Milton Friedman noticed long ago that the opportunity cost of holding money, the nominal interest rate on safe, short-term investment, i, is something the government can control-and that it can even eliminate! Friedman realized that if governments set the inflation rate so that the nominal rate of interest were zero, then people wouldn't be forced into a cruel tradeoff between holding "bonds" (i.e., interest-bearing safe assets) and money (i.e., non-interest bearing safe assets that have the added bonus of being useful in exchange). That cruel tradeoff, Friedman suggested, only existed because of poor government monetary policy.

Thus was born the famed "Friedman Rule," the policy suggestion that long run money growth shouldn't aim at zero inflation (price stability) but instead should aim at a zero nominal interest rate on safe assets (eliminating the opportunity cost of holding money). Notice that to get i=0%, that means, taking the Fisher relation into account:

i = real rate + expected inflation

0 = real rate + expected inflation expected inflation* = -(real rate) = r

So under the Friedman Rule, the optimal inflation rate is the negative of the equi- librium real interest rate on safe investments. That typically would mean persistent deflation-so that the buying power of money tends to naturally grow over time. This result flows in a wide variety of neoclassical models-it's not a result unique to the MIU approach-and you can see why, because the opportunity cost of holding money is a nominal problem, and monetary policy can surely, at least on average, solve nominal problems. With that fact in mind, answer these questions:

If the real rate on safe, short-term investments is 2% per year, what average rate of inflation would Milton Friedman recommend?

Today, in 2021, the real rate on safe, short-term investments appears to be perhaps -1% (since inflation is perhaps 1%, hard to say, and the nominal rate on 1 year T-Bills is essentially 0%). Under the Friedman rule, what is the optimal rate of inflation?

In 2021, is monetary policy operating according to the Friedman rule?

Suppose that the household only lives for one period. The household's optimization problem is:

max U=lnCt+tln(1Nt) Ct ,Nt

s.t.

Ct = wtNt In this problem, the household receives no dividend from the firm.

(a) Solve for the optimality condition characterizing the household problem.

(b) From this optimality condition, what can you say about the effect of wt on Nt? What is your explanation for this finding?