# Relationship between investment demand and interest rate

### Investment and real interest rates (video) | Khan Academy

Why is investment negatively related to the interest rate? .. us consider first the relation between the stock of capital and the flow of investment in an economy. Explanation of how interest rates influence investment. Diagrams of MEC. Therefore demand for investment becomes very interest inelastic. How does business determine the amount of investment they undertake? – Compare expected rate of return to interest cost. •If expected return > interest cost .

I'll make money off of that.

### Determinants of Investment

Project A will definitely be done. What about project B?

Actually, I would not do project B. I'll just say I would not do anything that has a even a lower real return. I wouldn't do B, and I definitely wouldn't do all these things that get a lower return. When I have high interest rates right over here the only thing I would do is project A. Let's think about what would happen if interest rates went down.

If real interest rates went down. Let's say real interest Real interest rates go down to Once again, project A you are definitely going to do. By the same logic, people would do project B.

You do all of these up to project E. You'll even do project E if you need to borrow it and still makes sense.

The only one that you would not do is project F right over here. Here you aren't actually covering your cost of borrowing. So, your definitely not going to do F in this scenario.

Obviously do it in neither scenario. Right over here, you'd do all of the above. You would do A, B, C, D, not all of the above. All of the above except for F.

A, B, C, D, and E. Let's just think about the rough level of investments. If we were to plot on this axis right over here, if we were to plot the investments as a function of real interest rate, and over here we actually have the At a high real interest we had a low level investment. We only did project A. That's right over there.

This is when we were at R1. Instead of discouraging investment, as the corporate income tax does for business, the personal income-tax encourages households to invest in housing. A house-owner is a landlord with a special tax treatment. The size of this subsidy to house-ownership depends on the rate of inflation. The reason is that, the tax law allows house-owners to deduct their nominal interest payments.

Since the nominal interest rate on mortgage rises when inflation rises, the value of the subsidy is higher at higher rate of inflation. Some economists have criticized the tax treatment of house-ownership, because of this; they believe that, there are too much investment in housing.

Inventory investment is one of the smallest components of spending, yet its remarkable volatility makes it important. Reasons for Holding Inventories: Before presenting a model to explain fluctuations in inventory investment, we must discuss the motives for holding inventories. One motive for holding inventories is to smooth the level of production over time. Consider a firm that experiences temporary booms and busts in sales. Rather than adjusting production to match the fluctuations in sales, it may be cheaper to produce goods at a steady rate, when sales are low, inventory accumulates, when sales are high, inventory de-cumulates.

A second motive for holding inventories is that they allow a firm to operate more efficiently. For example, retail firms can sell merchandise more efficiently if they have goods on hand to show to customers. Manufacturing firms keep inventories of spare parts in order to reduce the time that, the assembly line is shut-down when a machine breaks. Thus, we can view inventories as a factor of production: The third reason for holding inventories is to avoid running out of goods when sales are unexpectedly high.

If demand exceeds production and there are no inventories, the goods will be out of stock for a period, and the firm will lose sales and profit. Inventories can prevent this from happening. This motive for holding inventories is called stock-out avoidance. Lastly, inventories are often dictated by the production process. Many goods require a number of steps in production and, thus, take time to produce. The Acceleration Model of Inventories: There are many motives for holding inventories, and there are many models of inventory investment.

One simple model that, explains the data well is the accelerator model which is applied to all types of investment. Here we apply it to the type for which it works best i. There are various reasons for this assumption, when output is high, firms need more material and supplies on hand, and they have more goods in the process of production; when the economy is booming, retail firms want to have more merchandise on the shelves to show customers.

The accelerator model predicts that, inventory will be proportional to the change in output. When output rises, firms want to hold more inventories, so they invest in them.

### Investment Demand in Macroeconomics: An Overview

When output falls, firms want to hold less inventories, so they allow their inventories to run down. How the model earned its name? The model tells that, inventory investment depends on whether the economy is speeding up or slowing down. Inventories and the Real Interest Rate: Inventory investment also depends on the real interest rate. When a firm holds a good in inventory and sells it tomorrow it gives up the interest it could have earned between today and tomorrow.

Thus, the real interest rate measures the opportunity cost of holding inventories. When the real interest rate rises, holding inventories becomes more expensive, so firms try to reduce their stock.

Thus, an increase in the real interest rate depresses inventory investment. The purpose here has been to examine the determinants of investment. Out of the various models of investment, three themes arise. First, we have seen that, investment spending are inversely related to the real interest rate.

A higher interest rate rises the cost of capital to firms, raises the cost of borrowing to home buyers and also raises the cost of holding inventories. Thus, the models developed here justify the investment function discussed. Second, we have seen what causes the investment function to shift.

An improvement in technology raises the MPK and thus, raises business fixed investment. An increase in the population raises the demand for housing and thus residential investment.

- Investment Demand in Macroeconomics: An Overview

Importantly, various economic policies, such as, changes in the investment tax credit and the corporate income tax, alter the incentives to invest and thus, shift the investment function. Third, we have seen why investment is so volatile over the business cycle: In the neoclassical model of business fixed investment, high employment increases the MPK and the incentive to invest. Higher Y also raises the demand for houses, which increases house prices and residential investment.

Higher output raises the stock of inventories firms wish to hold, stimulating inventory investment. The models predict that, an economic boom should stimulate investment, and a recession should depress it. Now we wish to discuss other theories of investment demand. Investment spending is a very important topic in macroeconomics for two reasons. First, changes in investment accounts for fluctuation of GDP movement in the business cycle.

Faster growing economies generally invest a higher proportion of their GDPs than slower growing economies. Investment often refers to buying financial and physical assets.

In macroeconomics, investment is a flow of spending that adds to the physical stock of capital. Investment spending may be disaggregated into three categories. The first is business fixed investment.

## Investment and the Rate of Interest

The second category is residential investment. And the third is inventory investment. Investment may be either induced a autonomous. Investment that is induced by changes in the level of income or changes in the interest rate is known as induced investment. Shift in autonomous investment is influenced by factors other than rate of interest or level of income, such as, innovation, public policy, size and composition of population, etc.

In the simple Keynesian model, investment is assumed to be autonomous. Induced investment takes place either due to change in the level of income or due to change in the rate of interest. We can combine autonomous and induced investment in a single function.

Here g represents autonomous investment hY is induced investment.

## Investment and real interest rates

The part hY depends on income and. Marginal Efficiency of Capital: In the Keynesian theory, investment expenditure is assumed to be a function of interest rate. The Keynesian theory of investment is known as the marginal efficiency of investment theory MEI. Before considering the marginal efficiency of investment theory, let us consider first the relation between the stock of capital and the flow of investment in an economy.

Investment is an addition to the stock of capital which is measured at any point of time while investment is measured over a period of time. The capital stock can grow, if net investment takes place.

Since capital is a factor of production, it will be employed in such a manner as to maximise profit. There is an optimum amount of capital stock that maximises profit. For example, if the actual capital stock of a firm is less than the optimum, the firm is not in equilibrium with respect to its stock of capital. In such a situation, firm can increase profit by adding to its capital stock, so that, actual capital becomes equal to its optimum capital. In this case investment will take place.

Similarly, there will be disinvestment if the actual capital is greater than the optimum capital. Thus, it is clear that investment will take place only when the firm is not in equilibrium. If the actual stock of capital is equal to the optimum stock of capital the firm is in equilibrium and there will be no further investment.

This analysis can be generalized for the whole economy. For the economy as a whole we can get the volume of actual and an optimum stock of capital. Investment will take place if the actual stock of capital is less than the optimum stock of the economy.

The optimum stock of capital is that stock which maximises total profit. To maximise profit, a firm employs any factor up to the point where marginal cost is equal to the marginal revenue product or marginal revenue product is equal to the price of that factor.

However, it is difficult to apply this rule for any durable capital assets which remains productive for a number of periods and provides a series of yields over its life time.

Hence it is difficult to determine the marginal productivity of the durable capital asset. Even if we can determine the marginal productivity of capital, another problem remains: These problems can be resolved with the help of the marginal efficiency of capital theory, which helps to determine the optimum capital stock.

Yn are yield of capital in various years and C is the supply price of the machine. The marginal efficiency of capital is defined as that rate of discount for which the present value of the series of returns obtainable from the machine during its lifetime is equal to its supply price. The prospective yields Y1, Y2……. Yn and the supply price c are taken as given.

Thus, we have only one equation and one unknown, i, which can be determined from the above equation. We have one problem in solving the above equation. The equation has n roots as it is an nth degree equation. We can thus get n values of i, which one should be taken as the marginal efficiency of capital? Moreover, what is the guarantee that, there will be at least one real value of i? However, we can show that, if we assume a Y1, Y2…….

This can be given as follows: Yn are given and constants. Hence the value of V will depend on the value of i, i. Thus, V varies inversely with i. As i increases V decreases and vice versa. Therefore, the V i function will be downward sloping. This is shown in Fig. V i function is asymptotic. Since C is given and independent of i it is represented by a horizontal straight line. The equation If we assume that, C. It can be said that there is one positive real root for which the above equation is satisfied.

Investment could be conventional or non-conventional. The conventional investment is one where all the yields are non-negative. The non-conventional investment is one where some of the yields are negative. Now, let us find out how the MEC determines the optimum stock of capital. If the firm wants to get the same yields Y1, Y2 ……. Yn by lending money at market rate of interest it will have to lend an amount of money, D, which is given by the following equation: The firm can get the same yields Y1, Y2….

Yn etc, either by purchasing the capital goods at a cost of C or by lending the sum of money, D. The firm can either purchase the machine or can lend the sum. So far, we assumed that the firm has sufficient amount of money and the problem before the firm is whether to lend the money or to purchase the machine. Marginal Efficiency of Capital MEC is the proportional rate of return over cost from investment in real capital goods.

It depends on two factors: For any single firm the supply price of capital may be taken as given which means that the capital market is perfectly competitive. But the yields from the capital goods will not remain the same. If more and more r capital goods are employed in the production process other factors remaining unchanged, the marginal productivity of new capital goods will diminish. Thus, if the firm employs more units of capital, the yields from successive units will diminish which means the law of diminishing marginal productivity will operate.

Hence we can say that, the MEC will diminish as more capital goods are employed in the production process. If, as in Fig. With the MEC schedule we can determine the optimum stock of capital. If the market rate of interest is r0 the firm would be able to maximise profit by employing K0 units of capital goods, where the MEC is equal to the market rate of interest.

This process will stop when K0 units of capital will be employed where the MEC is equal to r0. Similarly, when the rate of interest is r1, the point B will be the point of maximum profit where the MEC is equal to the rate of interest and the capital stock is equal to K, as shown in Fig. Thus, we can say that the optimum stock of capital is K0, when the rate of interest is r0 and equals K1, if the rate of interest is r1 and so on. The MEC can give us the optimum stock of capital.

Proceeding in this way we can get the MEC schedule for the whole economy which will be downward sloping as well. It will give us the optimum stock of capital for the economy at different rates of interest. Determinants of the MEC: As we have seen above, the MEC is that value of i for which the following equations is satisfied: From this equation it can be seen that, the MEC directly depends on two factors: Other things remaining the same the MEC varies directly with the perspective yields and inversely with the supply price.

This means that if the yields diminish and the supply price increases, the MEC will fall. The expected yields are obtained by subtracting operating cost from the total revenue. Moreover, these yields are prospective and, thus, they may change when the expectations change. The higher the operating costs, the lower will be the yields and lower will be the MEC.

Thus, if the raw materials become more expensive or if the wage rate increases, the MEC will fall. If the price of output increases, other things remaining the same, the MEC will rise. On the other hand, if the price of output falls, other things remaining unchanged, the MEC will also fall. The expected yields may also change due to changes in the expectations of the entrepreneurs. If the entrepreneurs are more optimistic about the future, they will expect higher yields to prevail.

If, on the other hand, they are pessimistic about the future, they may expect lower yield. Thus, in a period of boom, they will have a bright outlook for the future and the MEC will be higher.

Alternatively, in a period of slump, the MEC will be lower. Apart from the above factors, the MEC may also depend upon the following exogenous factors, such as size of population, size of the market, changes in the methods of production, etc. Other things remaining the same, the bigger the size of the market or the greater the size of the population, the greater will be the MEC.

Similarly, if a new technology is invented which reduces the cost per unit of output, the yields will increase and the MEC will rise. The MEC schedule is downward sloping because it is assumed that, the yields diminish as more capital goods are used. Furthermore, it may be assumed that larger output can be sold at lower prices, other things remaining the same. For this reason, the MEC falls. However, when other factors change, the MEC schedule shifts its position.

The optimum stock of capital is determined by the MEC at different rate of interest. If the actual capital stock is not equal to the optimum capital stock then capital stock must be adjusted to make it equal to the optimum level. The problem is to determine how the rate at which the actual stock proceeds towards the optimum stock.

We have actually two problems: The first problem is solved by the MEC theory. The second problem require the MEI theory. Before, we discuss the MEI theory it is necessary to distinguish between gross and net investment.

Gross investment is the addition to the stock of capital during a period of time. Net investment is equal to the difference between gross investment and depreciation. Thus, in any period of time if gross investment is equal to zero, net investment is equal to depreciation and will be negative. Net investment will be zero if the gross investment is equal to the amount of depreciation. If the rate of gross investment is equal to the amount of depreciation, it is called the replacement investment, which is necessary to keep the stock of capital intact.

In calculating the MEC we assume that, the supply price of capital is constant and it is determined by the replacement level of investment. Let Ox be the amount of capital required for replacement, xy is the supply price for this level of capital stock.

This supply price, xy, is taken into account in calculating the MEC. Thus, the schedule of MEC corresponds to a supply price where net investment is zero. If net investment is positive the amount of capital stock required is greater than Ox and, hence, the supply price is greater than xy. Further, the supply price would be different for different level of investment. However, the expected yields of the MEI marginal efficiency of investment is calculated on the assumption that the supply price of capital is increasing.

Thus, the MEC is calculated on the assumption of a constant supply price of capital whereas the MEI is calculated on the assumption of variable supply price. The MEI will be different for different levels of investment. As the rate of investment increases, supply price increases and the MEI decreases. The relation between the two are given in Fig. Suppose the market rate of interest is Or2 and from the MEC schedule we can find out that the optimum stock of capital is OKm.

Now, suppose that the actual stock of capital is OK0 which is less than the optimum capital stock. Thus, there is scope for more investment. Now, we need to determine the rate at which investment will take place when the rate of interest is Or2. If the rate of interest is Or0 then the actual capital stock is K0 which is equal to the optimum stock of capital and the zero net investment. As capital stock increases above K0, there is positive net investment and the supply price of capital goods will increase.

The supply price increases as the rate of investment increases. We can get the MEI schedule for different rates of investment. As the rate of investment increases the MEI decreases which will depend on the rate of the supply schedule of capital goods.

Thus, the MEI schedule is regarded as a mirror image of the supply schedule of capital goods. Given the rate of interest of Or2, the rate of investment will be equal to K0I0, where the MEI is equal to the rate of interest. This schedule again shows the rate of investment at different rates of interest assuming that the present capital stock is Ol0.