1    Review questions

Indicate whether each statement is true, false, or uncertain, and give a brief explanation.

1. Suppose that, as a population policy, government taxes families for each car in excess of two in the family. Consequently no family has more than two cars and the government collects no revenue from the policy. Does this mean that the policy has no deadweight loss?

2. The theory of optimal commodity taxation argues that tax rates should be set equal across all commodities.

3. Taxing dividends distorts investment decisions for a firm.

4. Debt financing is cheaper than equity financing because it is tax deductible and is therefore always the preferred source of financing for firms.

2    Problems

2.1    Corporate Taxation

This question considers the effect of the corporate income tax on wages for a small open economy.

The value of the firm is given by

V = (1 − τc ) (F(K,L) − wL) − rK

where τc is the corporate income tax rate, = F(K,L) is output produced by the firm using labor L and capital K , w is the wage rate and r is world interest rate.  The production function has the form F(K,L) = Kα L1−α , with 0 < α < 1.  The firm’s problem is to choose L and K to maximize the value of the firm taking τc , w and r as given.

(a)  Show that the firm’s first-order condition for its choice of labor L is    =  (1 −

τc )(FL  − w) = 0.  Does the corporate tax distort the firm’s choice over how much labor to employ?

(b)  Show that the firm’s first-order condition for its choice of capital K is  = (1 −

τc )FK  − r  = 0.  Does the corporate tax distort the firm’s choice over how much capital to employ?

(c) Note that F(K,L) can be written as F(K,L) = F (  , 1) L = f(k)L where k =  is the capital to labor ratio and f(k) = F(k,1). Show that the first-order condition for labor can be re-expressed as w = f(k) − kf\ (k) and that the first-order condition for capital can be expressed as r = (1 − τc )f\ (k).

(d) Show that the total derivative with respect to k of the first-order condition for L is dw = −kf\\ (k)dk and that the total derivative with respect to k of the first-order condition for K is dr = −dτc f\ (k) + (1 − τc )f\\ (k)dk .

(e) In a small open economy, r is unaffected by changed in the home corporate tax rate so dr = 0.  Using dr = 0, combine the two expressions in part (d) to show that dw/dτc  = −kf\ (k) ·  .

(f) Using the result in part (e) and the functional form of the production function, show that elasticity of wages with respect to 1 − τc  is εw,(1−τc)  = kf\ (k)/(f(k) − kf\ (k)) =

α  

1−α .

(g) The parameter α is the elasticity of output with respect to capital. A typical value is α =  . Plug in this value to the result from (f) and interpret the result.

2.2    Tax Evasion

Consider the Allingham-Sandmo model of tax evasion. Suppose the probability of audit is p, there is a tax rate τ per dollar of income earned, and the penalty on detected evasion is equal to π per dollar of income underreported. Utility is given by u(c) = ln(c).

(a) For what values of p will a risk-averse taxpayer engage in at least some amount of evasion?

Yitzhaki (1974) argued that having the penalty be a function of the amount of tax evaded wasn’t realistic and proposed an alternative form of the penalty function.

(b) Assume the loss from being caught evading is πτe instead πe. Now for what values of p will a risk-averse taxpayer engage in at least some amount of evasion?

(c) Write down the maximization problem for the taxpayer’s decision over how much income to evade using Yitzhaki’s form of the penalty function and assuming the amount of income earned is fixed. Solve for the taxpayer’s optimal evasion choice.

(d) How does an increase in the tax rate τ affect the taxpayer’s optimal evasion choice? How does this differ from the result discussed in lecture using the classic Allingham- Sandmo penalty function?