(notice that income is held constant),then 血mo别 where Po and Q are the equilibrium price and quantity.We know that Po=$8 and=20 trillion eubic feet (Tef).Solving for e. /3),ore=3.75. 1.5=20y Similarly,if the generalform of the supplyquationsrepresetedas Qg=c+dPc+gPo the c laticity of supply which we know to be 0.1. Solving for g. 01-8)mg=0s The values for d and b may be found with equations 2.5a and 2.5b in Section 2.6.We know that Es=0.2.p*=2,and *=20.Therefore, 2 02=d20)ord=2 Als0,E=0.5,80 05=4 ,orb=-5. By substituting these values for d.g.b.and e into our linear supply and demand equations.we may solve for c and a: 20=c+(②2+(0.258).orc=14, and 20=a62+6.75)8.ora=0 If the price,these curves imply a free market price of $200for natural gas.Substitute the price of oil in the supply and demand curves to verify these equations.Then set the curves equal to each other and solve for the price of gas. 14+2P6+(0.25)8)=-5P6+3.75)8) 7P6=14 Pa=$2.00.(notice that income is held constant), then QG PO       = e. Substituting this into the cross-price elasticity, EPO = e PO * QG *       , where PO * and QG * are the equilibrium price and quantity. We know that PO * = $8 and QG * = 20 trillion cubic feet (Tcf). Solving for e, 1.5 = e 8 20     , or e = 3.75. Similarly, if the general form of the supply equation is represented as: QG = c + dPG + gPO, the cross-price elasticity of supply is g PO * QG *       , which we know to be 0.1. Solving for g, 0.1 = g 8 20     , or g = 0.25. The values for d and b may be found with equations 2.5a and 2.5b in Section 2.6. We know that ES = 0.2, P* = 2, and Q* = 20. Therefore, 0.2 = d 2 20     , or d = 2. Also, ED = -0.5, so −0.5 = b 2 20     , or b = -5. By substituting these values for d, g, b, and e into our linear supply and demand equations, we may solve for c and a: 20 = c + (2)(2) + (0.25)(8), or c = 14, and 20 = a - (5)(2) + (3.75)(8), or a = 0. If the price of oil is $8.00, these curves imply a free market price of $2.00 for natural gas. Substitute the price of oil in the supply and demand curves to verify these equations. Then set the curves equal to each other and solve for the price of gas. 14 + 2PG + (0.25)(8) = -5PG + (3.75)(8) 7PG = 14 PG = $2.00