The state of Petro has been subsidizing gasoline prices. Residents are paying $0

Question

The state of Petro has been subsidizing gasoline prices. Residents are paying $0.50 per gallon, but Petro is in some financial trouble and the IMF is requiring them to raise gas prices to $2. Bread is sold for $1.
A) HH 1 utility function is U(B,G) = B^3(G) and has an income of 100. What is the optimal choice before and after?
B) Suppose the government gives the people a payment of $20 to make up for the loss of a subsidy, raising income to $120. What is the optimal bundle now? Does the policy make sense? The state of Petro has been subsidizing gasoline prices. Residents are paying $0.50 per gallon, but Petro is in some financial trouble and the IMF is requiring them to raise gas prices to $2. Bread is sold for $1.
A) HH 1 utility function is U(B,G) = B^3(G) and has an income of 100. What is the optimal choice before and after?
B) Suppose the government gives the people a payment of $20 to make up for the loss of a subsidy, raising income to $120. What is the optimal bundle now? Does the policy make sense?
A) HH 1 utility function is U(B,G) = B^3(G) and has an income of 100. What is the optimal choice before and after?
B) Suppose the government gives the people a payment of $20 to make up for the loss of a subsidy, raising income to $120. What is the optimal bundle now? Does the policy make sense?

Explanation / Answer

A.

Before Price change of gasoline:

U = B^3*G ----------------------(1)

Differentiation of eq. 1 w.r.t. G

MU of G = B^3 -----------------(2)

Differentiation of eq. 1 w.r.t. B

MU of B = 3G*B^2 --------------(3)

MU of G / MU of B = Price of G/Price of B

B^3 / 3G*B^2 = .5/1

B/3G = .5/1   or B = 1.5G

Income = P1*G + P2*B

100 = .5*G + 1*B = .5G + 1.5 G = 2G

G = 100/2 = 50

B = 75

Thus, optimal choice will be : G = 50   and B = 75

After Price change of gasoline:

U = B^3*G ----------------------(1)

Differentiation of eq. 1 w.r.t. G

MU of G = B^3 -----------------(2)

Differentiation of eq. 1 w.r.t. B

MU of B = 3G*B^2 --------------(3)

MU of G / MU of B = Price of G/Price of B

B^3 / 3G*B^2 = 2/1             (new gasoline price = $2)

B/3G = 2/1

B = 6G

100 = P1*G + P2*B = 2G + 1*B = 2G + 1*6G = 8G

G = 100/8 = 12.5

B = 6*12.5 = 75

Thus, after price change : optimal choice is B = 75 and G = 12.5

B.

After government payment , income becomes $120

Then

U = B^3*G ----------------------(1)

Differentiation of eq. 1 w.r.t. G

MU of G = B^3 -----------------(2)

Differentiation of eq. 1 w.r.t. B

MU of B = 3G*B^2 --------------(3)

MU of G / MU of B = Price of G/Price of B

B^3 / 3G*B^2 = 2/1             (new gasoline price = $2)

B/3G = 2/1

B = 6G

120 = P1*G + P2*B = 2G + 1*B = 2G + 1*6G = 8G

G = 120/8 = 15

B = 6G = 6*15 = 90

Thus, optimal bundle will have: G = 15, B = 90

Government policy is not helping significantly because consumers are not getting what they were getting before price rise. Though, bread purchased is increased. But, intention of government is to help people buy more gasoline and it is not taking place properly.

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