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Intermediate Macroeconomics IID Essay Example
 Category:Macro & Microeconomics
 Document type:Assignment
 Level:Masters
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 Words:1039
Intermediate Microeconomics
Taxation of Labor Income

The consumer utility function is given by
Where C is the consumption level and N is the number of labor unit that is provided by the consumer.
The consumption Level of the consumer depends on the amount of income
which is aslo subject to the tax rate. The consumer’s income m
The Budget constraint for the consumer is therefore
Therefore the utility maximization problem of the consumers will be:
Max
such that
Therefore the solution
—
At optimal utility
which implies that at optimal utility then. Let
then replacing and solving gives:
Replacing this in the optimal utility equation then the optimal utility
Solving gives:
replacing
then optimal utility level is
Also
The tax due to be charged at the rate of
on the wage rate.If the total amount of labor supplies is N then the total wage will be given as:
Therefore the total tax revenue

If the consumer seeks to gain a higher utility from the tax charged, at the same wage rate, then the consumer will only vote for that politician that will give the tax rate for which
If the wage rate is constant, then a tax rate of 30% will result in a utility level of
If still the wage rate does not change and the tax rate is charged at 80%, then the utility level will be:
If the consumer was to vote on this logic, then the consumer would only vote for the politician that proposes 80% tax rate since at this rate the consumer will realize the highest level of utility.

If the logic for voting is to attain the lowest labor income tax, then the consumer will only vote for the tax rate that gives a low tax.
The total taxable income is given by. Asuuming the labor supply units do not change and the wage rate is kept constant, then if the tax rate is 30% then labor income tax is. If the tax rate is 80% then the llabor income tax is. Clearly, a tax rate of 80% will see the consumer pay higher in taxes than if the tax rate was 30%. Therefore, under this criterion, the consumer would vote for the politician offering 30% tax rate.

Pareto optimum implies an economic condition where the allocations of resources are efficiently allocated between all economic agents. An allocation is said to be Pareto efficient if there is absolutely no chance of making any one agent better off. The economic agents in this case can be said to be well off given the other agents’ situation if the consumer achieves maximum utility and if the politician has maximized bits tax revenue. Pareto efficient will be achieved therefore at that level where the consumer achieves maximum utility while the politician has achieved maximum taxation revenue.

The Pareto efficient allocation depends on the tax rate that will be implemented on that economy. The consumer will be gaining higher utility when the tax rate is higher, given the 30% and the 80% considerations. Moreover the higher the tax rate, the more labor income tax the consumer is paying and the more the tax revenue for the government. If the tax rate was set at 50%, then would be chances of making at least one agent better off because they would prefer a higher tax rate hence a tax rate of between 80% and 100% would be said to be optimal.
Question 2

In period, the households have endowment
that is subject to ta lump sum tax of. Therefore the available income for consumption is. In the second period the household has endowments of
subject to a lumpsum of. Therefore the available income for consumption in period 2 will be is.
The consumption level of the households are given as
and. The household can either consume this income or invest in bonds. Say the expenditure on bonds is given as. Then one period consumption decisions shall be:
With the income levels given as
Hence the budget constrain is:
The government budget constrain will be dependent on the amount of tax revenue that it can collect from the household for each period. However this government revenue ought to be
in present value. Therefore the government budget constraint will be
in its lifetime.

Say the total income is represented by I, then the budget constraint can be rewritten as
This income can be distributed between the two periods, rearranging the equation give:
graphing this equation we have

If
then the amount of income to be spent becomes larger, I’, and hence the budget constraint
will shift upwards. This is because the
intercept given as
will now be a higher value. A reduction of the tax value increases the amount available for spending.
This budget constraint results in a budget line that is above the current budget constraint. Therefore in order to maintain the same level of budget constraint, then the amount of tax in period two will be. Solving the above equation for the tax amount in period 2, then

If the government changes the amount of tax in period 2 to be
then the budget constraint becomes
The reduction in the tax sum will increase the amount of income that is available for spending if the discount rate is unchanging. This will result in a shift on the budget constraint above the prevailing budget constraint. Since I’’ will be higher than I, then the
will be higher. The same will also be true for the. Therefore the reduction of taxes in period 2 will result in a budget constraint represented by the red line on the graph. Therefore the only way in which the budget constraint (denoted by the black line) then the amount of tax that should be charged n period 1 should be. Solving for the new budget constraint, in the above equation, then

A benevolent government would like to charge a tax on the household for which the household will not have to pay much tax on their income. From the above, it has been shown that if in either period a tax rate of zero is charged then the other period will be charged a higher tax. This tax rate should therefore be.