We have discussed the meaning and characteristics of supply and demand, but our treatment has been largely qualitative. To use supply and demand curves to analyze and predict the effects of changing market conditions, we must begin to attach numbers to them. For example, to see how a 50 percent reduction in the supply of Brazilian coffee may affect the world price of coffee, we need to write down actual supply and demand curves and then calculate how those curves will shift, and how price will then change.

In this section we will see how to do simple "back of the envelope" calculations with linear supply and demand curves. Although they are often an approximation to more complex curves, we use linear curves because they are the easiest to work with. It may come as a surprise, but one can do some in-

During 1980, however, prices temporarily went just above $2.00 per pound as a result of export quotas imposed under the International Coffee Agreement (ICA). The ICA is essentially a cartel agreement implemented by the coffee-producing countries in 1968. It has been largely ineffective and in most years has had little impact on price. We discuss cartel pricing in detail in Chapter 12.

formative economic analyses on the back of a small envelope with a pencil and a pocket calculator.

First, we must learn how to "fit" linear demand and supply curves to market data. (By this we do not mean statistical fitting in the sense of linear regression or other statistical techniques, which we discuss later in the book.) Suppose we have two sets of numbers for a particular market. First are the price and quantity that generally prevail in the market (i.e., the price and quantity that prevail "on average," or when the market is in equilibrium, or when market conditions are "normal"). We call these numbers the equilibrium price and quantity, and we denote them by P* and Q*. Second are the price elasticities of supply and demand for the market (at or near the equilibrium), which we denote by Es and Ed, as before.

These numbers might come from a statistical study done by someone else; they might be numbers that we simply think are reasonable; or they might be numbers that we want to try out on a "what if" basis. What we want to do is write down the supply and demand curves that fit (i.e., are consistent with) these numbers. Then we can determine numerically how a change in a variable such as GNP, the price of another good, or some cost of production will cause supply or demand to shift and thereby affect the market price and quantity.

Let's begin with the linear curves shown in Figure 2.17. We can write these curves algebraically as

The problem is to choose numbers for the constants a, b, c, and d. This is done, for supply and for demand, in a two-step procedure:

Step One: Recall that each price elasticity, whether of supply or demand, can be written as

where AQIAP is the change in quantity demanded or supplied resulting from a small change in price. For linear curves, Aß/AP is constant. From equations (2.4a) and (2.4b), we see that Aß/AP = d for supply, and AQ/AP = -b for demand. Now, let's substitute these values for AQI AP into the elasticity formula:

where P* and Q* are the equilibrium price and quantity for which we have data and to which the curves will be fit. Because we have numbers for Es, ED, P*, and Q*, we can substitute these numbers in equations (2.5a) and (2.5b) and solve for b and d.

Step Two: Since we now know b and 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*

FIGURE 2.17 Fitting Linear Supply and Demand Curves to Data. Linear supply and demand curves provide a convenient tool for analysis. Given data for the equilibrium price and quantity P* and Q*, and estimates of the elasticities of demand and supply ED and Es, we can calculate the parameters c and diov the supply curve, and a and b for the demand curve. (In the case drawn here, c < 0.) The curves can then be used to analyze the behavior of the market quantitatively.

FIGURE 2.17 Fitting Linear Supply and Demand Curves to Data. Linear supply and demand curves provide a convenient tool for analysis. Given data for the equilibrium price and quantity P* and Q*, and estimates of the elasticities of demand and supply ED and Es, we can calculate the parameters c and diov the supply curve, and a and b for the demand curve. (In the case drawn here, c < 0.) The curves can then be used to analyze the behavior of the market quantitatively.

and then use our data for Q* and P*, together with the number we calculated in Step One for b, to obtain a.

Let's do this for 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* = 15 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 fluctuated 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* = 15.

Step One: Substitute these numbers in equation (2.5b) to determine d:

10 The supply elasticity is for total 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.

1.6 = d(0.75/7.5) = O.ld, so that d = 1.6/0.1 = 16.

Step Two: Substitute this number for d, together with the numbers for P* and Q*, into equation (2.4b) to determine c:

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