Capital - Text: Ch. 15 What is Capital? Physical Capital : machines, tools, factories, buildings. i.e. a productive, durable input, human-made. - Physical capital provides a stream of productive services over its lifetime. - The value of a unit of physical capital derives from the value of the productive services it generates. - Creation of physical capital requires investment spending. (investment: pay a cost now in expectation of future payoffs) - Investment spending must be financed: - via borrowing: cost determined in financial markets; or 1
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- Physical capital provides a stream of productive services over its lifetime.
- The value of a unit of physical capital derives from the value of the productive services it generates.
- Creation of physical capital requires investment spending.
(investment: pay a cost now in expectation of future payoffs)
- Investment spending must be financed:
- via borrowing: cost determined in financial markets; or
- from a firm’s own funds: opportunity cost is the return could obtain in financial markets.
- this creates a link between financial returns and returns on investment in physical capital.
- Physical capital is a ‘real asset’ producing a stream of real returns (productive services)
- Financial assets: provide a stream of financial returns to its owner.
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Demand for Physical Capital: Renting Capital to Use it in Production
- Call ‘K’ the quantity of physical capital.
- Logic of short-run labour demand model can be extended to capital.
- Marginal revenue product of capital (MRPK)= MR x MPK
MR = marginal revenue, i.e. extra revenue from sale of extra output
MPK = marginal (physical) product of K, i.e. extra output produced when a firm uses extra K.
- So MRPK measures the value of extra output produced when the firm uses extra K.
- if assume diminishing returns to K: MRPK falls as K rises.
- Let “r” be the rental or lease price of capital (rental rate):
- price paid per period to use one unit of K;
(equivalent of the wage rate in the labour demand model).
- Hiring (renting or leasing) K:
MRPK > r Firm will hire more K (benefit > cost)
MRPK < r Firm hires less K (benefit < cost)
MRPK = r Profit maximizing firm hires up to this point.
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- So demand for K is affected by:
- Factors affecting MRP of capital:
- Output market conditions (through MR) e.g. rise in price of oil leads to more K hired in oil industry
(MRPK shifts up)
- Factors affecting MPK (technology, quantity and quality of other inputs)
e.g. technology allows development of tar sands: more K hired there (rise in MP, MRPK shifts up)
- Rental price of K, i.e. “r”.
i.e. rise in r: less K is hired. (r = red line shifts up)
- Model works just like the short-run labour demand model.
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The Rental Price of Capital and the “User Cost of Capital”
- Interpretation of ‘r’: a per period price at which the firm can rent or lease K.
- Can define a 'per period’ cost measure for the owner of the unit of K.
i.e. the “user cost of capital”: cost to the owner of tying up their money in a unit of K.
- What determines the user cost of physical K?
- say it costs PK to buy a machine.
- Costs of owning a unit of capital for a period: - opportunity cost of funds: i∙ PK
- owner could have invested PK at an interest rate of i
(i = return on best alternative investment of similar risk)
- machine requires maintenance costs at rate “m∙ PK” per period
(m = maintenance cost as a share of PK)
- the machine loses value each period due to depreciation: d∙ PK d = depreciation cost as a share of PK
(depreciation: could be physical e.g. machine wears out or could reflect obsolescence)
- The user cost of K is the sum of these per period costs:
(i + m + d) ∙ PK
(this assumes no capital gains or losses due to changes in the resale price of the unit of K – see the extension below)
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- If a firm buys K for its own use the user cost plays the role of its "rental price" (it is what it costs the buyer on a per period basis)
- so a firm that buys K rather than rents it, should buy more K until: MRPK = (i + m + d) ∙ PK
- renting-to-use or owning-to-use are substitutes: capital users will choose the cheapest option. In equilibrium substitution implies
rental price = user cost).
- If the firm buys K to lease or rent it the "rental price" must cover the user cost if leasing is to be a profitable business.
- But: competition between suppliers of K implies a rental price no higher than the user cost i.e.
if: r > (i + m + d) ∙ PK more K will bought and rented out, the extra supply of rented K gives ↓r (PK
could rise too as firms enter the rental business)
if r < (i + m + d) ∙ PK no one supplies rental K, shortage
leads to ↑r. (PK could fall too – fewer firms in the rental business buying K)
Equilibrium requires:
r = (i + m + d) ∙ PK
or:r/PK = i + m + d
- m and d : think of as mainly technically determined
- then : r varies directly with i.
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(NOTATION INCONSISTENCY IN OLD EDITION: equation (15.1) and (15.2): r is a rental price (in $) – like above. Text p. 488 equation (15.3): r is a proportion (or %) i.e. it is the same as r/ PK above. In the new edition this is fixed by defining ‘k’=r/PK) ) - When supply and demand for rented capital are equal:
MRPK = r = (i + m + d) ∙ PK
↑ ↑ Demand Supply
- Demand downward sloping; supply – flat at (i + m + d) ∙ PK
- More K will be rented if:
- Rise in demand MRP rises (e.g. due to technological improvement, rise in
price of output produced with the K)
- Rise in the supply of K:
- will result if it becomes less costly to supply
- if i, m or d falls
- PK falls.
- Some common complications to the user cost setup:
- Capital gains / losses (PK change in resale price of K): - after using K for a period the owner of the K may sell it.
- if PK is higher than when purchased – this is a gain (deduct it from the user cost);
- if PK is lower than when purchased the capital loss must be added to the user cost.
( user cost is then: (i + m + d)∙PK - PK(1-d) )
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- Taxation of capital can affect the user cost in several ways (big topic in economics of business taxes)
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Basics of Asset Pricing:
- Value of an asset: determined by the stream of returns it will generate over it’s lifetime.
Simple asset: One payment one period in the future
Present value (PV) of returns = B1/(1+i)
B1 = payment received next period;
i = interest rate used in discounting future dollars.
i.e. going rate on a “similar” investment.
Present value: measures the value of future payments now.
i.e., how much would you have to invest at rate i to receive this payoff in the future.
(see text Chapter 5 discussion of present value)
- buy this asset if: Price < PV of returns
i.e. cost < benefit
or if: return on asset or yield (ir) > i
ir? internal rate of return or ‘yield’ on the asset.
Calculated by solving: Price = B1/ (1+ir) for ir
It is the rate of return that would generate the stream of payments (B1) given that you have invested ‘Price’ in this asset.
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- Don’t buy the asset if: Price > PV of returns.
cost > benefit
or if: rate of return (ir) < i
- Equilibrium: Price = PV of returns.
- at the equilibrium asset price the stream of returns gives exactly a rate of return of i
i.e. same return as on similar assets
- if not? say price too low, ir>i demand for this asset will rise pushing up its price.
General asset: N periods
PV of returns ¿B1
(1+i)+
B2
(1+i)2 +B3
(1+i)3 +…+BN
(1+i)N
B1 … BN = payments from asset in time periods 1 to N
- Present value of a payment Bt made t periods in the future:Bt
(1+i)t
- Equilibrium price of the asset equals PV of returns (using the going
rate on a similar investment as i)
- This idea can be applied to financial assets (bonds, treasury bills, shares, etc.) or real assets (houses, land, physical capital).
- Note: for a general asset its rate of return (yield) can be calculated by setting the PV formula (with ir replacing i) equal to price and solving for ir.
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Physical capital as an asset
- Text equation 15.4: gives a version of the equation above for physical K.
- For time period t= 1…N-1 with: Bt = R-M
R = extra revenues from having the extra (this is MRP! But may need a depreciation adjustment in later
periods)
M = maintenance cost.
- For t = N: BN = R – M + S
S = scrap value of the capital asset (could be the resale price of the capital if sold before it totally wears out)
- demand for physical capital linked to demand for loanable funds:
- need to finance investment in physical capital.
i.e. “i” cost of borrowing to finance K investment or opportunity cost of funds.
(An application: why are interest rates so low in 2016? Larry Summers Foreign Affairs reading)
Interest Rates
- Many interest rates not just one!
- Imagine a set of markets (one for each type of financial asset) operating like our loanable funds model.
- These markets are linked via flows of lending and borrowing between them (different financial assets are substitutes for one another).
- Why do interests rates differ?
- if different assets were identical (perfect substitutes) their interest rates would be the same in equilibrium (no one will lend in the form of an asset with low returns; no one will borrow in the form of an asset with a high interest rate)
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- So if interest rate differences persist the underlying assets must differ from the point of view of lenders or borrowers leading to different equilibrium interest rates.
- Result? An equilibrium structure of interest rates where differences in rates compensate lenders and borrowers for differences in these assets.
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- Differences in risk are one important source of differences in assets.
- Cdn. government bonds: basically riskless.
- Bonds of established well-known corporations: slightly more risky.
- Bonds of lesser-known corporations: more risky.
- Lenders appear to dislike risk.
- consequence: lenders demand higher return to hold risky assets.
- in equilibrium: iRisky = iSafe + Risk premium
(text version:lenders have indifference curves over safety (risk) and
expected return; “market” confronts lenders with a tradeoff between safety and
return)
- Some other factors affecting interest rate structure:
- long-term assets vs. short-term assets: expectations of future short- term interest rates an issue.
- liquidity and the existence of a good resale market for assets.
- foreign vs domestic assets: exchange rate changes during term of asset.
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Economic Rent
- Economic rent: the difference between what a factor of production is paid and the minimum amount the owner needs to supply it.
- Technically: difference between the price paid for the factor input and the height of the supply curve.
(Fig. 15-3)
- Measure of “surplus” that goes to the factor owner.
(closely related to “producer surplus” or idea of “economic profit)
- note the role of demand for the input in determining the size of economic rents: higher demand, higher price, higher rents.
- Special case: if the supply curve is vertical all earnings of the input are rent (minimum price to supply it is 0).
- is this the case for land?
- Labour and rents: wages in excess of the height of the labour supply curve are rents.