Alemayehu Geda Email: ag112526@gmail.com Web Page: www.alemayehu.com Lecture 3 Investment Theories Addis Ababa University Departement of Economics MSc/MA Program 2014

Outline of the Lecture (i) The Neoclassical or User Cost Model (The Jorngeson Model)

(ii) The Tobin-q Model (James Tobin)

(iii) The Accelerator Model (Naive, Flexible Partial Adjustment

Models and Models of Crowding-in /Out

Alemayehu Geda Dept. of Economics, Addis Ababa University, 2014-2015 E-mail AG112526@gmail.com & web : www.Alemayeh.com

In most investment studies investment theories are presented in the context of

Business fixed investment

Residential investment

Inventory investment

There are also various theoretical approaches:

The Neoclassical theory (User cost or Jorngson models)

The Tobin-q approach (Tobin)

The Accelerator model (Keynes, Chenery)

Various approached which modify one or the other of the above theoretical approaches

Some of the theories fits some kind of investment (eg the neoclassical theory is designed for business fixed

investment while accelerator fits best inventory investment)

We will discuss three theoretical approaches.

The User Cost (Neoclassical) Model The model attempts to evaluate the benefit and cost of

owning capital. Based on Keynes’ original approach the model attempts

to relate the level of investment with marginal product of capital, the interest rate and the tax rule affecting firms. So Investment=f(MPK, r, t)

For pedagogical reason (unrealistically) we will assume

two type of frim (a) a rental firms and (b) producer frim.

The producer firm produce goods and services using capital rented from the rental firm (which buy capital & rent only)

The Rental Price of Capital for Producer Firm

The firm rents capital at a rental rate of R and sells its output at price P. The real cost of capital for producer firm being R/P.

The real benefit of a unit of capital is the marginal product of capital (MPK). The MPK declines as capital increases.

To maximize profit the firm employs capital till the MPK=R/P. The MPK can be taken thus, as the demand for capitial curve. The curve is

downward sloping as MPK declines when K is large (see next diagram)

At any point in time the SS of capital is fixed , thus the real rental price of capital adjust to equilibrate the supply and demand for capital as shown below

MPK,R/P Capital Supply

MPK

K-fixed K

To see what variable influence the rental price of capital we will assume a CD production function

𝑌 = 𝐴𝐾𝛼 𝐿1−𝛼 𝑤ℎ𝑒𝑟𝑒 𝑀𝑃𝐾 = 𝛼𝐴𝐿

𝐾

1−𝛼 ; 𝛼<1

Because the rental price equals the MPK in equilibrium we

have : R/P= 𝑀𝑃𝐾 = 𝛼𝐴𝐿

𝐾

1−𝛼

This gives us the factors that determine the rental price of capital, which are: (a) The lower the stock of capital the higher the R/P ( the rental price of

capital).

(b) The greater the amount of labour employed the higher the R/P

(c) The better the technology (A), the higher the R/P

The Cost & Benefit of Capital for the Rental Firm The benefit is: the revenue from renting, R/P for each unit of

capital it owns and rents out. The cost of the rental firm includes the following: When it buys capital it losses interest that would have obtained by

depositing the capital (if borrowed, interest cost to banks). If Pk is price of capital, this interest cost is iPk (i = nominal interest rate)

While renting out, the price of capital can change. There could be capital gain or loss - let us call it ΔPk

While renting out, the capital suffers wear and tear, σ . The dollar cost of this

depreciation is given by σ Pk

Thus, the total cost of renting out a unit of capital for one period is therefore**:

𝐶𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑡𝑖𝑎𝑙 = 𝑖𝑃𝐾 − ∆ 𝑃𝐾+ 𝜎𝑃𝐾= 𝑃𝐾 𝑖 +∆𝑃𝐾

𝑃𝐾+ 𝜎

Given the above formulation, the rental firms decision to increase or decrease its capital stock (K) depends on its benefit/revenue, R/P, and

the real cost of capital = 𝑃𝐾

𝑃 (r+σ)

[assuming general and capital price changes are the same; & r=i-inflation]

Profit rate =Revenue [R/P]-Cost [𝑃𝐾

𝑃 (r+σ)]

Since in equilibrium the real rental price equals the MPK

Profit rate =MPK - [𝑃𝐾

𝑃 (r+σ)]

From this we see the economic incentive to invest depends on the

difference between MPK and real cost of capital= 𝑃𝐾

𝑃 (r+σ)

Eg If MPK>𝑃𝐾

𝑃 (r+σ) +veΔ K=Investment

Eg If MPK<𝑃𝐾

𝑃 (r+σ) -veΔ K=Capital stock shrink

We can now disregard the dichotomy that we have created b/n the rental and producer firm, as producer firms usually buy capital themselves. In that set-up the investment decision can be shown as:

ΔK= net Investment, Inet=f(MPK - [𝑃𝐾

𝑃 (r+σ)])

Gross Investment, Igross=f(MPK - [𝑃𝐾

𝑃 (r+σ)])+ σ K

This models shows investment is positively related to MPK and

negatively related to real interest rate which raises the cost of capital.

In equilibrium:ΔK=0 and hence MPK= [𝑃𝐾

𝑃 (r+σ)])

Thus in the long run MPK equals the cost of capital, the speed of adjustment to capital stock depends on how costly it is to build, deliver, and install new capital [see the partial adjustment model at the end of this lecture).

Is based on the work of J. Tobin (1965) –Nobel prize winner

Tobin noted a link b/n fluctuation in investment and fluctuation in stock market

Stock/share prices in stock market tends to be high when firms have many opportunities (as it entails high investment and high returns to share holders)

So stock prices show the incentive to invest (determinates of)

Tobin proposed: firms base their investment decision on the following ratio, called Tobin q.

𝑞 =𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙

𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙

The value of the numerator is determined by the stock market

The value of the denominator is the price of capital if it were purchased today.

According to Tobin, if q>1 The stock market value of installed capital is more than its

replacement cost.

Managers can raise the market value of their firms stock by buying more capital.

If q<1 manger will not replace capital as it wears out. Although this theory appears different, it is strongly related to the

user cost model because Tobin’s q depends on current and future expected profit from installed capital

If MPK exceeds the cost of capital, then, the installed capital is earning profit

These profits make the listed firms desirable, which raises the market value of this firms in the stock market, implying a higher value of q.

Similarly, if the MPK falls short of cost of capital , then installed capital is incurring losses, implying a low market value and low value of q.

Formally, the owners of capital received MPK for each unit of capital forever if MPK is constant. The present value in nominal

terms= 𝑃(𝑀𝑃𝐾)

1+𝑟

The advantage of Tobin’s q as measure of the incentive to invest is that it reflects the expected future profitability of capital as well as the current profitability. Eg. If corporate tax is reduced next year, the value of stock today, Tobin q, will

rise increase in Investment (I).

A fall in q shows investor’s pessimism.

----------------------------------End of Tobin q-------------------------------

-

Is based on Keynes, Samuelson, Chenery.. It is very much relevant for inventory investment but is also for all type of investment

The model assumes that firms hold a stock of inventories which is proportional to the firms level of output. Reason for this: When output is high firms need more materials and supplies on hand

they have more goods in the process of being completed.

When the economy booms firms need more goods on shelf (rather than adjusting through production)

Thus, inventory [N] is a certain [β] proportion of income [Y]/output

Inventory Investment I=ΔN=βΔY ▪ - is the naive accelerator model

The model predicts that [inventory] investment is proportional to the change in output. Note that ΔY is the accelerator of investment.

The accelerator model can also be derived, in principle, form the user cost mode. Given a CD production function the equilibrium condition for investment we had,

R/P= 𝑀𝑃𝐾 = 𝛼𝐴𝐿

𝐾

1−𝛼⇒

𝛼𝑌

𝐾=

𝑅

𝑃

𝐾 =

𝛼𝑌

(𝑅/𝑃)

∆𝐾 = ∆

𝛼𝑌

(𝑅/𝑃)=

𝛼

𝑅/𝑃∆Y= β∆Y

Here with no trend in the variables in the square bracket,

[R/P], growth of output or demand determines investment. The accelerator has also various variants used in applied

work and briefly shown in the rest of this lecture.

Here we can briefly see the different forms

the accelerator model takes in the applied work. This various forms include:

The partial adjustment model

The Naïve and Flexible accelerator model

The Crowding-out and Crowding-in model

NB: γ4=(1-λ) while γ1 to 4 = γβ