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?
Homework Answers
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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