Intermediate Macroeconomics IID Essay Example

Intermediate Microeconomics

Taxation of Labor Income

  1. The consumer utility function is given by

Intermediate Macroeconomics IID

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
Intermediate Macroeconomics IID 1 which is aslo subject to the tax rateIntermediate Macroeconomics IID 2. The consumer’s income m

Intermediate Macroeconomics IID 3

The Budget constraint for the consumer is therefore

Intermediate Macroeconomics IID 4

Intermediate Macroeconomics IID 5

Therefore the utility maximization problem of the consumers will be:

Intermediate Macroeconomics IID 6Max
Intermediate Macroeconomics IID 7 such that
Intermediate Macroeconomics IID 8

Therefore the solution
Intermediate Macroeconomics IID 9

Intermediate Macroeconomics IID 10

Intermediate Macroeconomics IID 11

At optimal utility
Intermediate Macroeconomics IID 12 which implies that at optimal utility thenIntermediate Macroeconomics IID 13. Let
Intermediate Macroeconomics IID 14 then replacing and solving gives:

Intermediate Macroeconomics IID 15

Replacing this in the optimal utility equation then the optimal utility
Intermediate Macroeconomics IID 16

Solving gives:
Intermediate Macroeconomics IID 17 replacing
Intermediate Macroeconomics IID 18 then optimal utility level is

Intermediate Macroeconomics IID 19

Also
Intermediate Macroeconomics IID 20

The tax due to be charged at the rate of
Intermediate Macroeconomics IID 21 on the wage rateIntermediate Macroeconomics IID 22.If the total amount of labor supplies is N then the total wage will be given as:

Intermediate Macroeconomics IID 23

Therefore the total tax revenue
Intermediate Macroeconomics IID 24

  1. 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
    Intermediate Macroeconomics IID 25Intermediate Macroeconomics IID 26

If the wage rate is constant, then a tax rate of 30% will result in a utility level of

Intermediate Macroeconomics IID 27

If still the wage rate does not change and the tax rate is charged at 80%, then the utility level will be:

Intermediate Macroeconomics IID 28

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.

  1. 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 byIntermediate Macroeconomics IID 29. 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 isIntermediate Macroeconomics IID 30. If the tax rate is 80% then the llabor income tax isIntermediate Macroeconomics IID 31. 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.

  1. 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.

  2. 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

  1. In period, the households have endowment
    Intermediate Macroeconomics IID 32 that is subject to ta lump sum tax ofIntermediate Macroeconomics IID 33. Therefore the available income for consumption isIntermediate Macroeconomics IID 34. In the second period the household has endowments of
    Intermediate Macroeconomics IID 35 subject to a lumpsum ofIntermediate Macroeconomics IID 36. Therefore the available income for consumption in period 2 will be isIntermediate Macroeconomics IID 37.

The consumption level of the households are given as
Intermediate Macroeconomics IID 38andIntermediate Macroeconomics IID 39. The household can either consume this income or invest in bonds. Say the expenditure on bonds is given asIntermediate Macroeconomics IID 40. Then one period consumption decisions shall be:

Intermediate Macroeconomics IID 41

Intermediate Macroeconomics IID 42

With the income levels given as

Intermediate Macroeconomics IID 43

Hence the budget constrain is:

Intermediate Macroeconomics IID 44

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
Intermediate Macroeconomics IID 45 in present value. Therefore the government budget constraint will be
Intermediate Macroeconomics IID 46 in its lifetime.

  1. Say the total income is represented by I, then the budget constraint can be rewritten as

Intermediate Macroeconomics IID 47

This income can be distributed between the two periods, rearranging the equation give:

Intermediate Macroeconomics IID 48graphing this equation we have

Intermediate Macroeconomics IID 49Intermediate Macroeconomics IID 50

Intermediate Macroeconomics IID 51

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  1. If
    Intermediate Macroeconomics IID 54 then the amount of income to be spent becomes larger, I’, and hence the budget constraint
    Intermediate Macroeconomics IID 55 will shift upwards. This is because the
    Intermediate Macroeconomics IID 56 intercept given as
    Intermediate Macroeconomics IID 57 will now be a higher value. A reduction of the tax value increases the amount available for spending.

Intermediate Macroeconomics IID 58

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 beIntermediate Macroeconomics IID 59. Solving the above equation for the tax amount in period 2, then
Intermediate Macroeconomics IID 60

  1. If the government changes the amount of tax in period 2 to be
    Intermediate Macroeconomics IID 61 then the budget constraint becomes

Intermediate Macroeconomics IID 62

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
Intermediate Macroeconomics IID 63 will be higher. The same will also be true for theIntermediate Macroeconomics IID 64. 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 beIntermediate Macroeconomics IID 65. Solving for the new budget constraint, in the above equation, then
Intermediate Macroeconomics IID 66

  1. 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 beIntermediate Macroeconomics IID 67.