Question

Use the following data to work.First Call, Inc., a smartphone company, plans to build an assembly plant that costs \(\$ 10\) million if the real interest rate is 6 percent a year or a larger plant that costs \(\$ 12\) million if the real interest rate is 5 percent a year or a smaller plant that costs \(\$ 8\) million if the real interest rate is 7 percent a year. Draw a graph of First Call's demand for loanable funds curve.

Short answer

Plot points at (6%, 10M), (5%, 12M), and (7%, 8M) and connect them to form a demand curve.

Step-by-step solution

- Identify the investment costs

List the different plant costs and the corresponding real interest rates: - \(10\) million at 6% interest rate - \(12\) million at 5% interest rate - \(8\) million at 7% interest rate.

- Understand the demand for loanable funds

In the context of loanable funds, a lower interest rate typically increases the quantity of funds demanded as investments become less expensive. Therefore, a higher cost plant is preferred when the interest rate is lower.

- Plot the demand curve points

On a graph, plot the points corresponding to the investment costs and interest rates. This means plotting points at: - \((6\text{%, } 10\text{ million})\) - \((5\text{%, } 12\text{ million})\) - \((7\text{%, } 8\text{ million})\).

- Draw the demand curve

Connect the plotted points to form a downward sloping curve. This curve will represent First Call's demand for loanable funds.

Key concepts

real interest rate

The real interest rate is the interest rate that has been adjusted for inflation. It reflects the true cost of borrowing and the real yield on investments. When you see an interest rate, it often hasn't accounted for the changes inflation will bring over time. The real interest rate helps you understand what you're really paying or earning over a period. To calculate it, you subtract the inflation rate from the nominal interest rate. For example, if the nominal interest rate is 6% and the inflation rate is 2%, the real interest rate would be 4%.

investment costs

Investment costs are the actual expenditures that firms need to make for their projects. In the case of First Call, Inc., an assembly plant could cost \(10 million, \)12 million, or $8 million, depending on the real interest rate. Higher interest rates typically mean higher cost of borrowing, which can lead to choosing cheaper investment options. Lower rates, on the other hand, can reduce borrowing costs and make more expensive projects financially viable. Knowing how investment costs vary with interest rates helps companies make cost-effective decisions.

loanable funds market

The loanable funds market is where savers supply funds and borrowers demand funds. Interest rates in this market are determined by the equilibrium of supply and demand for these funds. Here's how it works:
- **Low interest rates**: More people and businesses are willing to borrow money because it's cheaper to do so.
- **High interest rates**: Fewer people borrow money because it costs more.
In our context with First Call, Inc., the plant they choose to build depends on the interest rate in the loanable funds market. Understanding this helps you see how interest rates impact the broader economy and the specific decisions companies make. The demand curve for loanable funds slopes downward, showing that at lower interest rates, the quantity of loanable funds demanded increases.