Public Finance by John E. Anderson Power Point Slides to Accompany:

Chapter 11 Incentive Effects of Taxation

Copyright © by Houghton Mifflin Company. All rights reserved.3 Introduction The existence of taxes brings with it incentives to change behavior. In this chapter we examine how taxes provide incentives to change behavior in three specific ways: –Labor supply, –Savings, –Tax evasion.

Copyright © by Houghton Mifflin Company. All rights reserved.4 Taxation and Labor Supply Labor-leisure choice problem. People value both income and leisure. In order to earn income, one must work. The problem is to allocate time, a scarce resource, to labor and leisure.

Copyright © by Houghton Mifflin Company. All rights reserved.5 Labor-Leisure Choice Time endowment T. Allocate time to leisure activity l or work activity T-l. Work pays wage of w per hour. Wage income is y = w(T-l). Optimal combination of labor and leisure is that where the MRS between income and leisure equals the wage.

Copyright © by Houghton Mifflin Company. All rights reserved.6 Figure 11.1: Labor/Leisure Choice

Copyright © by Houghton Mifflin Company. All rights reserved.7 Figure 11.2: Labor Supply Effects of a Wage Reduction

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9 Figure 11.3: Substitution and Income Effects of a Wage Reduction

Copyright © by Houghton Mifflin Company. All rights reserved.10 Figure 11.4: Effects of a Wage Reduction When the Income Effect Dominates

Copyright © by Houghton Mifflin Company. All rights reserved.11 Figure 11.5: The Laffer Curve

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Copyright © by Houghton Mifflin Company. All rights reserved.14 Taxation and Saving/borrowing Life cycle model is used. Suppose that life consists of two periods: the present and the future. Income in the present is y 0 while income in the future is y 1. The discounted present value of lifetime income is then y 0 +y 1 /(1+r), where r is the discount rate.

Copyright © by Houghton Mifflin Company. All rights reserved.15 Lifetime Consumption Lifetime consumption can be written similarly as c 0 +c 1 /(1+r). Over the lifetime, a budget constraint requires that these two be equal. If we set them equal and solve for c 1 as a function of c 0 we get. c 1 =[(1+r)y 0 +y 1 ]-(1+r)c 0.

Copyright © by Houghton Mifflin Company. All rights reserved.16 Figure 11.6: The Lifetime Budget Constraint

Copyright © by Houghton Mifflin Company. All rights reserved.17 Figure 11.7: Life Cycle Model of Consumption and Savings

Copyright © by Houghton Mifflin Company. All rights reserved.18 Figure 11.8: Effect of a Tax on the Lifetime Budget Constraint

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Copyright © by Houghton Mifflin Company. All rights reserved.20 Figure 11.9: Saver Responds to a Tax by Saving Less

Copyright © by Houghton Mifflin Company. All rights reserved.21 Figure 11.10: Saver Responds to a Tax by Saving More

Copyright © by Houghton Mifflin Company. All rights reserved.22 Figure 11.11: Borrower Responds to a Tax by Borrowing More

Copyright © by Houghton Mifflin Company. All rights reserved.23 Taxation and Risk-taking Taxation reduces the return to a risky asset, hence it reduces the willingness to take risk. But, taxation also reduces risk through loss deductions, hence it increases willingness to take risk. We must consider both aspects of the influence of taxation on risk-taking.

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Copyright © by Houghton Mifflin Company. All rights reserved.25 Expected Value of the Consequence Let c 1 and c 2 be the consequences of taking risk under the two states of nature, low return and high return, occurring with probability 1- p and p. Expected consequence is then: E[c] = (1-p)c 1 + pc 2.

Copyright © by Houghton Mifflin Company. All rights reserved.26 Expected Utility of the Risky Venture The expected utility of the risky venture with these two potential consequences is the weighted average of the utilities that would arise from the two potential consequences: EU[c] = (1-p)u(c 1 ) + pu(c 2 )

Copyright © by Houghton Mifflin Company. All rights reserved.27 Marginal Rate of Substitution The marginal rate of substitution between the two consequences is given by: MRS = [(1-p)mu(c 1 )] / [pmu(c 2 )]. This is the rate at which the person is willing to trade one consequence for the other, holding total utility constant, given risk.

Copyright © by Houghton Mifflin Company. All rights reserved.28 Marginal Rate of Substitution [continued] Notice that we can write the MRS as: MRS = [(1-p)/p][mu(c 1 ) / mu(c 2 )]. The first term is the rate at which one can trade in the market (1-p)/p, i.e. the odds of a low return. So, the MRS in the face of risk is the usual MRS multiplied by the odds of a low return.

Copyright © by Houghton Mifflin Company. All rights reserved.29 Effect of a Tax First, a tax reduces the size of both consequences proportionately: (1-t)c 1, (1- t)c 2. Since c 1 < c 2, we know (1-t)c 1 < (1-t)c 2. The expected after-tax consequence is now: E[(1-t)c] = (1-p)(1-t)c 1 + p(1-t)c 2. Which is (1-t) E[c], or simply the after-tax expected consequence.

Copyright © by Houghton Mifflin Company. All rights reserved.30 A Second Effect There is a second effect to consider. Since the tax system permits deduction of losses, the riskiness of the project is affected. Suppose that we measure risk using the standard deviation in the returns. Consider the effect of the tax on the standard deviation SD[c].

Copyright © by Houghton Mifflin Company. All rights reserved.31 A Second Effect [continued] Using the properties of the variance from statistics, we know the relationship between the variance of the after-tax consequences and the before-tax consequences. SD[(1-t)c] = (1-t)SD[c]. Notice that the tax reduces the standard deviation and thereby reduces risk.

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Copyright © by Houghton Mifflin Company. All rights reserved.33 Expected Value of Venture EV = 0.6(300) + 0.4(-100) = $140 million. Suppose there is a 25% tax with full loss offset. EV = 0.6(225) + 0.4(-75) = $105 million. The tax has reduced the expected return from 40% to 5%.

Copyright © by Houghton Mifflin Company. All rights reserved.34 Riskiness of Project The tax also changes the riskiness of the project. Consider the standard deviation in the outcomes as a measure of risk. Originally SD = $196 million. Now SD = $147 million. The tax reduces the risk of the project, and does so by a factor of (1-.25).

Copyright © by Houghton Mifflin Company. All rights reserved.35 Government Role In effect, the government is acting as a silent partner with the business. The tax system acts to reduce the riskiness of the venture. That encourages the business to take more risk.

Copyright © by Houghton Mifflin Company. All rights reserved.36 A Portfolio Model Consider a household with initial wealth w that they want to divide between two available assets. The safe asset provides a certain return of r. A risky asset provides expected return  over the interval (-1, +infinity).

Copyright © by Houghton Mifflin Company. All rights reserved.37 A Portfolio Model Let a be the amount invested in the risky asset that provides an uncertain return , either  1 where things go well, or  2 where things go badly:  1 >  2. Final wealth of the household is given by: y = (w-a)(1+r) + a(1+  ). Figure 12 illustrates.

Copyright © by Houghton Mifflin Company. All rights reserved.38 Figure 11.12: Portfolio Choice

Copyright © by Houghton Mifflin Company. All rights reserved.39 Taxation and Risk-taking The proportion of the portfolio invested in the risky asset is given by bc/bd. The effect of a wealth tax is to move points b and d back toward the origin the the budget line shifting in parallel fashion. The net effect of a tax on risk-taking is ambiguous. Figure 13 illustrates.

Copyright © by Houghton Mifflin Company. All rights reserved.40 Figure 11.13: Effects of a Wealth Tax on Portfolio Choice

Copyright © by Houghton Mifflin Company. All rights reserved.41 Effects of an Income Tax An income tax acts differently, simply reducing the rate of return. Consider the simplest case where the safe asset provides a zero rate of return. Figure 14 illustrates the effect of an income tax. The income tax induces the family to take more risk.

Copyright © by Houghton Mifflin Company. All rights reserved.42 Figure 11.14: Portfolio Choice With a Zero Return to the Safe Asset and an Income Tax

Copyright © by Houghton Mifflin Company. All rights reserved.43 Tax Evasion Tax evasion refers to illegal activity, whereas tax avoidance is legal. Tax evasion is an application of portfolio composition. Consider holding a tax reporting portfolio. Honestly reported income is the safe asset with certain liability. Under-reported income is the risky asset with uncertain liability.

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Copyright © by Houghton Mifflin Company. All rights reserved.45 The Tax Evader’s Problem Figure 15 illustrates the tax evader’s problem. The honest taxpayer operates on the 45- degree ray from the origin, at a point like b. The tax evader operates off the 45-degree ray, somewhere on the line segment bd. Point d is the point of complete dishonesty, where the taxpayer under-reports all of his income. At point c, for example, the tax evader is evading tax on the share of income bc/bd.

Copyright © by Houghton Mifflin Company. All rights reserved.46 Figure 11.15: The Tax Evader’s Problem

Copyright © by Houghton Mifflin Company. All rights reserved.47 Limiting Tax Evasion Increase the probability of detection. That flattens the indifference curve by reducing the MRS (due to a reduction in the odds of not being caught). The tax evader moves up the budget line closer to point b where he evades tax on less income.

Copyright © by Houghton Mifflin Company. All rights reserved.48 Limiting Tax Evasion [continued] Increase the surcharge applied to detected evasion. This makes the budget line steeper. That forces the tax evader to move to a steeper point on his indifference curve, where he is evading less.

Copyright © by Houghton Mifflin Company. All rights reserved.49 Policy Study: Do Ira’s Increase Private Savings? One form of saving is the Individual Retirement Account (IRA) that permits savings at a tax-favored rate. The question is whether people are responsive to this type of incentive and save more.