Question

Suppose that the only tax levied in the economy is the business income tax at a rate of 40%. The government is planning to finance a public project by selling $10 million worth of bonds to the public. It is estimated that the bond sale will displace $6 million worth of private consumption expenditure, and $4 million worth of private investment. The market rate of interest is 4% and all private investment projects are perpetuities.
a) what is the before-tax rate of return on private investment.

b)what is the present value, at the market rate of interest, of the before-tax return on $1 worth of private investment?
c) what is the opportunity cost to the economy of the reduction in private consumption and investment resulting from the bond sale?

d) what is the marginal cost of public funds obtained by borrowing from the public?

Answer 1

a) Before-tax rate of return on private investment:

The before-tax rate of return on private investment is the return that an investor earns before paying taxes

In the given question, the before-tax rate of return on private investment is the market rate of interest of 4%

b) Present value, at the market rate of interest, of the before tax-return on $1 worth of private investment:

The market rate of interest is given to be 4%

4% of $1= $0.04

Hence, the present value of the before tax-return on $1 worth of private investment= $1+ $0.04= $1.04

c) Opportunity cost to the economy of the reduction in private consumption and investment resulting from the bond sale:

The opportunity cost of a choice is what had to be given up to make that choice.

In the given question, it is said that the government's plan to sell $10 million worth of bonds will displace $6 million worth of private consumption expenditure, and $4 million worth of private investment.

Hence, for the government to sell $10 million worth of bonds, the economy would have to forgo $6 million worth of private consumption expenditure, and $4 million worth of private investment.

$4 million worth of private investment would have in turn yielded a return of 4%= 4% of $4 million= $160,000

Hence the opportunity cost to the economy from the bond sale is $6 million worth private consumption expenditure, $4 million worth of private investment, and $160,000 worth interest

4) Marginal cost of public funds obtained:

The marginal cost of public funds is the measure of the loss incurred by the society in raising additional revenues to finance government spending.

The marginal cost of public funds obtained by borrowing from the public is the interest rate of 4% in the given question.