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?

Solutions

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 1 year ago

Next > < Previous

Related Solutions

If the government decides to impose a tax of 20 cents per litre on petrol, illustrate...

If the government decides to impose a tax of 20 cents per litre on petrol, illustrate the impact of the tax on market equilibrium price, and discuss whether the outcome is efficient by demonstrating the change of consumer’s and producer’s surplus as a result of the tax. •Draw a demand and supply model, with demand curve. •Show the shift of S as a result of 20 cent tax. •Identify new equilibrium. •Mark the price paid by consumer and received by...

•If the government decides to impose a tax of 20 cents per litre on petrol, draw...

•If the government decides to impose a tax of 20 cents per litre on petrol, draw a graph the impact of the tax on market equilibrium price, and discuss whether the outcome is efficient by demonstrating the change of consumer’s and producer’s surplus as a result of the tax. •Draw a demand and supply model, with demand curve. •Show the shift of S as a result of 20 cent tax. •Identify new equilibrium. •Mark the price paid by consumer and...

The tax system is how the U.S. Government raises the revenue it needs to provide goods...

The tax system is how the U.S. Government raises the revenue it needs to provide goods and services for its citizens. Do you think our tax system shares the burden of these goods and services fairly amongst all Americans? If you were in charge, what would be your policy position--or approach--to the U.S. tax system?

If the government decides to impose a tax of 20 cents per liter on petrol, illustrate the impact of the tax on market equilibrium price

If the government decides to impose a tax of 20 cents per liter on petrol, illustrate the impact of the tax on market equilibrium price, and discuss whether the outcome is efficient by demonstrating the change of consumer’s and producer’s surplus as a result of tax . - Draw a demand and supply model with demand curve - Show the shift of S as a result of 20 cent tax. - Mark the price paid by consumer and received by...

Suppose the government raises its revenue by a net tax of 20 percent on income, t...

Suppose the government raises its revenue by a net tax of 20 percent on income, t = 0.2, the marginal propensity to consume out of disposable income is 0.75, the marginal propensity to import is 0.06, and the government has an outstanding public debt of 800. In addition, the autonomous expenditure in households, business and foreign sectors (C + I + X - IM) is 340 and government expenditure is 340. Note: Keep as much precision as possible during your...

Suppose that in the market for coffee, the government decides to impose a tax on the...

Suppose that in the market for coffee, the government decides to impose a tax on the consumption of coffee. Illustrate the equilibrium market for coffee reflecting the new tax. On your graph, label the new price that consumers pay as Pc On your graph, label the new price that sellers receive as Ps On your graph, shade in the area representing the tax revenue received by the government and label it (TR). On your graph, shade in the area of...

One of the major sources of revenue for the government is Tax. The government spends the...

One of the major sources of revenue for the government is Tax. The government spends the tax that it collected on various activities which include nation building and social welfare of citizens and residents. The government charges tax to individuals and corporates as per the tax provision in the country, but there have been many incidences where the payers have not paid taxes to the government. The country’s tax authority is empowered to implement the tax laws and also penalise...

32. Suppose that in the market for coffee, the government decides to impose a tax on...

32. Suppose that in the market for coffee, the government decides to impose a tax on the consumption of coffee. a. Illustrate the equilibrium market for coffee reflecting the new tax. b. On your graph, label the new price that consumers pay as Pc c. On your graph, label the new price that sellers receive as Ps d. On your graph, shade in the area representing the tax revenue received by the government and label it (TR). e. On your...

Assume that the government decides to impose a tax on sellers of foods that are high...

Assume that the government decides to impose a tax on sellers of foods that are high in sugar content. a) Using a demand and supply diagram (half an A4 page), demonstrate and explain how such a tax that is imposed on sellers in fact creates a burden on consumers as well. Indicate the government revenue on your diagram. b) What is price elasticity of demand and how is it calculated? Briefly explain using diagrams, how price elasticity of demand will...

Suppose that the U.S. government decides to charge cola producers a tax. Before the tax, 50...

Suppose that the U.S. government decides to charge cola producers a tax. Before the tax, 50 million cases of cola were sold every month at a price of $7 per case. After the tax, 44 million cases of cola are sold every month; consumers pay $10 per case, and producers receive $4 per case (after paying the tax).

Subjects