Question

If the cquilibrium rate of interest is 7 percent and market price of a U.S. government bond is \(\$ 1,000\), what is the most likely interest rate and bond price if the Fed increases the money supply by a substantial amount? (1.05) a) 8 percent; 51,100 b) 8 percent; \(S 1,000\) c) 8 percent; 5900 d) 6 percent; 51,100 c) 6 percent; \(\$ 1,000\) f) 6 percent; \(\$ 900\)

Short answer

The most likely interest rate is 6 percent and the most likely bond price after the Fed increases the money supply by a substantial amount is \(\$51,100\). The correct answer is option d.

Step-by-step solution

Understand the relationship between interest rates and bond prices

When interest rates rise, bond prices generally fall, and when interest rates fall, bond prices generally rise. The reason for this inverse relationship is because bond yields (which is the return on investment) must be competitive with other interest rates available in the market.

Analyze the effect of an increase in money supply on interest rates

Increasing the money supply leads to a decrease in the interest rates. This is because an increase in the money supply represents an additional amount of funds available to borrowers, creating an abundant supply of money that leads to a decrease in the cost of borrowing, i.e. the interest rates.

Determine the new interest rate

Based on the given choices and the fact that an increase in money supply leads to a decrease in interest rates, we can narrow down our options to: - d) 6 percent; 51,100 - c) 6 percent; \(\$ 1,000\) - f) 6 percent; \(\$ 900\)

Analyze the effect of a decrease in interest rates on bond prices

As mentioned earlier, when interest rates decrease, bond prices generally increase. This is because existing bonds paying a higher interest rate become more attractive to investors, so their market value goes up to reflect this increased demand.

Determine the most likely bond price

With the new interest rate being 6 percent, which is lower than the original 7 percent, the bond price should increase. Out of the remaining options, only option d) has a bond price higher than the original \(\$1,000\) value; thus, it is the most likely outcome. - d) 6 percent; 51,100 So the most likely interest rate is 6 percent and the most likely bond price after the Fed increases the money supply by a substantial amount is \(\$51,100\). The correct answer is option d.

Key concepts

Equilibrium Rate of Interest

The equilibrium rate of interest is a crucial aspect of monetary economics. In simple terms, it represents the interest rate at which the quantity of money demanded equals the quantity of money supplied. This balance is vital for the smooth operation of the economy. When the Federal Reserve (often referred to as the Fed) modifies the money supply, it can cause shifts in this equilibrium interest rate.

For example, if the money supply is increased significantly, as posed in our textbook exercise, more cash is available for banks to lend. With an abundance supply of money, the cost for borrowing—that is, the interest rate—tends to go down. This adjustment encourages more borrowing and spending, which can stimulate economic activity. Consequently, the new equilibrium interest rate will settle at a lower level, as the demand for money adjusts to the increased supply.

Understanding the equilibrium rate is essential for students not only in grasping the conceptual framework of the exercise but also for applying this knowledge to real-world economic scenarios and personal financial decisions.

Money Supply and Interest Rates

When discussing the money supply and interest rates, we're delving into the very heart of macroeconomic policy. The supply of money within an economy is predominantly controlled by its central bank—like the Federal Reserve in the United States—which can adjust it to steer economic growth.

Increasing the money supply typically results in reduced interest rates. How? When there is more money circulating in the economy, banks find themselves with excess reserves. To profit from these reserves, they are inclined to offer loans at lower rates, encouraging consumers and businesses to borrow. This increased borrowing can lead to enhanced investments and consumer spending, thereby influencing economic growth.

Conversely, a decrease in money supply results in higher interest rates, as the funds become scarcer. Higher rates then lead to reduced borrowing, investment, and potentially a cooling of economic activity. This concept is key in the textbook exercise and shows the direct influence that monetary policy has on everyday economic functions and the overall economic climate.

Inverse Relationship between Bond Prices and Interest Rates

The inverse relationship between bond prices and interest rates is one of the fundamental principles of finance. To put it simply, when interest rates go up, bond prices go down, and vice versa. This happens because bonds pay a fixed interest rate, known as the coupon rate, over their lifetime.

If new bonds are issued with higher interest rates due to a spike in the general interest rate environment, existing bonds with lower rates become less desirable. Therefore, their price decreases to compensate investors for the lower income they provide compared to newer bonds. This point is vividly illustrated in our textbook exercise, demonstrating that when the Fed increases the money supply, and interest rates subsequently fall, existing bonds with higher rates than the new equilibrium become more valuable. As a result, their prices increase.

For students tackling such topics, it's not merely about memorizing the relationship but understanding why this relationship exists. It's akin to a seesaw: when one side (interest rates) goes up, the other side (bond prices) must come down to maintain the financial balance, and understanding this can be key for making informed investment decisions.