Chap002 - Chapter 2: Answers to Questions and Problems 1....

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Chapter 2: Answers to Questions and Problems 1. a. Since X is a normal good, an increase in income will lead to an increase in the demand for X (the demand curve for X will shift to the right). b. Since Y is an inferior good, a decrease in income will lead to an increase in the demand for good Y (the demand curve for Y will shift to the right). c. Since goods X and Y are substitutes, a decrease in the price of good Y will lead to a decrease in the demand for good X (the demand curve for X will shift to the left). d. No. The term “inferior good” does not mean “inferior quality,” it simply means that income and consumption are inversely related. 2. a. The supply of good X will decrease (shift to the left). b. The supply of good X will decrease. More specifically, the supply curve will shift vertically up by exactly $1 at each level of output. c. The supply of good X will decrease. More specifically, the supply curve will rotate counter-clockwise. d. The supply curve for good X will increase (shift to the right). 3. a. ( 29 ( 29 50 0.5 500 5 30 50 s x Q = - + - = units. b. Notice that although ( 29 ( 29 50 0.5 50 5 30 175 s x Q = - + - = - , negative output is impossible. Thus, quantity supplied is zero. c. To find the supply function, insert 30 z P = into the supply equation to obtain ( 29 50 0.5 5 30 200 0.5 s x x x Q P P = - + - = - + . Thus, the supply equation is 200 0.5 s x x Q P = - + . To obtain the inverse supply equation, simply solve this equation for x P to obtain 400 2 s x x P Q = + . The inverse supply function is graphed in Figure 2-1. $0.0 $200.0 $400.0 $600.0 $800.0 $1,000.0 $1,200.0 $1,400.0 $1,600.0 0 100 200 300 400 500 Quantity of X Price of X S Figure 2-1 2-1
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4. a. Good Y is a substitute for X, while good Z is a complement for X. b. X is a normal good. c. ( 29 ( 29 ( 29 ( 29 000 , 5 000 , 55 $ 10 1 90 $ 8 900 , 5 $ 4 1 910 , 4 $ 2 1 200 , 1 = + - + - = d x Q d. For the given income and prices of other goods, the demand function for good X is ( 29 ( 29 ( 29 1 1 1 1,200 $5,900 8 $90 $55,000 , 2 4 10 d x x Q P = - + - + which simplifies to 7,455 0.5 d x x Q P = - . To find the inverse demand equation, solve for price to obtain 14,910 2 . d x x P Q = - The demand function is graphed in Figure 2-2. $0 $2,982 $5,964 $8,946 $11,928 $14,910 0 1000 2000 3000 4000 5000 6000 7000 8000 Quantity of X Price of X Demand Figure 2-2 5. a. Solve the demand function for x P to obtain the following inverse demand function: 1 115 4 d x x P Q = - . b. Notice that when $35 x P = , ( 29 460 4 35 320 d x Q = - = units. Also, from part a, we know the vertical intercept of the inverse demand equation is 115. Thus, consumer surplus is $12,800 (computed as ( 29 ( 29 .5 $115 $35 320 $12,800 - = ).
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Chap002 - Chapter 2: Answers to Questions and Problems 1....

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