The Laffer curve Governments often place \"sin\" taxes on \"undesirable\" goods

Question

The Laffer curve Governments often place "sin" taxes on "undesirable" goods or services such as cigarettes, alcohol, and pornography. These kinds of taxes are popular with politicians because they are usually more palatable to voters than income taxes. Taxing a "bad" product is an easy way to generate extra government revenue. However, as you'll see in this question, raising sin taxes doesn't always generate more tax revenue. Consider, for example, the market for gin shown by the following calculator. The orange curve represents supply, and the blue curve represents demand. Use the calculator to help you answer the following questions. You will not be graded on any changes you make to the calculator. Tool tip: Use your mouse to drag the green line on the graph. The values in the boxes on the right side of the calculator will change accordingly. You can also directly change the values in the boxes with the white background by clicking in the box and typing. When you click the Calculate button, the graph and any related values will change accordingly. Using the calculator, the equilibrium quantity of gin when the government imposes a $20-per-bottle tax on suppliers is and the government collects in tax revenue. Use the process from the previous question to fill in the following table.

Explanation / Answer

Answer for fill in the blanks :- (You can get this from the graph itself)

Quantity of gin is 40,000 bottles

Tax revenue is 20*40,000 =$800,000 (Tax Rate * Quantity of Bottles)

Table filled up as below :-

You should enter the value of tax as per the tax values in the first column of the above table. You should pick up the quantity amount from the calculator for the respective tax rate. To get the tax revenue, simply multiply quantity with the tax rate.

You should use the following table to plot the graph. Take the last two columns which are marked in bold.

Graph is also given below for your reference :-

Learning from the above exercise is that increasing tax rates will not ensure that the tax revenues also increase. Increase in tax rates will eventually lead to a decrease in demand and thereby decrease in tax revenues.

For a detailed explanation of the above problem,

Supply curve equation -> y = -x + 100

Demand curve equation -> y = x

When tax of $20 is applied, demand equation is y = x +20

Solve demand and suuply equations for different tax/bottle

e.g. x+20 = -x + 100 -> x =40 (i.e. 40,000 bottles) Price is y = x +20 =40+20 =$60

Solve for all tax/bottle in the given table

Tax Quantity Sold Tax Revenue 0            50,000 0 20            40,000            800,000 40            30,000        1,200,000 60            20,000        1,200,000 80            10,000            800,000 100 0 0

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