Assigned prob - chap 2-5 -- 7th edition

# Assigned prob - chap 2-5 -- 7th edition - Baye Solutions...

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Baye Solutions Chapters 1 – 5 : Chapter 2 – 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 - = ). c. When price decreases to \$25, quantity demanded increases to 360 units, so consumer surplus increases to \$16,200 (computed as ( 29 ( 29 .5 \$115 \$25 360 \$16,200 - = ). 1

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d. So long as the law of demand holds, a decrease in price leads to an increase in consumer surplus, and vice versa. In general, there is an inverse relationship between the price of a product and consumer surplus. 6/. a. Equating quantity supplied and quantity demanded yields the equation 1 50 10 2 P P - = - . Solving for P yields the equilibrium price of \$40 per unit. Plugging this into the demand equation yields the equilibrium quanity of 10 units (since quantity demanded at the equilibrium price is ( 29 50 40 10 d Q = - = ). b. A price floor of \$42 is effective since it is above the equilibrium price of \$40. As a result, quantity demanded will fall to 8 units ( 29 8 42 50 = - = d Q , while quantity supplied will increase to 11 units ( 29 = - = 11 10 42 2 1 s Q . That is, firms produce 11 units but consumers are willing and able to purchase only 8 units. Therefore, at a price floor of \$42, 8 units will be exchanged. Since s d Q Q < there is a surplus amounting to 3 8 11 = - units. c.
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## This note was uploaded on 12/03/2011 for the course MANEC 387 taught by Professor Crawford,l during the Fall '08 term at BYU.

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Assigned prob - chap 2-5 -- 7th edition - Baye Solutions...

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