If a firm hires a specific capital good for a unit of time, the payment is the rental price of the capital good. For example, suppose that a warehouse pays $100,000 per year to an independent company that maintains fleets of forklifts. These annual payments are clearly due to the “marginal product” of the forklifts; the warehouse can sell more of its own services to its customers when it has use of the forklifts.
However, these technological facts tell us nothing about the rate of interest enjoyed by the owners of the forklifts. In order to determine that, we would have to know the market price of the forklifts. For example, if the forklifts that the independent company rents out to the warehouse could be sold on the open market for $1 million, then their owners would enjoy a 10-percent return each year on their invested capital. But if the forklifts could be sold for $2 million, then the $100,000 payments—due to the “marginal product” of the forklifts—would correspond to only a 5-percent interest rate. As this simple example illustrates, knowledge of the marginal product of capital, per se, does not allow us to pin down the rate of interest.
I am not sure what to take as exogenous and what to take as endogenous. My inclination would be to treat the interest rate and the marginal product of forklifts as exogenous and the market price of forklifts as endogenous. That is because I was brought up by the folks who lost the Cambridge controversy but went ahead writing down neoclassical production functions, anyway. While Murphy comes from yet another tradition, I doubt that he has the same agenda as, say, Jamie Galbraith.
Let’s back up, though, and try to think of a general equilibrium model. (Nick Rowe does something similar, with diagrams.)
In the entire economy, we have:
–one type of consumable output
–a technology for producing consumable output using forklifts and labor
–a technology for producing forklifts using labor
–many households, all with a utility function that includes leisure and the consumable output
Next, make the following assumption (to be changed later):
(a) all production takes place instantaneously, meaning that you can produce forklifts and immediately use them in the production of consumable output
In this case, the price system has to solve the problem of allocating labor efficiently among three uses: producing forklifts; working in the consumable output sector; and leisure. However, there are only two actual goods in the economy–consumable output and leisure. Hence, there is only one relative price, which is the real wage rate. Labor has a direct marginal product (in the consumable output industry) and an indirect marginal product (the marginal product of forklifts times the marginal productivity of workers in the forklift industry). You equate those two. You equate them to the real wage. We can use the price of consumable output as the numeraire, meaning that we fix the price of consumable output at one nominal dollar. Then the nominal wage is the real wage. Along the way, we might calculate the price of a forklift as a sort of “shadow price.”
Obviously, in this economy, there is no interest rate, and the technology cannot determine the interest rate.
Next, make this a two-period economy, with an alternative assumption:
(b) forklifts produced in the first period cannot be used to produce consumable output until the second period.
We need some further assumptions to fill out the two-period model:
–we may or may not have an initial endowment of forklifts available for producing consumable output the first period. If there is no endowment of forklifts, it is still possible to produce nonzero consumable output using just labor. If there is an endowment of forklifts, some fraction of them may be useless next period (depreciation).
–households want to consume output in both periods, and they want leisure in both periods, but they prefer more of each today than tomorrow.
Now, the economy has four goods: leisure this period, leisure next period, consumable output this period, and consumable output next period. The problem is to allocate labor among the four goods.
Taking consumable output in the second period as the numeraire (that is, setting its nominal price equal to one dollar), there are three relative prices: the real price of output this period, the real wage this period, and the real wage next period.
Under assumption (a), we had no interest rates. Under assumption (b), there is a sense in which we have (at least) two interest rates. One pertains to the real price of output this period (if it is $1.10, one could say that the interest rate is 10 percent). Another pertains to the ratio of the price of leisure this period to the price of leisure next period.
Once again, the price of forklifts is implicit–it is a shadow price. The ratio of the marginal product of forklifts in the second period to the price of forklifts probably relates to the interest rates in the model, but not in an obviously neat way that I can see.
The neoclassical production function nonetheless proceeds as if the there is a single interest rate, and it implies that the shadow price of forklifts will turn out to be the future marginal product of forklifts discounted at “the” interest rate. In defense of this tradition, there are assumptions one can make about utility functions or production functions that can get you a single interest rate, and those assumptions may be a reasonable first approximation of reality.
Isn’t there more to the story than this? Forklifts aren’t some good that simply materialize from the owners’ sheds into the users’ sheds to do work and then rematerialize back into the owners’ sheds.
If a capital good is going to be continually used in production, there is only one reason that you rent it rather than own it — namely that the company you rent from has a comparative advantage over you in acquiring, owning, maintaining, and retiring the capital good.
Even beyond the expertise and comparative advantage, the leasing company has expenses that an owning user would not have, including marketing, warehousing, and carrying excess inventory. So it is virtually certain that the rental price is well above the interest rate of the price of the capital good itself. But it’s worth it to the renting company because it reduces their hassles and lets them focus on their comparative advantages.
I don’t know that this fundamentally affects the model you are putting together. It simply is worth noting that the price of the capital good is but a possibly arbitrary portion of its cost to its owner.
I don’t see any reason for it to be true, but I think administrative pricing is adopted to make it true. Only those firms that adopt it survive over the long term.
“there are assumptions one can make about utility functions or production functions that can get you a single interest rate, and those assumptions may be a reasonable first approximation of reality.”
Are there any readers out there who know what assumptions Kling is referencing? I have been trying to read up on the Cambridge Capital Controversy over the past few days, and it seems as if the responses from mainstream economists to this are to shrug their shoulders and just go about their business, presumably because they think that the assumptions underlying their work, while clearly lacking in a sort of analitical rigor, are still useful none the less. But why are they useful?
I assume that if everyone has an identical rate of time preference across all goods that you get a single interest rate. But even that does not ensure that you can aggregate capital.