CHAPTER • The Basics of Supply and Demand 51 so that c = 18 - 27 = -9 We now know c and d, so we can write our supply curve: Supply: Q = -9 + 9P We can now follow the same steps for the demand curve equation (2.5a) An estimate for the long-run elasticity of demand is −0.5.15 First, substitute this number, as well as the values for P* and Q*, into equation (2.6a) to determine b: -0.5 = -b(3/18) = -b/6 so that b = (0.5)(6) = Second, substitute this value for b and the values for P* and Q* in equation (2.5a) to determine a: 18 = a = (3)(3) = a - so that a = 18 + = 27 Thus, our demand curve is: Demand: Q = 27 - 3P To check that we have not made a mistake, let’s set the quantity supplied equal to the quantity demanded and calculate the resulting equilibrium price: Supply = -9 + 9P = 27 - 3P = Demand 9P + 3P = 27 + or P = 36/12 = 3.00, which is indeed the equilibrium price with 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 (2.7) where I is an index of the aggregate income or GDP 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 (2.7), we can then calculate f by using the formula for the income elasticity of demand: E = (I/Q)(⌬Q/⌬I) Taking the base value of I as 1.0, we have 1.3 = (1.0/18)( f ) Thus f = (1.3)(18)/(1.0) = 23.4 Finally, substituting the values b = 3, f = 23.4, P* = 3.00, and Q* = 18 into equation (2.7), we can calculate that a must equal 3.6 15 See Claudio Agostini, “Estimating Market Power in the U.S Copper Industry,” Review of Industrial Organization 28 (2006), 17Ϫ39