Question

The government impose a 20%tax on the sale of milk. Given that Sam has an income...

The government impose a 20%tax on the sale of milk. Given that Sam has an income of 100 pennies, the price of milk is 5 pennies, the price of bread is 4 pennies, and Sam's utility function is U=(M)2/3(B)1/3. how much revenue will this tax raise?

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Answer #1

U = M2/3B1/3

At 20% tax on sale of milk will effectively increase price of milk by 20%, so

New price of milk (pennies) = 5 x 1.2 = 6

Budget line: 100 = 6M + 4B (where M: Quantity of milk, B: Number of bread)

Utility is maximized when MUM/MUB = PM/PB = 6/4 = 3/2

MUM = U/M = (2/3) x (B/M)1/3

MUB = U/B = (1/3) x (M/B)2/3

MUM/MUB = 2 x (B/M) = 3/2

2B/M = 3/2

4B = 3M

Substituting in budget line,

100 = 6M + 3M = 9M

M = 11.11

B = 3M/4 = (3 x 11.11) / 4 = 33.33/4 = 8.33

Tax revenue (pennies) = Tax per unit x M = (5 x 0.2) x 11.11 = 11.11

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