Daniel l. Rubinfeld

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46 Part 1 Introduction: Markets and Prices where P* and Q* are the equilibrium price and quantity for which we have data and to which we want to fit the curves. Because we have numbers for Es, ED, P*, and Q*, we can substihlte these numbers in equations (2.5a) and (2.5b) and solve for band d. II Step 2: Since we now know band d, we can substitute these numbers, as well as P* and Q*, into equations (2.4a) and (2.4b) and solve for the remaining constants a and c. For example, we can rewrite equation (2.4a) as a = Q* + bP* and then use our data for Q* and P*, together with the number we calculated in Step 1 for b, to obtain a. Let's apply this procedure to a specific example: long-run supply and demand for the world copper market. The relevant numbers for this market are as follows: 10 Quantity Q* = 7.5 million metric tons per year (mmt/yr) Price P* = 75 cents per pound Elasticity of supply = 1.6 Elasticity of demand ED = - 0.8 (The price of copper has fluchlated during the past decade between 50 cents and more than $1.30, but 75 cents is a reasonable average price for 1980-1990.) We begin with the supply curve equation (2.4b) and use our two-step procedure to calculate numbers for c and d. The long-run price elasticity of supply is 1.6, P* = .75, and Q* = 7.5. II Step 1: Substitute these numbers in equation (2.5b) to determine d: so that d 1.6/0.1 = 16. 1.6 d(0.75/7.5) = O.ld, II Step 2: Substitute this number for d, together with the numbers for P* and Q*, into equation (2.4b) to determine c: 7.5 = c + (16)(0.75) = c + 12, so that c = 7.5 - 12 = - 4.5. We now know c and d, so we can write our supply curve: Supply: Q - 4.5 + 16P We can now follow the same steps for the demand curve equation (2.4a). An estimate for the long-run elasticity of demand is - 0.8. First, substitute this number, as well as the values for P* and Q*, into equation (2.5a) to determine b: - 0.8 = b(0.75/7.5) = O.lb, lOT~e supply elasticity is for primary supply, as shown in Table 2.3. The demand elasticity is a regIOnally aggregated number based on Fisher, Cootner, and Baily, "An Econometric ModeL" Quantities refer to what was then the non-Communist world market. f 2 The Basics of Supply and Demand so that b = 0.8/0.1 = 8. Second, substitute this value for b and the values for P* and Q* in equation (2.4a) to determine a: 7.5 = a (8)(0.75) a - 6, so that a = 7.5 + 6 = 13.5. Thus, our demand curve is Dell/alld: Q = 13.5 - 8P To check that 'Ne have not made a mistake, let's set the quantity supplied equal to the quantity demanded and calculate the resulting equilibrium price: Supply = - 4.5 + 16P = 13.5 16P + 8P = 13.5 + 4.5 8P = Demand or P = 18/24 = 0.75, which is indeed the equilibrium price vvith which we began. Although we have written supply and demand so that they depend only on price, they could easily depend on other variables as welL Demand, for example, might depend on income as well as price. We 'would then write demand as Q = a bP + fI, (2.6) where I is an index of aggregate income or GNP. For example, I might equal 1.0 in a base year and then rise or fall to reflect percentage increases or decreases in aggregate income. For our copper market example, a reasonable estimate for the long-run income elasticity of demand is 1.3. For the linear demand curve (2.6), we can then calculate f by using the formula for the incom.e elasticity of demand: E = (I/Q)PQ/j.I). Taking the base value of I as 1.0, ,,",'e haw 1.3 = (1.0/7.5)(f) TI1Usf = (1.3)(7.5)/(1.0) = 9.75. Finally, substituting the values b = 8,f = 9.75, P* = 0.75, and Q* = 7.5 into equation (2.6), we can calculate that a must equal 3.75. We have seen how to fit linear supply and demand curves to data. Now, to see how these curves can be used to analyze markets, let's look at Example 2.7, vvhich deals with the behavior of copper prices, and Example 2.8, ''"''hich concerns the world oil market. After reaching a level of about $1.00 per pound in 1980, the price of copper fell sharply to about 60 cents per pound in 1986. In real (inflation-adjusted) terms, this price was even lower than during the Great Depression 50 years ==
48 Part 1 Introduction: Markets and Prices earlier. Only in 1988-1989 did prices recO\'er somevvhat, largely as a result of strikes by miners in Peru and Canada and disrupted supplies. Figure 2.19 shows the beha\'ior of copper prices in 1965-1999 in both real and nominal terms. Worldwide recessions in 1980 and 1982 contributed to the decline of copper prices; as mentioned above, the income elasticity of copper demand is about 1.3. But copper demand did not pick up as the industrial economies recovered during the mid-1980s. Instead, the 1980s saw a steep decline in demand. This decline occurred for two reasons. First, a large part of copper consumption is for the construction of equipment for electric pO\ver generation and transmission. But by the late 1970s, the growth rate of electric power generation had fallen dramatically in most industrialized countries. In the United States, for example, the growth rate fell from over 6 percent per annum in the 1960s and early 1970s to less than 2 percent in the late 1970s and 1980s. This decline meant a big drop in what had been a major source of copper demand. Second, in the 1980s, other materials, such as aluminum and fiber optics, were increasingly substituted for copper. 140 Copper producers are concerned about the possible effects of further declines in demand, particularly as strikes end and supplies increase. Declining demand, of course, will depress prices. To find out how much, we can use the linear supply and demand curves that we just derived. Let's calculate the effect on price of a 20-percent decline in demand. Because ,ve are not concerned here with the effects of GNP growth, we can leave the income term tl out of demand. . We want to shift the demand curve to the left by 20 percent. In other words, we want the quantity demanded to be 80 percent of what it would be otherwise for every value of price. For our linear demand curve, we simply multiply the right-hand side by 0.8: Q = (0.8)(13.5 8P) = 10.8 - 6AP Supply is again Q = - 4.5 + 16P. Now we can equate the quantity supplied and the quantity demanded and solve for price: 16P + 6.4P = 10.8 + 4.5, or P = 15.3/22.4 68.3 cents per pound. A decline in demand of 20 percent, therefore, entails a drop in price of roughly 7 cents per pound, or 10 percent,l1 2 The Basics of Supply and Demand 49 120 "0 ~ 100 5.. 80 t; c... 11 c 2- '"' 60 ,~ '"' c::: 40 20 Real Price (51972) 10 TTl -;-111;-;-1-;--''-Tl;-;----'-I'1;-;-1---'-1-,"-'-'---'1'I-,-,-,----,--;--r--,--.--,----,-.,..,--r-.-~ 1965 1970 1975 1980 1985 1990 1995 2000 Copper prices are shown in both nominal (no adjustment for inflation) and real (inflation-adjusted) terms. In real terms, copper prices declined steeply from the ~arly 1970s through the mid-1980s as demand felL In 1988-1990, copper prices rose ill response to supply disruptions caused by strikes in Peru and Canada but later fell after the strikes ended. Prices declined Since the early 1970s, the world oil market has been buffeted by the OPEC cartel and by political turmoil in the Persian Gulf. In 1974, by collectively resh'aining output, OPEC (the Organization of Peh'oleum Exporting COlmh'ies) pushed world oil prices well above what they would have been in a competitive market. OPEC could do this because it accounted for much of vwrld oil production. During 1979-1980, oil prices shot up again, as the Iranian revolution and the outbreak of the Iran-Iraq war sharply reduced Iranian and Iraqi production. During the 1980s, the price gradually declined, as demand fell and competitive (i.e., non-OPEC) supply rose in response to price. Prices remained relatively stable during 1988-1999, except for a temporary spike in 1990 following the Iraqi invasion of Kmvait, a decline during 1997-1998, and an increase in 1999. Figure 2.20 shO\·..,s the world price of oil from 1970 to 1999, in both nominal and real terms. The Persian Gulf is one of the less stable regions of the world, which has led to concern over the possibility of new oil supply disruptions and sharp increases in oil prices. What would happen to oil prices-in both the short rill) and longer run-if a war or revolution in the Persian Gulf caused a sharp cutback in oil production Let's see how simple supply and demand curves can be used to predict the outcome of such an event. 11 You can obtain recent data and learn more about the beha\'ior of copper prices by accessing the Web site of the US Geological Survey at ",i:'d·.'!~ L'ell
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Daniel l. Rubinfeld

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