3. (20 points) Currently, Alaska has no state income tax. One option being consi

Question

3. (20 points) Currently, Alaska has no state income tax. One option being considered by the governor, Bill Walker, is to close the state budget deficit by instituting a 7.5% proportional tax on labor income. There are 283,000 households in Alaska, and current average household labor income is $61,000.

a. (10 pts) Calculate the deadweight loss of this tax, assuming an uncompensated labor supply elasticity of 0.25.

b. (5 pts) Is your estimate of the deadweight loss in part a. an accurate measure? Why or why not? If you believe it to be inaccurate, is it an underestimate or an overestimate of the true deadweight loss? Be sure to buttress your answers with economic reasoning.

c. (4 pts) What is the average deadweight loss?

d. (1 pt) What is the marginal deadweight loss?

Explanation / Answer

3.a) The average household labor income is $61,000 and there are total 283,000 households in Alaska.The tax rate is 7.5% proprotional income tax.

Hence,the average tax collected by the government=(0.075*$61,000)=$4575

The average disposable income of the household becomes=($61,000-$4575)=$56,425

The uncompensated elasticity of labor supply is 0.25 and the labor supply prior to the tax imposition is 283,000 household in the workforce.

We know that elasticity of labor supply=% change in quantity of labor supply/%change in the income level

Therefore,we assume that following the tax imposition the labor supply becomes x and we know that the initial labor supply before the tax is 283,000.

Percentage change in quantity of labor supply=283,000-x/283,000

Now,the disposable income previously was $61,000 and following the tax imposition becomes $56,425.

Hence,percentage change in income level=$61,000-$56,425/$61,000=0.075

Elasticity of labor supply:(283,000-x/283,000)/0.075=0.25

(283,000-x)/283,000*0.075=0.25

283,000-x/21,225=0.25

283,000-x=5306.25

-x=-283,000+5306.25

-x=-277,693.75

x=277,693.75

Based on above calculations,the labor supply decreases to 277,693.75 households in the workforce following the tax imposition.

Now,we know that deadweight loss of the tax=0.5*(Original income before tax-Latter income after tax)*(Original labor supply prior to tax-Latter labor supply after tax)

=0.5*($61,000-$56,425)*(283,000-277,693.75)

=0.5*4575*5306.25

=$121,38,046.875 which is the deadweight loss from the state income tax imposed by Alaska.

b) Here deadweight loss basically measures the loss in economic efficiency that occurs due to the labor market distortion which in this case is the proportional income tax imposition.As a result of the income tax,the households will basically suffer due to lower disposable income which causes reduction in labor supply in the labor market.On the other hand,the government collects an average tax revenue of $4575 per household and thus the total tax revenue collected by the Alaska state government=(277,693.75*$4574)=$1,27,04,48,906.25 so the government gains revenue which can used for public spending on welfare goods and state development.The rest of the wealth in the state economy that is wasted or lost due to tax imposition is reflected by the deadweight loss.However,realistically,deadweight loss cannot portray the actual or practical economic loss incurred by the society due to any market distortions or in this case the additional income tax burden.Due to reduction in household labor supply due to tax imposition the production level in the state economy will also expectedly decrease due to loss in laborforce becuase of the tax burden as notice that labor demand is still uchanged meaning that companies still want to hire as much labor as before.But due to labor supply reduction the unemployment will rise and it will also affect the companies/firms and decrease the production level in the state as well thereby reducing state GDP level.

Hence,in this deadweight loss only accounts for the economic loss to the households due to extra tax burden and only depicts the partial picture.It doeas not explicitly reveal the true practical loss of tax imposition as higher unemployment level,loss in productive capacity,lower GDP or output level in the state,wastage of labor skill and credibility and so forth.

c) The Average Deadweight Loss can be represented as Total Deadwight loss/Number of households in the workforce

In this case,the total deadweight loss is calculated as $121,38,046.875 and the total number of households under workforce after the tax imposition is 277,693.75

Hence,the average deadweight loss=$121,38,046.875/277,693.75=$43.71 approximately

d) Now let us calculate the deadweight loss before the tax imposition.

Recall that the original income before the tax is $61,000 and the original labor supply before the tax is 283,000 households

Therefore,deadweight loss before the tax=0.5*($61,000-0)*(283,000-0)

=0.5*$61,000*283,000

=$8,63,15,00,000

We calculated the deadweight loss after the tax as $121,38,046.875.Hence,the difference in deadweight loss before and after the tax=($8,63,15,00,000-$121,38,046.875)=$8,61,93,61,953.125

Notice that when the labor supply changes by (283,000-277,693.75)=5306.25 the deadweight loss changes by the above ammount.

Thus,for 1 unit change in labor supply the deadweight loss changes by=$8,61,93,61,953.125/5306.25=$16,24,379.16 approximately which represents the marginal deadweight loss approximately.

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