Question

6. Modou has a utility function U(X1,X2) = 2X1 + X2

The prices of X1 & X2 are $1 each and Modou has an income of $20 budgeted for this two goods.

a. Draw the demand curve for X1 as a function of p1.:

b. At a price of p1 = $1, how much X1 and X2 does Modou consume?:

c. A per unit tax of $0.60 is placed on X1. How much of good X1 will he consume now?:

d. Suppose the government decides to combine this with a lump-sum subsidy that makes Modou as well-off as he was before the tax. With this new income, how much of X1 will Modou demand? How much is the subsidy?:

e. Based on you answer to d) what are the Income and Substitution effects of the original per-unit tax on X1?:

Answer 1

11 Q UCXI,X 2) = 2X1 + X2, P= P2= 1, M=20. a) then MRS12= MOL = 2, as MRS> PilP2. MO2 I> MU2 g only Good l is 80. X = MIPI consumed , So Of P2=1, then If MRS > Pi. . 2>P,. then X,=MIP, so.dd funch x* = { 2011, P,<2. "lo. Pi>2. 1! Piza b.) P. = 1, X1*= 20, xq*=0. c.) Pi= to 6=106, then still Pila "P1=2 80 Xi' = 20 = 12.5 P, <a ddcurve d) Let with Lump sum subsidy, New Income Utility before tax U1= 2 X, * = 40, After tax U2= 2X12.5=25 80 to make as well off , 2x' =VI = 40. xi= 20 = M' M'= $32 subsidy = M'_M= $12 Ans e) Income effect = x,1-X, * = 12.5-20 = Sule effect 8E = -7.52 . =M XI. y Ang