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. Qxs=−50+0.5(500)−5(30)=50 units.
b. Notice that although Qxs=−50+0.5(50)−5(30)=−175, negative output is impossible. Thus, quantity supplied is zero.
c. To find the supply function, insert Pz=30 into the supply equation to obtain
Qxs=−50+0.5Px−5(30)=−200+0.5Px. Thus, the supply equation is
Qxs=−200+0.5Px. To obtain the inverse supply equation, simply solve this equation for Px to obtain Px=400+2Qxs. The inverse supply function is graphed in Figure 2-1.
Price of X$1,600.0$1,400.0$1,200.0$1,000.0$800.0$600.0$400.0$200.0$0.0
0
100
200
300
400
S
500
Quantity of X
Figure 2-1
Managerial Economics and Business Strategy, 6e Page 1
4.
a. Good Y is a substitute for X, while good Z is a complement for X. b. X is a normal good.
111
c. Qxd=1,200−($4,910)+($5,900)−8($90)+($55,000)=5,000
2410
d. For the given income and prices of other goods, the demand function for good X
111d
is Qx=1,200−Px+($5,900)−8($90)+($55,000), which simplifies to
2410
dQx=7,455−0.5Px. To find the inverse demand equation, solve for price to
obtain 14,910−2Qxd. The demand function is graphed in Figure 2-2. Px=
Price of X
$14,910
$11,928$8,946$5,964$2,982
$0
0
1000
2000
3000
4000
5000
6000
7000
8000Quantity of X
Demand
Figure 2-2
5.
a. Solve the demand function for Px to obtain the following inverse demand
1
function: Px=115−Qxd.
4
d
b. Notice that when Px=$35, Qx=460−4(35)=320 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 (.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 (.5)($115−$25)360=$16,200). 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.
Page 2 Michael R. Baye
6.
a. Equating quantity supplied and quantity demanded yields the equation
1
50−P=P−10. Solving for P yields the equilibrium price of $40 per unit.
2
Plugging this into the demand equation yields the equilibrium quanity of 10 units (since quantity demanded at the equilibrium price is Qd=50−(40)=10). 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 (Qd=50−42=8), while quantity
1⎛⎞
supplied will increase to 11 units ⎜Qs=(42)−10=11⎟. That is, firms produce
2⎝⎠
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 Qd ⎜Q=(30)−10=5⎟. That is, while firms are willing to produce only 5 units 2⎝⎠ consumers want to buy 20 units at the ceiling price. Therefore, at the price ceiling of $30, only 5 units will be available to purchase. Since Qd>Qs, there is a shortage amounting to 20−5=15 units. Since only 5 units are available at a price of $30, the full economic price is the price such that quantity demanded equals the 5 available units: 5=50−PF. Solving yields the full economic price of $45. 7. a. The shortage is 3 units (since at a price of $6, Qd−Qs=4−1=3 units). The full economic price is $12. b. The surplus is 1.5 units (since at a price of $12, Qs−Qd=2.5−1=1.5 units. The cost to the government is $18 (computed as ($12)(1.5) = $18). c. The excise tax shifts supply vertically by $6. Thus, the new supply curve is S1 and the equilibrium price increases to $12. The price paid by consumers is $12 per unit, while the amount received by producers is this $12 minus the per unit tax. Thus, producers receive $6 per unit. After the tax, the equilibrium quantity sold is 1 unit. d. At the equilibrium price of $10, consumer surplus is .5($14−$10)2=$4. Producer surplus is .5($10−$2)2=$8. e. No. At a price of $2 no output is produced. Managerial Economics and Business Strategy, 6e Page 3 8. a. Equate quantity demanded and quantity supplied to obtain 7− 111Px=Px−. 242 Solve this equation for Px to obtain the equilibrium price of Px=10. The equilibrium quantity is 2 units (since at the equilibrium price quantity demanded 1 is Qd=7−(10)=2). The equilibrium is shown in Figure 2-3. 2 Price of X $20$18$16$14$12$10$8$6$4$2$0 0 1 2 3 4 SupplyDemand 5 6 Quantity of X Figure 2-3 b. A $6 excise tax shifts the supply curve up by the amount of the tax. Mathematically, this means that the intercept of the inverse supply function increases by $6. Before the tax, the inverse supply function is P=2+4QS. After the tax the inverse supply function is P=8+4Qs, and the after tax supply 1 function (obtained by solving for Qs in terms of P) is given by Qs=P−2. 4 Equating quantity demanded to after-tax quantity supplied yields 11 7−P=P−2. Solving for P yields the new equilibrium price of $12. 24 Plugging this into the demand equation yields the new equilibrium quantity, which is 1 unit. c. Since only one unit is sold after the tax and the tax rate is $6 per unit, total tax revenue is only $6. Page 4 Michael R. Baye 9. A technological breakthrough that reduces production costs will lead to a rightward shift in the supply curve for RAM chips, resulting in a lower equilibrium price of RAM chips. If in addition, income increases, the demand for RAM chips will also increase since they are a normal good. This increase in demand would tend to increase the price of RAM chips. The ultimate effect of both of these changes in supply and demand on the equilibrium price of RAM chips is indeterminate. Depending on the relative magnitude of the increase in supply and demand, the price you will pay for chips may rise or fall. The tariff reduces the supply of raw sugar, resulting in a higher equilibrium price of sugar. Since sugar is an input in making generic soft drinks, this increase in input prices will decrease the supply of generic soft drinks (putting upward pressure on the price of generic soft drinks and tend to reduce quantity). Coke and Pepsi’s advertising campaign will decrease the demand for generic soft drinks (putting downward pressure on the price of generic soft drinks and further reducing the quantity). For these reasons, the equilibrium quantity of generic soft drinks sold will decrease. However, the equilibrium price may rise or fall, depending on the relative magnitude of the shifts in demand and supply. No. this confuses a change in demand with a change in quantity demanded. Higher cigarette prices will not reduce (shift to the left) the demand for cigarettes. To find the equilibrium price and quantity, equate quantity demanded and quantity supplied to obtain 175−P=2P−200. Solving yields the new equilibrium price of $125 per pint. The equilibrium quantity is 50 units (since Qd=175−125=50 units 1 at that price). Consumer surplus is ($175−$125)×50=$1,250. Producer surplus is 2 1 ($125−$100)×50=$625. See Figure 2-4. 2 10. 11. 12. Price $200.0$175.0$150.0$125.0$100.0$75.0$50.0$25.0$0.0 0 10 20 30 40 50 60Quantity Producer Surplus = $625SupplyDemand Consumer Surplus = $1,250 Figure 2-4 Managerial Economics and Business Strategy, 6e Page 5 13. This decline represents a leftward shift in the supply curve for oil, and will result in an increase in the equilibrium price of crude oil. Since oil is an input in producing gasoline, this will decrease the supply of gasoline, resulting in a higher equilibrium price of gasoline and a lower equilibrium quantity. Furthermore, the higher price of gasoline will increase the demand for substitutes, such as small cars. The equilibrium price of small cars is likely to increase, as is the equilibrium quantity of small cars. Equating the initial quantity demanded and quantity supplied gives the equation: 250−5P=4P−110. Solving for price, we see that the initial equilibrium price is $40 per month. When the tax rate is reduced, equilibrium is determined by the following equation: 250−5P=4.171P−110. Solving, we see that the new equilibrium price is about $39.25 per month. In other words, a typical subscriber would save about 75 cents (the difference between $40.00 and $39.25). Dry beans and rice are probably inferior goods. If so, an increase in income shifts demand for these goods to the left, resulting in a lower equilibrium price. Therefore, G.R. Dry Foods will likely have to sell its products at a lower price. Figure 2-5 illustrates the relevant situation. The equilibrium price is $2.75, but the ceiling price is $0.75. Notice that, given the shortage of 12 million transactions caused by the ceiling price of $0.75, the average consumer spends an extra 12 minutes traveling to another ATM machine. Since the opportunity cost of time is $20 per hour, the non-pecuniary price of an ATM transaction is $4 (the $20 per hour wage times the fractional hour, 12/60, spent searching for another machine). Thus, the full economic price under the price ceiling is $4.75 per transaction. 14. 15. 16. ATM Fee Supply$4.75 $2.75$0.75 Shortage = 12 Million416Quantity (Millions of Transactions) Ceiling PriceDemand Figure 2-5 Page 6 Michael R. Baye 17. The unusually cold temperatures have caused a decrease in the supply of grapes used to produce Chilean wine, resulting in higher prices. These grapes are an input in making wine, so the supply of Chilean wine decreases and its price increases. Since California and Chilean wines are substitutes, an increase in the price of Chilean wine will increase the demand for Californian wines causing an increase in both the price and quantity of Californian wines. d Substituting Pdesktop=940into the demand equation yields Qmemory=9060−80Pmemory. 18. Similarly, substituting N=100into the supply equation S yieldsQmemory=1100+20Pmemory. The competitive equilibrium level of industry output dSand price occurs whereQmemory, which occurs when industry output =Qmemory **Qmemory=2692 (in thousands) and the market price is Pmemory=$79.60per unit. Since 100 competitors are assumed to equally share the market, Viking should produce d 26.92 thousand units. If Pdesktop=$1040, Qmemory=8960−80Pmemory. Under this condition, the new competitive equilibrium occurs when industry output is 2672 thousand units and the per-unit market price is $78.60. Therefore, Viking should produce 26.72 thousand units. Since demand decreased (shifted left) when the price of desktops increased, memory modules and desktops are complements. Managerial Economics and Business Strategy, 6e Page 7 19. Mid Towne IGA aimed to educate consumers that its contract with Local 655 union members was different than its rivals, so it engaged in informative advertising. Mid Towne IGA’s informative advertising increases demand (demand shifts rightward) resulting from (1) Local 655 union members locked out of rival supermarkets (2) consumers who are sympathetic to the Local 655 union, and (3) consumers who do not like the aggravation of picketing employees and other disruptions at the supermarket. This shift is depicted in Figure 2-6, where the equilibrium price and quantity both increase. It is unlikely that demand will remain high for Mid Towne IGA. As contracts are renegotiated and Local 655 union members are back to work, demand will likely settle back around its original level. Price S1 P2 P1 D2 D1 Q1 Q2 Quantity 20. Figure 2-6 The price gouging statute imposes an effective price ceiling on necessary commodities during times of emergencies; legally retailers cannot raise prices by a significant amount. When a natural disaster occurs, the demand for necessary commodities such as food and water can dramatically increase, as people want to be stocked-up on emergency items. In addition, since it can be difficult for retailers to receive shipments during emergency periods, the supply of these items is often reduced. Given the simultaneous reduction in supply and increase in demand, one would expect the price to increase during times of emergencies. However, since the price gouging statute acts as a price ceiling, the price will probably remain at its normal level, and a shortage will result. Page 8 Michael R. Baye 21. While there is undoubtedly a link between unemployment and crime, the governor’s plan is likely flawed since it only examines one side of the market. Raising the minimum wage will make the prospect of working more appealing for teenagers, but it will also have an effect on business owners and managers in the state. The minimum wage is a price floor. Raising the minimum wage will reduce the quantity demand for labor within the state, and result in a labor surplus. More teenagers will seek jobs, but fewer businesses will hire teenagers. In all likelihood, the governor’s plan will result in greater juvenile delinquency. Managerial Economics and Business Strategy, 6e Page 9 因篇幅问题不能全部显示，请点此查看更多更全内容