Given the following demand and supply equation for a market,...

Given the following demand and supply equation for a market, answer the following questions: $$ \begin{aligned} & M_S=1 / r_w(\mathrm{TR}) \\ & M_D=45-125(i)+1.0(Y) \\ & M_S \equiv M_D \end{aligned} $$ where $i$ represents the rate of interest, $Y$ represents national income, $\pi_m$ represents the fractional reserve requirement ratio, and $\mathrm{TR}$ represents total reserves. Assume national income in 2015 was $$\$ 1,200$$ and is projected to be $5 \%$ higher in 2016. Also, assume the reserve requirement ratio is 0.25 and total reserves are equal to 140 . a. What market clearing interest rate would you project for 2016? b. What level of the money supply would be needed to achieve an interest rate of $8.5 \%$ in 2016

Given the following demand and supply equation for a market, answer the following questions:
$$
\begin{aligned}
& M_S=1 / r_w(\mathrm{TR}) \\
& M_D=45-125(i)+1.0(Y) \\
& M_S \equiv M_D
\end{aligned}
$$
where $i$ represents the rate of interest, $Y$ represents national income, $\pi_m$ represents the fractional reserve requirement ratio, and $\mathrm{TR}$ represents total reserves.
Assume national income in 2015 was $$\$ 1,200$$ and is projected to be $5 \%$ higher in 2016. Also, assume the reserve requirement ratio is 0.25 and total reserves are equal to 140 .
a. What market clearing interest rate would you project for 2016?
b. What level of the money supply would be needed to achieve an interest rate of $8.5 \%$ in 2016

Key Concepts

Interest Rate Determination

Interest rate determination in the context of the money market involves finding the rate at which the quantity of money demanded equals the quantity supplied. Changes in factors such as central bank policies, income levels, and economic outlooks can shift either side of the equilibrium, causing adjustments in the interest rate as the market seeks a new balance.

National Income Effects on Money Demand

National income plays a crucial role in money demand because higher income levels increase the volume of transactions and, therefore, the need for liquidity. Changes in national income can shift the money demand curve, which, under market-clearing conditions, affects the equilibrium interest rate and overall monetary conditions in the economy.

Fractional Reserve Banking

In a fractional reserve banking system, banks keep only a fraction of deposits in reserve and loan out the remainder. This system enhances the money supply through the money multiplier effect, where an initial deposit can lead to a greater final increase in the total money supply. The reserve requirement ratio is a key component in determining the scale of this multiplier effect.

Money Demand Function

The money demand function represents the relationship between the amount of money households and businesses want to hold and various economic variables such as the interest rate and national income. Typically, the demand for money is inversely related to the interest rate (the opportunity cost of holding money) and directly related to income, since higher income usually increases transaction needs.

Money Supply Function

This function describes how the amount of money available in an economy is determined, often being set by central bank policies and the banking system’s operations. It takes into account mechanisms like the base money supply provided by the central bank and the way in which banks create additional money through lending, often constrained by regulatory requirements such as the reserve ratio.

Money Market Equilibrium

This concept refers to the state in which the quantity of money that economic agents wish to hold (money demand) equals the amount made available by financial institutions or the central bank (money supply). In this equilibrium, the prevailing interest rate adjusts such that the supply and demand for money are balanced, ensuring that there is neither an excess of money that could lead to inflation nor a scarcity that could hamper economic transactions.

Transcript

00:01 Part a, the economy is surprisingly strong, leading to an increase in the amount of checkable deposits.

00:12 An increased demand for reserves, holding the supply constant, will drive up the federal funds rate.

00:48 Higher federal funds rates may encourage banks to borrow more from the federal reserve.

01:24 Non -borrowed reserves might decrease as banks use these reserves to meet their obligations or lend them in the federal funds market to earn interest.

02:23 Part b, banks expect an unusually large increase in withdrawals from checking deposit accounts in the future.

02:33 If banks anticipate more withdrawals, they'll want to hold more reserves to ensure that they can meet these obligations.

02:41 With an increased demand for reserves and a constant supply, the federal funds rate will rise.

03:14 Borrowed reserves are likely to increase as banks might borrow more from the fed in anticipation of withdrawals.

03:56 Non -borrowed reserves might decrease as banks hold onto them, anticipating the withdrawals.

04:37 Part c, the fed raises the target federal funds rate.

04:43 When the fed raises the target rate, they often conduct open market operations to make the market rate align with the target.

04:51 The federal funds rate will increase as its target is set by the fed.

05:04 Borrowed reserves may decrease because borrowing from the fed becomes more expensive.

05:16 And non -borrowed reserves may increase as banks rely less on borrowing due to higher costs.

05:37 Part d, the fed raises the interest rate on reserves above the current equilibrium federal funds rate.

05:47 When the fed pays a higher interest rate on reserves, banks are more inclined to hold onto their reserves rather than lending them out...

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