ifa sales tax on food were to cause the price of food to increase to price elasticity measures an arc elasticity,rather than a point elasticity.) The price of food increases from $2to $2.50.so arc elasticity should be used: P+P 6-( We know that Ep=-1.P=2.AP=0.5.and Q=5000.We also know that the new quantity,is +AO.Thus,if there is no change in income,we may solve for AQ: 2+2.5 5.000+(5.000+△Q 2 By cross-multiplying and rearranging terms,we find that AQ=-1.000. This means that she decreases her consumption of food from 5,000 to 4,000 units. Suppose that she is given a tax rebate of500 toease the effect of the ales tax. What would her consumpt tion of food be now? A tax rebate of $2.500 implies an income increase of $2500.To calculate the response of demand to the tax rebate,use the definition of the arc elasticity ofincome (L+1 -( 2 We know thatE=0.5./25.000.Al=2500.4.000 (from the answer to 11.a).Assuming no change in price,we solve for AQ. 25,000+27,500 (品 4.000+4.000+△ 2 By cross-multiplying and r anging terms. wef nd that△O=195 (approx This she in umption of food from.000to,195 unitsa. If a sales tax on food were to cause the price of food to increase to $2.50, what would happen to her consumption of food? (Hint: Since a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity.) The price of food increases from $2 to $2.50, so arc elasticity should be used: EP = Q P     P1 + P2 2 Q1 + Q2 2           . We know that EP = -1, P = 2, P = 0.5, and Q=5000. We also know that Q2, the new quantity, is Q + Q. Thus, if there is no change in income, we may solve for Q:  −1= Q 0.5     2 + 2.5 2 5,000 + (5,000 + Q) 2           . By cross-multiplying and rearranging terms, we find that Q = -1,000. This means that she decreases her consumption of food from 5,000 to 4,000 units. b. Suppose that she is given a tax rebate of $2,500 to ease the effect of the sales tax. What would her consumption of food be now? A tax rebate of $2,500 implies an income increase of $2,500. To calculate the response of demand to the tax rebate, use the definition of the arc elasticity of income. EI = Q I     I 1 + I 2 2 Q1 + Q2 2           . We know that EI = 0.5, I = 25,000, I = 2,500, Q = 4,000 (from the answer to 11.a). Assuming no change in price, we solve for Q.  0.5 = Q 2,500       25,000 + 27,500 2 4,000 + (4,000 + Q) 2           . By cross-multiplying and rearranging terms, we find that Q = 195 (approximately). This means that she increases her consumption of food from 4,000 to 4,195 units