Question

The interest rate falls from 10 to 5 per cent. Discuss in detail how this affects the rental on capital services and the level of the capital stock in an industry in the short and long run.

Short answer

A lower interest rate decreases the rental cost of capital services immediately and increases capital stock over time as firms invest more.

Step-by-step solution

Understand the Problem

The problem is focused on analyzing the effects of a decrease in the interest rate, from 10% to 5%, on the rental rate of capital services and the capital stock both in the short and long run. We need to understand the economic principles behind interest rates, capital costs, and capital stock adjustment.

Interest Rate Impact on Capital Costs

The interest rate is a key component of the cost of capital, which is the cost incurred for using capital. A decrease in the interest rate reduces the cost of borrowing funds for investment purposes, making capital cheaper.

Effect on Rental Rate of Capital Services

In the short run, a lower interest rate reduces the rental cost of capital services because firms can refinance or reduce their borrowing costs. The rental rate for capital services is calculated based on the current interest rate. Hence, the immediate effect is a reduction in the rental cost for utilizing capital.

Short-run Impact on Capital Stock

In the short run, the capital stock remains relatively unchanged because the adjustment of capital stock through investment takes time. However, the lower rental cost can increase the profitability of using additional capital, encouraging firms to consider expanding their capital stock.

Long-run Impact on Capital Investment

In the long run, the reduced interest rate leads to increased investment as firms find it more cost-effective to purchase and maintain more capital. Over time, firms will adjust their capital stock upwards, leading to a higher level of capital stock in the industry.

Integration of Concepts

Summing up, a decrease from 10% to 5% in interest rates lowers the rental rate of capital services in the short run while potentially increasing capital stock as firms invest more due to lower capital costs in the long run.

Key concepts

Capital Stock

The capital stock of an industry refers to the total value of its physical assets that are used for production. These assets include machinery, buildings, and equipment. Capital stock is a crucial part of a company's capability to produce goods and services. It determines its productivity and efficiency.
When we talk about changes in capital stock, especially following a shift in interest rates, it's important to distinguish between short-run and long-run effects.

• In the short run, capital stock tends to remain stable.
• Changes in interest rates don't immediately influence the amount of existing capital assets.
• Capital is generally tied up in long-term commitments and can't be adjusted instantly.

However, in the long run, things are different. As interest rates fall, borrowing becomes cheaper, facilitating more investments in new capital. This leads to an increase in capital stock over time. Firms are more likely to invest in new projects, upgrade facilities, or expand operations, all of which can increase the capital stock.

Rental Rate of Capital

The rental rate of capital represents the cost of using capital for production purposes over a specific period. It is influenced by several factors, with the interest rate being one of the most significant.
The rental rate can be seen as analogous to rent for a house but instead for capital equipment. This cost is crucial for firms because it affects their overall expenses and investment decisions.

• When interest rates drop, the rental rate of capital typically decreases because the cost of borrowing funds to acquire or use capital becomes lower.
• In the short run, firms can benefit from refinancing existing debts at the new, lower interest rate, thereby reducing their capital costs.
• This makes capital more attractive and often leads to increased production activities utilizing existing equipment.

Over the long run, a sustained lower interest rate can have broader implications, such as allowing firms to commit to larger investments, further influencing the rental rate. However, the immediate impact is seen in the short-term cost reduction, which positively affects firm's budget for operations.

Investment

Investment in capital is the key process through which firms increase their capital stock. It involves spending on new equipment, buildings, or technology, allowing businesses to grow and stay competitive. Investment decisions are heavily influenced by the cost of capital, which is tied to the prevailing interest rates.

• A decrease in interest rates makes financing through borrowing cheaper, encouraging firms to invest more.
• This increased investment initially doesn't alter capital stock swiftly, as expanding or setting up new capital takes time and planning.

Over the long run, however, the lower interest rates can lead to significant increases in investment levels. As firms continuously invest in newer technologies and infrastructure, the aggregate capital stock rises. This growth can enhance overall production capacity, improve efficiency, and optimize operational costs.
Ultimately, the choice to invest is influenced by expected returns. Lower capital costs mean that potential returns on investment are more attractive, prompting more companies to allocate funds toward expansion.