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INVESTMENT:The Rental Price of Capital, The Cost of Capital

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Macroeconomics ECO 403
VU
LESSON 40
INVESTMENT
·
Investment is the most volatile component of GDP. When expenditure on goods and
services fall during a recession, much of the decline is usually due to a drop in investment
spending.
·
Economists study investment to better understand the fluctuations in the economy's output
of goods and services.
·
The models of GDP, such as IS-LM model, were based on a simple investment function
relating investment to real interest rate: I = I(r)
·
That function states that an increase in the real interest rate reduces Investment.
·
Here we look more closely at the theory behind this investment function.
Three types of Investment Spending
·
We shall build models of each type of investment to explain the fluctuations in the economy.
Also these models will shed light on the questions such as:
­  Why is investment negatively related to the interest rate?
­  What causes investment function to shift?
­  Why does investment rise during booms and fall during recessions?
Business Fixed Investment
·
The largest piece of investment spending (about ¾ of total) is business fixed investment
­  Business: these investment goods are bought by firms for use in future production.
­  Fixed: This spending is for capital that will stay put for a while (as opposed for inventory
investment)
·
Business Fixed investment includes everything from fax machines to factories, computers
to company cars
The standard model of business fixed investment is called the neoclassical model of
investment. It examines the benefits and costs of owning capital goods. Here are three
variables that shift investment:
1) The marginal product of capital
2) The interest rate
3) Tax rules
·  To develop the model, imagine that there are two kinds of firms:
1. Production firms that produce goods and services using the capital that they
rent
2. Rental firms that make all the investments in the economy.
In reality, however, most firms perform both functions
The Rental Price of Capital
·
A typical production firm decides how much capital to rent by comparing the cost and
benefit of each unit of capital.
·
The firm rents Capital at a rental rate R and sells its output at a price P
·
The real cost of a unit of capital to the production firm is R/P
·
The real benefit of a unit of capital is the marginal product of capital, MPK (the extra output
produced with one more unit of capital)
·
MPK falls as the amount of capital rises
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Macroeconomics ECO 403
VU
·
So, to maximize profit, the firm rents capital until the MPK falls to:
MPK = R/P
·
Hence MPK determines the downward sloping demand curve for capital for a firm
·
While at point in time, the amount of capital in an economy is fixed, so supply curve is fixed
·
The real rental price of capital adjusts to equilibrate the demand for capital and the fixed
supply.
Capital supply
Real rental
price, R/P
Capital demand (MPK)
K
Capital stock, K
The Cobb-Douglas production function serves as a good approximation of how the
·
actual economy turns capital and labor into goods and services.
The Cobb-Douglas production function is:
·
Y = AKαL1-α
Where
Y ⇒ is output
K ⇒ capital
L ⇒ labor
A ⇒ a parameter measuring the level of technology
α ⇒ a parameter between 0 and 1 that measures capital's share of output.
The marginal product of capital (MPK) for the Cobb-Douglas production function is:
·
MPK = αA (L/K) 1-α
Because the real rental price (R/P) equals MPK in equilibrium, we can write:
·
R/P = αA (L/K) 1-α
This expression identifies the variables that determine the real rental price.
·
It shows the following:
·
The lower the stock of capital, the higher the real rental price of capital
·
The greater the amount of labor employed, the higher the real rental price of capitals
·
The better the technology, the higher the real rental price of capital.
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Macroeconomics ECO 403
VU
Events that reduce the capital stock, or raise employment, or improve the technology, raise
the equilibrium real rental price of capital.
The Cost of Capital
·
The Rental firms, just like car rental firms merely buy capital goods and rent them out.
·
Let's consider the benefit and cost of owning capital.
­  The benefit of owning capital is the real rental price of capital R/P for each unit of capital
it owns and rents out.
For each period of time that a firm rents out a unit of capital, the rental firm bears three costs:
1. Interest on their loans, which equals the purchase price of a unit of capital PK times the
interest rate, i, so iPK
2. The cost of the loss or gain on the price of capital denoted as  -ΔPK
3. Depreciation δ defined as the fraction of value lost per period because of the wear and
tear, so δPK
·
Therefore,
Total cost of capital = iPK - ΔPK + δPK
Or
= PK (i - ΔPK/PK +δ)
The cost of capital depends upon the price of capital, the interest rate, rate of change
of capital prices and the depreciation rate.
·
Example: A Car rental company
­  Buys cars for Rs.1, 000,000 each and rents them out to other businesses
­  If it faces an interest rate i of 10% p.a. so the interest cost,   iPk = Rs.100, 000 p.a.
­  Car prices are rising @ 6% per year, so excluding maintenance costs the firm gets a
capital gain, ΔPk = Rs.60,000 p.a
­  Cars depreciate @ 20% p.a. so loss due to wear and tear,
δPk = Rs.200, 000
·
So,
Total cost of capital = iPK - ΔPK + δPK
= 100,000 ­ 60,000 +200,000
= Rs.240, 000
Summary
·
Investment
­  Business Fixed Investment
· Rental Price of Capital
· Cost of Capital
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Table of Contents:
  1. INTRODUCTION:COURSE DESCRIPTION, TEN PRINCIPLES OF ECONOMICS
  2. PRINCIPLE OF MACROECONOMICS:People Face Tradeoffs
  3. IMPORTANCE OF MACROECONOMICS:Interest rates and rental payments
  4. THE DATA OF MACROECONOMICS:Rules for computing GDP
  5. THE DATA OF MACROECONOMICS (Continued…):Components of Expenditures
  6. THE DATA OF MACROECONOMICS (Continued…):How to construct the CPI
  7. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES
  8. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  9. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  10. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  11. MONEY AND INFLATION:The Quantity Equation, Inflation and interest rates
  12. MONEY AND INFLATION (Continued…):Money demand and the nominal interest rate
  13. MONEY AND INFLATION (Continued…):Costs of expected inflation:
  14. MONEY AND INFLATION (Continued…):The Classical Dichotomy
  15. OPEN ECONOMY:Three experiments, The nominal exchange rate
  16. OPEN ECONOMY (Continued…):The Determinants of the Nominal Exchange Rate
  17. OPEN ECONOMY (Continued…):A first model of the natural rate
  18. ISSUES IN UNEMPLOYMENT:Public Policy and Job Search
  19. ECONOMIC GROWTH:THE SOLOW MODEL, Saving and investment
  20. ECONOMIC GROWTH (Continued…):The Steady State
  21. ECONOMIC GROWTH (Continued…):The Golden Rule Capital Stock
  22. ECONOMIC GROWTH (Continued…):The Golden Rule, Policies to promote growth
  23. ECONOMIC GROWTH (Continued…):Possible problems with industrial policy
  24. AGGREGATE DEMAND AND AGGREGATE SUPPLY:When prices are sticky
  25. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…):
  26. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…):
  27. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  28. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  29. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  30. AGGREGATE DEMAND IN THE OPEN ECONOMY:Lessons about fiscal policy
  31. AGGREGATE DEMAND IN THE OPEN ECONOMY(Continued…):Fixed exchange rates
  32. AGGREGATE DEMAND IN THE OPEN ECONOMY (Continued…):Why income might not rise
  33. AGGREGATE SUPPLY:The sticky-price model
  34. AGGREGATE SUPPLY (Continued…):Deriving the Phillips Curve from SRAS
  35. GOVERNMENT DEBT:Permanent Debt, Floating Debt, Unfunded Debts
  36. GOVERNMENT DEBT (Continued…):Starting with too little capital,
  37. CONSUMPTION:Secular Stagnation and Simon Kuznets
  38. CONSUMPTION (Continued…):Consumer Preferences, Constraints on Borrowings
  39. CONSUMPTION (Continued…):The Life-cycle Consumption Function
  40. INVESTMENT:The Rental Price of Capital, The Cost of Capital
  41. INVESTMENT (Continued…):The Determinants of Investment
  42. INVESTMENT (Continued…):Financing Constraints, Residential Investment
  43. INVESTMENT (Continued…):Inventories and the Real Interest Rate
  44. MONEY:Money Supply, Fractional Reserve Banking,
  45. MONEY (Continued…):Three Instruments of Money Supply, Money Demand