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Investment
Financial vs physical capital
• In the consumption-saving model studied earlier, we studied the role of
financial capital and investment.
• Financial capital consists of IOUs like stocks, bonds, and money.
• Financial capital may facilitate production of final goods and services, but
does not directly produce output.
• In contrast, physical/human capital serves as an input in the production
process.
• Think of physical capital as an intertemporal production technology.
Investment
• Investment refers to newly produced capital goods.
— machinery, inventory, homes, office buildings, roads, sewers, maintenance and repair.
• NIPA only records investment in non-human forms of capital.
— in reality, human capital investment is hugely important.
• But physical capital is obviously important too (just look around you).
• Most of the business cycle is accounted for by swings in investment.
Intertemporal production
• How might Robinson Crusoe transport coconuts today into the future?
• In the consumption-saving model, RC transported his private consumption
into the future at the expense of his debtor’s consumption—no additional
output was produced.
• But suppose RC can physically transport his coconuts to the future?
— e.g., by planting a coconut or holding it as inventory.
— this can be done even independently of financial markets.
The investment demand function
• Suppose that  units of investment today yields an expected output  ()
•  () is an increasing and strictly concave function,  0()  0  00()  0
•  is an expected productivity parameter.
•  0() is the expected marginal product of investment (future capital).
— an increasing function of  and a decreasing function of 
The investment demand function
• Let  denote the gross real rate of interest.
• Expected net present value (NPV) of capital spending  is given by
(
 ()
 () = − +

)
• The investment demand function ( ) maximizes  () i.e.,  0() =
0 or
 0() = 
•  is a decreasing function of  and an increasing function of 
Stock market value
• Define  ∗( ) ≡  (( ))
• Can interpret  ∗ as the value of business sector capital (corporate stocks
and bonds).
•  ∗ is a decreasing function of  and an increasing function of 
• Re: increase in  = “good news” and decrease in  = “bad news.”
• Good news leads to boom in desired capital spending and stock market
values.
Investment and saving
• Earlier, we studied the consumption-saving choice of Robinson Crusoe assuming only financial capital.
• Suppose now that RC can invest in domestic capital .
• GDP flow is now given by {1 2} = {  ()}
• Consumption-saving decision is solution to
2
max  (1 2) subject to 1 +
≤  +  ∗( )

Investment and saving
• Solution implies a desired domestic saving function (  )
•  is increasing in  increasing in  and decreasing in 
— note: an increase in  and  elicits a weaker response in desired saving
than changes in  or  individually (why?).
• Recall  ≡  +  +  +   and  ≡  −  −  implies  ≡  +  
• In our model,  = (  ) − ( )
Closed economy
• In a closed economy,  = 0 so that saving must equal investment
(  ) = ( )
• One can think of equation above as defining an “IS curve”—combinations
of ( ) that are consistent with  = 
• Alternatively, one can think of IS curve as representing the aggregate demand for output   as a function of  and 
• This framework can accommodate many different views of the business
cycle.
Classical view
• Level of  is determined in labor market, largely independent of  and 
• In this case, (∗  ) = (∗ ) determines the equilibrium interest
rate ∗
• Fluctuations in  reflect rational changes in expectations, inducing cyclical
fluctuation in capital spending, stock market valuations, and interest rates.
• No obvious role for government stabilization policies.
Keynesian view
• Level of  is determined by aggregate demand, a function of  and 
• In this case, (  ∗ ) = ( ) determines equilibrium level of  ∗
• But  ∗ may be either too high or too low because market expectations 
can be overly optimistic or pessimistic (animal spirits).
• Stabilization policies are desirable, e.g., lower  (add stimulus) if overly
pessimistic decline in .