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1、Chapter 2: The Basics of Supply and DemandEXERCISES1. Suppose the demand curve for a product is given by Q = 300 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Q = 3P 50.a. If I = 25, find the market clearing price and quantity for the product.Given I = 25,
2、the demand curve becomes Q = 300 - 2P + 4(25), or Q = 400 - 2P. Setting demand equal to supply we can solve for P and then Q:400 - 2P = 3P - 50P = 90Q = 220.b. If I = 50, find the market clearing price and quantity for the product.Given I = 50, the demand curve becomes Q = 300 - 2P + 4(50), or Q = 5
3、00 - 2P. Setting demand equal to supply we can solve for P and then Q:500 - 2P = 3P - 50P = 110Q = 280.c. Draw a graph to illustrate your answers.It is easier to draw the demand and supply curves if you first solve for the inverse demand and supply functions, i.e., solve the functions for P. Demand
4、in part (a) is P = 200 - 0.5Q and supply is P = 16.67 + 0.333Q. These are shown on the graph as Da and S. Equilibrium price and quantity are found at the intersection of these demand and supply curves. When the income level increases in part (b), the demand curve shifts up and to the right. Inverse
5、demand is P = 250 - 0.5Q and is labeled Db. The intersection of the new demand curve and original supply curve is the new equilibrium point.2. Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:Price(Dollars)Demand(Millions)
6、Supply(Millions) 602214 80201610018181201620a. Calculate the price elasticity of demand when the price is $80 and when the price is $100.With each price increase of $20, the quantity demanded decreases by 2 million. Therefore,.At P = 80, quantity demanded is 20 million and thusSimilarly, at P = 100,
7、 quantity demanded equals 18 million andb. Calculate the price elasticity of supply when the price is $80 and when the price is $100.With each price increase of $20, quantity supplied increases by 2 million. Thus,At P = 80, quantity supplied is 16 million andSimilarly, at P = 100, quantity supplied
8、equals 18 million andc. What are the equilibrium price and quantity?The equilibrium price is the price at which the quantity supplied equals the quantity demanded. As we see from the table, the equilibrium price is P* = $100 and the equilibrium quantity is Q* = 18 million.d. Suppose the government s
9、ets a price ceiling of $80. Will there be a shortage, and if so, how large will it be?With a price ceiling of $80, price cannot be above $80, so the market cannot reach its equilibrium price of $100. At $80, consumers would like to buy 20 million, but producers will supply only 16 million. This will
10、 result in a shortage of 4 million.3. Refer to Example 2.5 (page 38) on the market for wheat. In 1998, the total demand for U.S. wheat was Q = 3244 283P and the domestic supply was QS = 1944 + 207P. At the end of 1998, both Brazil and Indonesia opened their wheat markets to U.S. farmers. Suppose tha
11、t these new markets add 200 million bushels to U.S. wheat demand. What will be the free-market price of wheat and what quantity will be produced and sold by U.S. farmers? Note: The answer at the end of the book (first printing) used the wrong demand curve to find the new equilibrium quantity. The co
12、rrect answer is given below.If Brazil and Indonesia add 200 million bushels of wheat to U.S. wheat demand, the new demand curve will be Q + 200, orQD = (3244 - 283P) + 200 = 3444 - 283P.Equate supply and the new demand to find the new equilibrium price.1944 + 207P = 3444 - 283P, or490P = 1500, and t
13、hus P = $3.06 per bushel.To find the equilibrium quantity, substitute the price into either the supply or demand equation. Using demand,QD = 3444 - 283(3.06) = 2578 million bushels.4. A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound. Unlimited quantities
14、 are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows:U.S. SupplyU.S. Demand Price(Million Lbs.)(Million Lbs.) 3 2 34 6 4 28 9 6 22 12 8 16 15 10 10 18 12 4a. What is the equation for demand? What is the equa
15、tion for supply?The equation for demand is of the form Q = a - bP. First find the slope, which is . You can figure this out by noticing that every time price increases by 3, quantity demanded falls by 6 million pounds. Demand is now Q = a - 2P. To find a, plug in any of the price and quantity demand
16、ed points from the table. For example: Q = 34 = a - 2(3) so that a = 40 and demand is Q = 40 - 2P.The equation for supply is of the form Q = c + dP. First find the slope, which is You can figure this out by noticing that every time price increases by 3, quantity supplied increases by 2 million pound
17、s. Supply is now To find c, plug in any of the price and quantity supplied points from the table. For example: so that c = 0 and supply is b. At a price of $9, what is the price elasticity of demand? What is it at a price of $12?Elasticity of demand at P = 9 is .Elasticity of demand at P = 12 is .c.
18、 What is the price elasticity of supply at $9? At $12?Elasticity of supply at P = 9 is .Elasticity of supply at P = 12 is .d. In a free market, what will be the U.S. price and level of fiber imports?With no restrictions on trade, the price in the United States will be the same as the world price, so
19、 P = $9. At this price, the domestic supply is 6 million lbs., while the domestic demand is 22 million lbs. Imports make up the difference and are 16 million lbs.5. Much of the demand for U.S. agricultural output has come from other countries. In 1998, the total demand for wheat was Q = 3244 283P. O
20、f this, total domestic demand was QD = 1700 107P, and domestic supply was QS = 1944 + 207P. Suppose the export demand for wheat falls by 40 percent.a. U.S. farmers are concerned about this drop in export demand. What happens to the free-market price of wheat in the United States? Do the farmers have
21、 much reason to worry?Before the drop in export demand, the market equilibrium price is found by setting total demand equal to domestic supply:3244 - 283P = 1944 + 207P, orP = $2.65.Export demand is the difference between total demand and domestic demand: Q = 3244 - 283P minus QD = 1700 - 107P. So e
22、xport demand is originally Qe = 1544 - 176P. After the 40 percent drop, export demand is only 60 percent of the original export demand. The new export demand is therefore, Qe = 0.6Qe = 0.6(1544 - 176P) = 926.4 - 105.6P. Graphically, export demand has pivoted inward as illustrated in the figure below
23、.The new total demand becomesQ = QD + Qe = (1700 - 107P) + (926.4 - 105.6P) = 2626.4 - 212.6P.Equating total supply and the new total demand,1944 + 207P = 2626.4 - 212.6P, orP = $1.63,which is a significant drop from the original market-clearing price of $2.65 per bushel. At this price, the market-c
24、learing quantity is about Q = 2281 million bushels. Total revenue has decreased from about $6609 million to $3718 million, so farmers have a lot to worry about.b. Now suppose the U.S. government wants to buy enough wheat to raise the price to $3.50 per bushel. With the drop in export demand, how muc
25、h wheat would the government have to buy? How much would this cost the government?With a price of $3.50, the market is not in equilibrium. Quantity demanded and supplied areQ = 2626.4 - 212.6(3.50) = 1882.3, and QS = 1944 + 207(3.50) = 2668.5. Excess supply is therefore 2668.5 - 1882.3 = 786.2 milli
26、on bushels. The government must purchase this amount to support a price of $3.50, and will have to spend $3.50(786.2 million) = $2751.7 million.6. The rent control agency of New York City has found that aggregate demand is QD = 160 8P. Quantity is measured in tens of thousands of apartments. Price,
27、the average monthly rental rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. The citys board of realtors acknowledges that this is a good demand est
28、imate and has shown that supply is QS = 70 + 7P.a. If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who cannot find an apartment leave the c
29、ity?Set supply equal to demand to find the free-market price for apartments:160 - 8P = 70 + 7P, or P = 6, which means the rental price is $600 since price is measured in hundreds of dollars. Substituting the equilibrium price into either the demand or supply equation to determine the equilibrium qua
30、ntity:QD = 160 - 8(6) = 112andQS = 70 + 7(6) = 112.The quantity of apartments rented is 1,120,000 since Q is measured in tens of thousands of apartments. If the rent control agency sets the rental rate at $300, the quantity supplied would be 910,000 (QS = 70 + 7(3) = 91), a decrease of 210,000 apart
31、ments from the free-market equilibrium. Assuming three people per family per apartment, this would imply a loss in city population of 630,000 people. Note: At the $300 rental rate, the demand for apartments is 1,360,000 units, and the resulting shortage is 450,000 units (1,360,000 - 910,000). Howeve
32、r, excess demand (the shortage) and lower quantity demanded are not the same concept. The shortage of 450,000 units is the difference between the number of apartments demanded at the new lower price (including the number demanded by new people who would have moved into the city), and the number supp
33、lied at the lower price. But these new people will not actually move into the city because the apartments are not available. Therefore, the city population will fall by 630,000, which is due to the drop in the number of apartments available from 1,120,000 (the old equilibrium value) to 910,000. b. S
34、uppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50 percent of any long-run increases in apartment offerings come from new construction, how many apartments are constructed?At a rental rate of $900,
35、 the demand for apartments would be 160 - 8(9) = 88, or 880,000 units, which is 240,000 fewer apartments than the original free-market equilibrium number of 1,120,000. Therefore, no new apartments would be constructed.7. In 1998, Americans smoked 470 billion cigarettes, or 23.5 billion packs of ciga
36、rettes. The average retail price was $2 per pack. Statistical studies have shown that the price elasticity of demand is 0.4, and the price elasticity of supply is 0.5. Using this information, derive linear demand and supply curves for the cigarette market. Let the demand curve be of the form Q = a -
37、 bP and the supply curve be of the form Q = c + dP, where a, b, c, and d are positive constants. To begin, recall the formula for the price elasticity of demand.We know the demand elasticity is -0.4, P = 2, and Q = 23.5, which means we can solve for the slope, -b, which is DQ/DP in the above formula
38、. To find the constant a, substitute for Q, P, and b in the demand function to get 23.5 = a - 4.7(2) and a = 32.9. The equation for demand is therefore Q = 32.9 - 4.7P. To find the supply curve, recall the formula for the elasticity of supply and follow the same method as above:To find the constant
39、c, substitute for Q, P, and d in the supply function to get 23.5 = c + 5.875(2) and c = 11.75. The equation for supply is therefore Q = 11.75 + 5.875P.8. In Example 2.8 we examined the effect of a 20-percent decline in copper demand on the price of copper, using the linear supply and demand curves d
40、eveloped in Section 2.6. Suppose the long-run price elasticity of copper demand were 0.75 instead of 0.5.a. Assuming, as before, that the equilibrium price and quantity are P* = $2 per pound and Q* = 12 million metric tons per year, derive the linear demand curve consistent with the smaller elastici
41、ty.Following the method outlined in Section 2.6, we solve for a and b in the demand equation QD = a - bP. Because -b is the slope, we can use -b rather than DQ/DP in the elasticity formula. Therefore, . Here ED = -0.75 (the long-run price elasticity), P* = 2 and Q* = 12. Solving for b, or b = 0.75(6
42、) = 4.5.To find the intercept, we substitute for b, QD (= Q*), and P (= P*) in the demand equation:12 = a - 4.5(2), or a = 21.The linear demand equation is thereforeQD = 21 - 4.5P.b. Using this demand curve, recalculate the effect of a 20-percent decline in copper demand on the price of copper.The n
43、ew demand is 20 percent below the original (using our convention that quantity demanded is reduced by 20% at every price); therefore, multiply demand by 0.8 because the new demand is 80 percent of the original demand:= (0.8)(21 - 4.5P) = 16.8 - 3.6P.Equating this to supply,16.8 - 3.6P = -6 + 9P, orP
44、 = $1.81.With the 20-percent decline in demand, the price of copper falls from $2.00 to $1.81 per pound. The decrease in demand therefore leads to a drop in price of 19 cents per pound, a 9.5 percent decline.9. In Example 2.8 (page 52), we discussed the recent increase in world demand for copper, du
45、e in part to Chinas rising consumption.a. Using the original elasticities of demand and supply (i.e. ES = 1.5 and ED = 0.5), calculate the effect of a 20-percent increase in copper demand on the price of copper.The original demand is Q = 18 - 3P and supply is Q = -6 + 9P as shown on page 51. The 20-
46、percent increase in demand means that the new demand is 120 percent of the original demand, so the new demand is QD = 1.2Q. QD = (1.2)(18 - 3P) = 21.6 - 3.6P. The new equilibrium is where QD equals the original supply:21.6 - 3.6P = -6 + 9P.The new equilibrium price is P* = $2.19 per pound. An increa
47、se in demand of 20 percent, therefore, increases price by 19 cents per pound, or 9.5 percent.b. Now calculate the effect of this increase in demand on the equilibrium quantity, Q*.Using the new price of $2.19 in the supply curve, the new equilibrium quantity is Q* = -6 + 9(2.19) = 13.71 million metr
48、ic tons (mmt) per year, an increase of 1.71 mmt per year. Except for rounding, you get the same result by plugging the new price of $2.19 into the new demand curve. So an increase in demand of 20 percent increases quantity by 1.71 mmt per year, or 14.3 percent.c. As we discussed in Example 2.8, the U.S. produc