Investment and Saving Prof Mike Kennedy

Investment There is a trade-off between the present and the future. A firm commits its resources to increasing its capacity to produce and earn profits in the future. Investment spending fluctuates sharply over the business cycle and typically contributes half of the total decline in spending. Investment plays a crucial role in determining the long- run productive capacity of the economy and its growth.

The relationship between consumption and investment

Investment over the business cycle

Total investment plus inventories

Business investment broken down into main components

Investment in Housing Residential investment is the construction of housing or apartment buildings. An apartment builder will compare the expected benefits of renting out apartments with the respective user costs (depreciation of the building and interest cost).

Investment in Inventories A firm’s inventories are unsold goods, unfinished goods, and raw materials. Inventory investment is the most volatile component of investment spending. It’s future marginal product can be defined as expected future commissions or profits. The user cost would be depreciation and interest costs.

Investment in Inventories has Fallen as a Per Cent of Sales

The Desired Capital Stock Desired capital stock is an amount of capital that allows a firm to earn the largest expected profit. The marginal product of capital (MPK) is the firm’s increase in output due to adding a unit of capital (other factors held constant). Managers compare the cost and benefit of using additional capital, e.g. a new machine. The firm’s benefit is MPK f – the future MPK. It is the future MPK f since the benefits won’t be seen immediately. The firm’s cost of employing or putting in place capital is the “user cost of capital”.

The User Cost of Capital User cost of capital is the expected real cost of using a unit of capital for a specified period of time. For now we will assume that it has two components: uc is the user cost of capital r is the expected real rate of interest d is the rate at which capital depreciates p K is the real price of capital goods

Taxes and the Desired Capital Stock The after-tax MPK f is (1 – τ)MPK f. This implies that: is tax-adjusted user cost of capital. An increase in the tax rate τ raises the tax-adjusted user cost and so reduces the desired stock of capital. The effective tax rate is a single measure of the tax burden on capital.

Determining the Desired Capital Stock The desired capital stock is the capital stock at which the MPK f equals the uc. Expected profits are maximized when the MPK f equals the uc. The MPK f curve slopes downward because the marginal product of capital falls as the capital stock increases. It comes from the production function already discussed. The uc curve does not depend on the amount capital and is a horizontal line. The next slide shows that firms have an incentive to employ capital up to the point where MPK f = uc.

Changes in the Desired Capital Stock If r falls (other factors held constant), the uc line falls (shifts downward), then MPK f > uc, and K rises. The same is true when d or p K fall (other factors held constant). When technology improves (other factors held constant) the MPK f curve shifts upward, then MPK f > uc, and K rises. Finally, if τ is lowered it will lower the user cost of capital and the desired capital stock will rise.

Deriving the desired demand for capital

Investment Gross investment is the total purchase or construction of new capital goods. We say gross because part of the money spent is to replace capital that is wearing out – depreciation. Net investment is the difference between gross investment and depreciation. K t+1 – K t = I t – dK t I t is gross investment during year t. K t and K t+1 is capital stock at the beginning of year t and t+1. This says that gross investment is equal to changes in the capital stock and depreciation.

Investment (cont’d) The firm’s gross investment during the year has two parts: – the desired net increase in capital stock over the year (K* – K t ); – the investment needed to replace worn-out or depreciated capital (dK t ). I t = K* – K t + dK t = K* – (1 – d)K t Typically there are lags in achieving K*. To derive the investment function as a function of the interest rate, we need start plugging in some numbers.

Investment (cont’d) If we know the value of K t and (1 – d) (say K t and (1 – d) are 10 and 0.20 respectively), then: I t = K* + 8 Next it is just a question of substituting values for the various coefficients and variables into our demand for capital: While it looks complicated, it is doable. As well there are simpler, less complicate versions of the MPK f

Goods Market Equilibrium The real interest rate is the key economic variable whose adjustments help bring the quantities of goods supplied and demanded into balance. The goods market equilibrium condition is: Y = C d + I d + G Y is the quantity of goods supplied by firms. The right hand side is the aggregate demand for goods. The income-expenditure identity for a closed economy (Y = C + I + G) is always satisfied. The goods market is in equilibrium when desired national saving equals desired investment (S d = I d ), since: S d = Y – C d – G.

What saving looks like in Canada

A look at government and total private saving: We will be talking about each

The Saving-Investment Diagram The saving curve, S, is upward sloping. A higher real interest rate raises desired national savings. The investment curve, I, is downward sloping. A higher interest rate increases the user cost of capital and, thus, reduces investment. Adjustments of the real interest rate, in response to excess supply or demand for saving, bring the goods market into equilibrium.

The Saving-Investment Diagram (Continued) Goods market equilibrium: – C d depends on r because a higher r raises S d. – I d depends on r because a higher r raises uc, which lowers I d. Adjustments of r eliminate excess supply or demand for saving.

Shifts of the Saving Curve The saving curve shifters are all factors, excluding the real interest rate, which affect national saving. Example. The crowding out of investment by government purchases: – increase in G causes a decrease S d; – S d curve shifts to the left; – the equilibrium r goes up; – I d falls because of higher uc.

Shifts of the Investment Curve The investment curve shifters are all the factors which affect investment, excluding the real interest rate (it determines the movement along the curve). Example: – An innovation or economic reform that raises MPK f. – The increase in I d shifts the investment curve to the right. – r rises to a new equilibrium level. – S increases.

An Equivalent Method We can start with a consumption and an investment equation. We then use the definition of income: Y = C + I + G Then solve for the interest rate that gets goods market equilibrium

A simple analytic model of goods market equilibrium Here is a basic model for goods market equilibrium: Y = C d + I d + G C d = c 0 – c r r + c y (Y – T) where 0 < c y < 1 I d = λ 0 – λ 1 r S d = Y – C d – G First get an equation for S d, using the C d equation S d = Y – C d – G = Y – c 0 + c r r – c y (Y – T) – G = {– c 0 + (1 – c y )Y + c y T – G} + c r r The terms/variables within {} can be considered shifters of S d Note: Satisfy yourselves that you understand how changes in these factors would shift desired saving

A simple analytic model of goods market equilibrium (cont’d) In equilibrium S d = I d. Thus: {– c 0 + (1 – c y )Y + c y T ) – G} + c r r = λ 0 – λ r r Note: We want to re-arrange the expression above with r on the LHS, since it is changes in r that will set S d = I d (c r + λ r )r = λ 0 + c 0 – (1 – c y )Y – c y T + G or

A simple analytic model of goods market equilibrium (cont’d) In exercise 6 Chapter 4, you are given the following values: c 0 = 360; λ 0 = 120; c y = 0.10; Y = 600; G = 120; T = 0; c r = 200 ; and λ r = 400. Plugging these into the equation for r we get: r = [ – 0.90×600 – 0.10× ]/( ) = 0.10 or 10% We need to check that the interest rate we found will yield values of consumption and investment consist with GDP = 600. C d = c 0 – c r r + c y (Y – T) = 360 – 200× ×(600 – 0) = 400 I d = λ 0 – λ r r = 120 – 400×0.10 = 80 G = 120 Y = C + I + G = = 600 Note that there are no superscripts on C and I. The reason is that the interest rate has moved to put desired consumption and investment equal to actual values

Budget deficits and interest rates We can re-organise the interest rate equation to isolate the effect of government saving. Thus: where S Gov’t = T – G (there are no transfers nor interest payments).