# Government Budget, the public debt, and social security

Congress passes and the President signs into law a bill authorizing the construction of two public recreational facilities, each of which costs $400,000 now and will last for ten years. Each project is financed by government borrowing at an interest rate of 5%. The benefits of the first project are $40,000 per year for the first five years, $60,000 per year for the next two years, and $80,000 per year for the last three years. The benefits of the second project are $70,000 per year for the first four years, $50,000 in the fifth year, $40,00 in the sixth year, and $30,000 per year for the last four year. Evaluate whether the spending on each of these projects adds to the burden of government debt over the next ten years.

Suppose that nominal GDP equals $14,000 billion, the current budget deficit is $112 billion, and the government's debt-GDP ration is 20%. (a) Given that the government wishes to maintain the debt-GDP ratio at 20%, explain whether the government needs to decrease its budget deficits, maintain the current budget deficit, or can increase its budget deficit if over the next year, nominal GDP grow by: (i) 2 percent; (ii) 4 percent; and (iii) 6 percent. Suppose that the only differences between the three nominal GDP growth rates given in part a are the growth rates of real GDP. Given your answers to part a, do the fiscal policies imposed by the desire to maintain a constant debt-GPD ratio seem appropriate from the standpoint of stabilization policy? (c) Do you answers to part B strengthen or weaken the argument that monetary policy should be the primary tool for smoothing the business cycle?

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#### Solution Preview

For the first question we need to find the present value of all future cash flows and compare that to the present value of the cost to build the recreational facilities. The cost of each recreational facility today is $400 K and the cost of borrowing is 5%. Hence the discount rate is 5%. The present value of all benefits from the first project are:

(40000/1.05) + (40000/1.05^2) + (40000/1.05^3) + (40000/1.05^4) + (40000/1.05^5) + (60000/1.05^6) + (60000/1.05^7) + (80000/1.05^8) + (80000/1.05^9) + (80000/1.05^10)

= 415 ...

#### Solution Summary

This solution maintains that monetary policy should be the primary tool for smoothing business cycles.