b. (6)d. (7)d. (8)c. (9)c. (10)a. (11)b. (12)a. (13)d. (14)c. (15)e. (16)a. (17)d. (18)a. (19)c. (20)d. (21)b. (22)c. (23)c. (24)b. (25)c. (26)d. (27)d. (28)d. (29)b. (30)b. II. PROBLEMS (1) a. 150 = 10 q 1 + 5 q 2. b. MRSC = MU 2 /MU 1 = (q 1 +2) / q 2. c. q 1 * = 14, q 2 * = 8.
Q
P
1000 Q
P
Demand curve Demand curve
b. q 1 * = (4I) / (5p 1 ). c. q 2 * = I / (5p 2 ). (3) a. The function is indeed homogeneous of degree zero in income and prices. Justification:
1 2 1 2 1 1 2
p
I p
p
I p
q p p I
b. Own-price elasticity =
1 2 1 2 1 2 1 1 1
p I p p p I p q p p q
. An alternative derivation rewrites the demand function as. 2 6 1 *^2 1 ^1 p I p q (^) Holding I and p 2 constant, this can be viewed as a power function in p 1. For all power functions, the exponent is the elasticity, so the own-price elasticity = -1. c. Good #1 is an ordinary good because the own-price elasticity is negative. d. Income elasticity = (^2) 1 (^112) 1 6 2
I p
I
p I p
I
q p
I
I
q
e. Good #1 is a normal good because the income elasticity is positive. f. Cross-price elasticity of demand for good #1 with respect the price of good #2 = 2 2 1 2 2 1 1 2 2 1 6
I p p p I p p q p p p q
g. Goods #1 and #2 are complements because the cross-price elasticity is negative. (Note that I-6p 2 > 0 if q 1 * > 0, as assumed at the beginning of the question.) III. CRITICAL THINKING Same as Version A. [end of answer key]
