Question

1-Using the following budget constraint: 200 1X+2Y, Utility UvXY A. How many Xs and Ys do you buy, how do you divide your budget, and what is the level of utility achieved? B. The government grants a Subsidy (the opposite of a tax) of $1 on Y C. What are the new quantities of X and Y purchased? D. What is the total amount the government spends on the Subsidy? E. What is the level of Utility achieved? F. If the same amount of Subsidy is added to income would you achieve a higher utility level? Calculate, Graph and Explain using the logic of the Lump-Sum Principle we saw in class

Answer 1

U = (XY)^0.5

Utility is maximized when MUx/MUy = Px/Py.

MUx = $\partial$ U/ $\partial$ X = 0.5 x (Y/X)^0.5

MUy = $\partial$ U/ $\partial$ Y = 0.5 x (X/Y)^0.5

MUx/MUy = Y/X

(A) Budget line: 200 = X + 2Y

MUx/MUy = Y/X = 1/2

X = 2Y

Substituting in budget line,

200 = X + X = 2X

X = 100

Y = X/2 = 100/2 = 50

Share of budget for good X = (X.Px)/I = (100 x 1) / 200 = 1/2 = 50%

Share of budget for good Y = (Y.Py)/I = (50 x 2) / 200 = 1/2 = 50%

U = (100 x 50)^0.5 = 31.62

(B) and (C) The subsidy will decrease PY by $1 and new Py = 2 - 1 = 1

New budget line: 200 = X + Y

MUx/MUy = Y/X = 1/1 = 1

X = Y

Substituting in new budget line,

200 = X + X = 2X

X = 100

Y = X = 100

(D) Total subsidy spending = Unit subsidy x Units of Y consumed after subsidy = $1 x 100 = $100

(E) When X = Y = 100, U = (100 x 100)^0.5 = 100

NOTE: As per Answering Policy, 1st 4 parts are answered.