Question

In this question, assume all dollar units are real dollars in billions, so $150 means $150 billion. It is year 0. Argentina thinks it can find $150 of domestic investment projects with an MPK of 10% (each $1 invested pays off $0.10 in every later year). Argentina invests $84 in year 0 by borrowing $84 from the rest of the world at a world real interest rate r* of 5%. There is no further borrowing or investment after this. Use the standard assumptions: Assume initial external wealth W (W in year -1) is 0. Assume G = 0 always; and assume I = 0 except in year 0. Also, assume NUT= KA = 0 and that there is no net labor income so that NFIA = r*W. The projects start to pay off in year 1 and continue to pay off all years thereafter. Interest is paid in perpetuity, in year 1 and every year thereafter. In addition, assume that if the projects are not done, then GDP = Q = C = $200 in all years, so that PV(Q)= PV(C) =200 + 200/0.05 = 4,200.

Should Argentina fund the $84 worth of projects? Explain your answer

Why might Argentina be able to borrow only $84 and not $150?

From this point forward, assume the projects totaling $84 are funded and completed in year 0. If the MPK is 10%, what is the total payoff from the projects in future years?

Assume this is added to the $200 of GDP in all years starting in year 1. In dollars, what is Argentina’s Q = GDP in year 0, year 1, and later years?

Answer 1

Solution:

a. The criteria for taking an investment project is:

Since MPK is 10% which is greater than r (5%), the project will be beneficial for Argentina

So the answer is Yes

b. 150 units of output will be almost equal to 75% of the entire country's production. When lending amount is so high, the lenders may be hestant to allow such a borrowing even if the investment is highly productive.

c. The computation is given below:

MPK x Delta K = 0.10 x 84 = 8.4

This will result in an increase of 8.4 in Q for each period.

d. The computation is given below:

Q₀ = 200 and the increase as per the above calculation is 8.4 for subsequent years

So, Q₀ = 200 and Q = 208.4