http://www.gmu.edu/departments/economics/bcaplan

Econ 816

Spring, 2000

**Week 3: Basics of Monetary Economics**

__monetary base__.

__net wealth__; non-base money is not. If I hold $1 in currency and the price level declines, my wealth isgreater, and no one else's is smaller. In contrast, if a price level decline merely increases the holder'swealth but reduces someone else's wealth by an equal amount, the item held isnot base money.

*increasedthe Fed's debts to the public* by the same amount (since the Fedpledges to redeem a fixed quantity of gold per dollar).

*nowhere*counted as money (e.g. credit cards), that still seem to be very closesubstitutes for money.

*is*money, or is merely a * close substitute* for money?

*real*money, not nominal money. Inconsequence, a *price* of money has to appear in the utility function - as itnormally would not. (Of course, pricesdo normally appear in the indirect utility function).

_{}; an infinitely-lived agentderives utility from consumption and real balances.

_{t} and pay 1 next period. (They could also just hold real goods between periods, but since realgoods pay no interest and give no utility unless consumed, this would make nosense).

_{}; consumption this period must equal the agent's per-periodendowment (W) plus the agent's transfer from the government (TR - note: thiscan be negative, i.e., a tax) plus the current real value of bonds purchasedlast period, minus the current real value of bonds purchased this period, minusadditions to his cash balance.

. The present value of consumption equals thepresent value of endowments

_{}

_{}

_{}

_{}

_{} - and that transfersare proportional to pre-existing real balances, so _{}. This implies a __constantmoney growth rate__ of _{}.

*i* and the bond price *s*:_{}.

_{}. Proof: According tothe first equation in IV.I, _{}. According to thesecond equation in IV.I, _{}. Then just sub infor s_{t}.

_{} rises, 1-s_{t}by definition rises; U_{2} tends to rise and U_{1} tends tofall. (Slippage: Intertemporalmargin). From the principle ofdiminishing MU, this means that * when the nominal interest rate rises, agents want tohold less money*.

*the realinterest rate has to be just the inverse of the discount factor*,

*the inflation rate must be exactly equal to the money growth rate*:_{}.

_{}. It then followsthat real money demand falls when the rate of money creation rises, AND whenthe discount factor falls (i.e., people get more impatient).

__one__good leaves both arguments in the utility function unchanged.

*real*money demand. But as the above sectionmakes clear, once you've got the real money demand function, you can quicklyderive what the price level has to be for a given money supply. How is this possible?

__possible__, so it makes sense todeliberate over the advantages and disadvantages of different conceivablemonetary regimes (as will be done throughout the course).

*inverse* of the fraction ofyour income that you keep in the form of cash.

*income-adjusted*money demanded.

*nominal*GDP.

_{}.

_{}. There is also asimilar second constraint, that __next__ period's money holdings equal thisperiod's __sales__ of endowment and bonds: _{}. Then just maximizeO.F. subject to both constraints.