Question

In: Economics

A). The government needs revenue. It decides to tax lemon pie sales by 20%. Jimmy is...

A). The government needs revenue. It decides to tax lemon pie sales by 20%. Jimmy is a fan of lemon pies. He has an income of 100 pence. The price of lemon pies is 5 pence, the price of mascarpone pies is 4 pennies. Jimmy's utility is U=(lp)^2/3(mp)^1/3. How much revenue will the tax generate?

B). The tax on lemon pies is a burden on Jimmy. How big of a burden is it? Calculate the income increase that would be required to compensate Jimmy for the imposition of the tax. How does this compare to the revenue raised from the tax?

Expert Solution

U = lp^2/3mp^1/3

(A) The tax will increase price of lemon pies by 20%, to (5 x 1.2) = 6 pence.

Budget line: 100 = 6 x lp + 4 x mp, or 50 = 3 x lp + 4 x mp

Utility is maximized when MU(lp) / MU(mp) = Price of lp / Price of mp = 6/4 = 3/2

MU(lp) = U/lp = (2/3) x (mp / lp)^1/3

MU(mp) = U/mp = (1/3) x (lp / mp)^2/3

MU(lp) /MU(mp) = 2 x (mp / lp) = 3/2

4 x mp = 3 x lp

Substituting in budget line,

50 = 3 x lp + 3 x lp = 6 x lp

lp = 8.33

mp = 3 x lp / 4 = (3 x 8.33) / 4 = 6.25

Tax revenue (pennies) = Tax per unit x lp = 5 x 20% x 8.33 = 8.33

(B) Budget line before tax: 100 = 5 x lp + 4 x mp

MU(lp) / MU(mp) = 2 x (mp / lp) = 5/4

8 x mp = 5 x lp

Substituting in budget line,

100 = 8 x mp + 4 x mp = 12 x mp

mp = 8.33

lp = 8 x mp / 5 = (8 x 8.33) / 5 = 13.33

(i) Tax burden (pennies) = (1/2) x Tax per unit x Change in quantity of lp = (1/2) x 1 x (13.33 - 8.33) = (1/2) x 5 = 2.5

(ii) Required income to afford old bundle (pennies) = 6 x 13.33 + 4 x 8.33 = 80 + 33.32 = 113.32

Required compensation in income (pennies) = 113.32 - 100 = 13.32

Required compensation is higher than tax revenue, meaning there is a deadweight loss from tax.

Rahul Sunny answered 2 years ago

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