Question

Ed's utility from vacations (V) and meals (M) is given by the function U(V,M) = V M. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, the price of vacations remained the same. Both years, Ed had an income of $1500. Ed's ordinary demands are V=21/3p, and M=1/3PM- Where / is income, pv is the price of vacations and pm is the price of meals. 12. Calculate the compensating variation for the price change in meals. 13. Calculate the equivalent variation for the price change in meals.

Answer 1

S PAGE Py = 200 Py = 200 U=V²M pm = 50 Py=75 Demand! v= 2I 3Pv M= 1 T 3PM I = $1500 Compensating variation - the amount of money to give to the consumers to completly offut the peace increase, so the consumers utility. unchanged (ie he stays on the same coriginal) id). since demands are given can directly calculate in the the question, consumption we bundle original 1= 1500 pv=200 PM=50 VE 2X100 3X200 [V=5) Meso 3x50 M=10 U15, 10) = (3) (10) ucs, 10) = 250 1 11 PM'=75 now U=250 Pr'=200 I = ? ICS Scanned with CamScanner

u=v²m follow plugging in demand equations 4= (37) Csid u=250 PV = 200 to Pm = 75 250 = 9x75 X10,000 X3 250 X 9X75X10,000x3 13 12001, 5000,000 Du 5063,500,000 = 171.7.07 = I 300 compensating variation = $1717 – $123 = Boone F $ 217) 101 I T 1 1=1717 , Pv=200, Pm as much utility as M quer just = 1500 pv 200 PM = 50) - Scanned with CamScanner

| lquivalent wariation the consumer that alent variation: Tumor that the amt. of money would lower her to take utility from up the o amount as the feuce increase = 1500 pv=200 PM=75 V= 2X1500 3 x 200 1- 16p 3x75 = 6.67 (approx) =5 u=u²m 365)?(6.67) u= 166.67 (approx) when a- 166.67 Pu= 200, PM=50, I=? 166.67 = 4. 13 27 (2003(50) 166.67 x 27 xeevoox 50 - 10 16oras cosas 2,250,045,000 = I3 I = $1310.37 [affron) CS Scanned with CamScanner

equivalent variation and let than - = 1500- 1310.37 k $189. 63. Caffron) Wave combination 1= 1500 - 200 PM=45 ques as much utility as - 1= 1310, 67 lv = 200 Px= 30 ac Scanned with CamScanner

Sorry about all the scribbles. The calculations got messy. Let me know if anything is unclear :)