Question

Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is -1.0. Suppose also that you spends $10,000 a year on food, the price of food is $2, and that your income is $25,000. Ifa sales tax on food caused the price of food to increase to $2.50, what would happen to her consumption of food (i.e. how many units of food does she consume)? (Hint: Because a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity and so use the midpoint formula. a. Suppose that you gets a tax rebate of $2500 to ease the effect of the sales tax. What is your consumption of food now? b. Are you better or worse off when given a rebate equal to the sales tax payments? Draw a graph and explain. (Note: your graph should indicate the numerical values on the horizontal and vertical axis for before tax budget line (BL), after tax BL, after tax plus rebate BL, initial consumption choice when $10000 is spent on food and the new food consumption you found in part (b)) c. All other Goods (S) Food

Answer 1

(P2 - P.) /CP+1)/2 Budget constraint CBC) & C F I Pe F = 10,000. a) Fa soro C+ 2F = 25,000 PE = $2.5 plastucty of Demand Ep = (Q2-0 p/ Costa)/2 - Ora P2TP, Oto Clip) - - A- soor &(2.5+2) - + 5000 (2-5-2) -1 - 441 Q2 stopne 9(estom) - (a +5000 960-2000) - 45000 tot 5000=0. a log = 4oooo Q2 = 4ooo Food consumption falls to - 4000. (6) (TR) torx rebate – $2500 New Budget line: Blz: C+ pt F = It TR o.5 Ost 500o) 1 Oz + soon Ct4 +2.5F 327,500 Increase in income – 42500 Income elastruly of Denard. (Eg) = 0.5 0.5 = Dz-O 'Izt II)/2 In-I, Cote / 0.5 = - 4000 & (27500+28000) "Qz+ 4000) 05 = 210-4000) 2500 A 4000

0 - 84000 0.50 + 400o) e 20-4000) = osca + 2000 - 21% - 84000 86000 = 20.5 z 4195.12 I eple - (c) Theree Budget Constrants By: C+2= 20000 (A) F=5000, c=15,000 - B4=C+2.5F = 25000 (BF-4000, ca 15,000. BLC+2.55 = 27500 (CF = 4195.12 - 170122 Plothing these B.C & the corresponding Consumption bundles 27500 25000 al 1701221 LLULOODULIDUUUUUUUUUUUU Isovo UK QA) Baby B4 4000 10000 llom 2500 Better off with tax rebate as compared to the tax imposition (BL2). This happens only when consumer is on the upper part (KN) of BL3 as compard to BLI