So this question is in regards to capital gains tax in New Zealand, I can understand the theory but I struggle turning the equation into a graph. If anyone can help that would be great!
Before we get to the responses, we can put a theoretical framework around the idea of taxing capital incomes (whether income from assets or capital gains). The main targets for raising tax revenue are labour income, capital income, and consumption. These taxes are all imposed on households, but we should expect that they will elicit different behavioural responses. From the perspective of the household, taxes influence the decision about how much to work and how much to save. To keep the model simple, we will assume that the labour income is fixed (and so people will not work less if we increase taxes on labour income). The model is as follows: People live for two periods. In the first period they earn labour income w and consume C1. In the second period they consume C2, which is the amount saved in period 1 plus the return on capital, r. We can write the household problem as: c2 max U(C1,C2) = u(c) + u(cz) subject to c1 + sw 1+r Which is to say that households maximise their utility by choosing their consumption in period 1 and period 2, subject to the constraint that they not consume more than they earn (earnings include returns on savings). 2. Draw a system of axes and label the vertical axis consumption in period 2 and the horizontal axis consumption in period 1. Draw the budget constraint and a set of indifference curves. Show optimal consumption in each period and the amount of savings in period 1. Then: a. Show the effect of a tax on labour income only. The tax is a constant percentage of income, so that after-tax income is now (1 - TL)w. b. Explain why taxing consumption is equivalent to taxing labour income. C. Show the effect of a tax on capital income. The capital tax is imposed on the returns, so that the after-tax consumption in period 2 is (w c)(1+r)(1 - Tk). d. Explain the income and substitution effects of the tax on capital, and why the net effect of a tax on savings is ambiguous. Before we get to the responses, we can put a theoretical framework around the idea of taxing capital incomes (whether income from assets or capital gains). The main targets for raising tax revenue are labour income, capital income, and consumption. These taxes are all imposed on households, but we should expect that they will elicit different behavioural responses. From the perspective of the household, taxes influence the decision about how much to work and how much to save. To keep the model simple, we will assume that the labour income is fixed (and so people will not work less if we increase taxes on labour income). The model is as follows: People live for two periods. In the first period they earn labour income w and consume C1. In the second period they consume C2, which is the amount saved in period 1 plus the return on capital, r. We can write the household problem as: c2 max U(C1,C2) = u(c) + u(cz) subject to c1 + sw 1+r Which is to say that households maximise their utility by choosing their consumption in period 1 and period 2, subject to the constraint that they not consume more than they earn (earnings include returns on savings). 2. Draw a system of axes and label the vertical axis consumption in period 2 and the horizontal axis consumption in period 1. Draw the budget constraint and a set of indifference curves. Show optimal consumption in each period and the amount of savings in period 1. Then: a. Show the effect of a tax on labour income only. The tax is a constant percentage of income, so that after-tax income is now (1 - TL)w. b. Explain why taxing consumption is equivalent to taxing labour income. C. Show the effect of a tax on capital income. The capital tax is imposed on the returns, so that the after-tax consumption in period 2 is (w c)(1+r)(1 - Tk). d. Explain the income and substitution effects of the tax on capital, and why the net effect of a tax on savings is ambiguous
