# 9 Inflation, Money Growth, and Interest Rates

Topic video: video 1

## 9.1 Realized and expected real interest rate

When we see in the bank that saving interest rate is 2%,

1. if we expected the inflation rate to be 1% tomorrow, then how much is the expected real interest rate?

2. if we believe in money neutrality and somehow the expected inflation rises to be 2%, what will happen to the expected real interest rate? What will happen to the nominal interest rate?

3. when tomorrow comes we realize that the inflation rate is actually 3%, instead of 1 %, what kind of impact will an unexpected inflation rate rise affect the households?

## 9.2 The interest rates on money

Suppose we have $$$P_{1}$$ today (which is equivalent to one basket of consumption). 1. If we hold it as money for saving one period, tomorrow with$$$P_{2}$$ price level how much does our purchasing power grow? What is the real rate of return of money?

2. If we save it in the bank, tomorrow we have $$(1+i_{1})$$$$$P_{1}$$ back. How much does our purchasing power grow? What is the real rate of return of bank saving? 3. The difference of the real rate of returns between money and bank saving determines the opportunity cost of holding money. What is that difference? 4. For money demand, we write it as $$M^{d}=P\times L(Y,i)$$. Do you think i here should refer to the real interest rate or the nominal interest rate? ## 9.3 Money growth and inflation rate Based on the money equilibrium $$M=PL(Y,i)$$ where $$L(Y,i)$$ is the real money demand which represents the average transaction volume that requires money to facilitate. Suppose that real output Y and the expected real interest rate $$r^{e}$$ are constant. (Remember $$i=r^{e}+\pi^{e}$$ where $$\pi$$ is the inflation rate tomorrow.) 1. If a country unexpected increases its money supply tomorrow, what would happen to its price level today? 2. If a country announces today that tomorrow’s money supply will increase, what would happen to its price level today? 3. Prove that if L(.) is fixed, then if a country has a money growth rate $$(M_{t+1}-M_{t})/M_{t}=\mu$$, its inflation rate $$(P_{t+1}-P_{t})/P_{t}=\mu$$. ## 9.4 Assume money neutrality What are the effects on the price level, $$P$$, and the nominal interest rate, $$i$$, from the following events? 1. A once-and-for-all increase in the nominal quantity of money, $$M$$. 2. A once-and-for-all increase in the money growth rate, $$\mu$$. 3. A credible announcement that the money growth rate, $$\mu$$, will rise beginning one year in the future. ## 9.5 Household budget constraints 1. Write down household’s budget constraint for today in nominal terms. 2. Write down household’s budget constraint for today in real terms. 3. Write down household’s two-period intertemporal budget constraint in nominal terms. 4. Write down household’s two-period intertemporal budget constraint in real terms. ## 9.6 Money neutrality In our model, any economic change that can affect household decisions must work through one of the three effects: wealth effect, substitution effect, and intertemporal substitution effect. Among them, if money is fully for transaction needs, it does not enter household budget constraint directly. It does not creat wealth for households. We can ignore wealth effect of money for the following questions. 1. Consider today’s labor versus today and tomorrow’s consumptions. What are the trade-offs that govern substitution and intertemporal subsitution effects of labor? Will these trade-offs be affected by money supply change? 2. Consider today’s consumption versus today’s leisure and tomorrow’s consumptions. What are the trade-offs that govern substitution and intertemporal subsitution effects of consumption? Will these trade-offs be affected by money supply change? ## 9.7 Money creation In general, money supply includes all sorts of the medium of exchange that facilitates transaction in a given period of time, which includes at least not the last cash (C) and saving deposits (D). For the following question, assume that money supply is C+D. 1. If whenever a person, say AA, gets$100 payment, he will always keep $10 in his pockets and save the rest in a bank, how much money will be the money that is supplied to this person? 2. Continue from (a). When the bank accepts his$90 deposit, it loans out $81 to another person, say BB. Loans, when approved, are usually proceeded through depositing in borrower’s account. How much C and D do both AA and BB hold now? 3. Continue from (b). If B keeps$21 in his pocket, carries out a transaction of a $60 payment to another persion, say CC, how much C and D do all three of them hold? 4. Continue from (c). What happens to aggregate C and D, if CC deposits$30 and the bank makes another loan of \$20 to the fourth person DD?

5. What we witnessed is the process called Money (Supply) Creation. What do you think are the key elements that determine the total amount of money created?

6. Does more money created imply more wealth created?

7. How will the money creation story be different if there is no bank?

## 9.8 The Economist

1. “Government-bond yields set the benchmark for the borrowing costs of companies and consumers.” From here, what a high yield can mean for consumers and companies?

2. “Last year, however, the global economy seemed to pick up again. Central banks withdrew some monetary stimulus. At the same time, governments started to ease fiscal austerity. The developed world may have reached a turning-point, where the amount of QE steadily dwindles and the amount of government-bond issuance rises.” How does it explain the high yield?

3. The article mentions several reasons that such a 3%-threshold passing does not necessarily imply a higher interest-rate trend in the future. What are those reasons?