Consider a very simple economy in which two goods, ale and corn, are produced from inputs of labor, land, and produced ale and corn. Ale and corn are each both consumption and capital goods. All production processes in this example require a year to complete and exhibit Constant Returns to Scale. One process is known for producing ale, and two processes are known for producing corn. These processes are shown in Table 1.
| INPUTS HIRED AT START OF YEAR | ALE PRODUCING PROCESS | FIRST CORN- PRODUCING PROCESS | SECOND CORN- PRODUCING PROCESS |
|---|---|---|---|
| Labor | 1 Person-Year | 4 Person-Years | 7 Person-Years |
| Land | 9/8 Acre | 5/6 Acre | 1 Acre |
| Ale | 0 Barrels | 1 Barrel | 1/2 Barrel |
| Corn | 1/8 Bushel | 0 Bushels | 0 Bushels |
| OUTPUTS | 1 Barrel Ale | 1 Bushel Corn | 1 Bushel Corn |
Assume that endowments of labor and land are given for this economy. In particular, the firms in this economy have access to 320 person-years of labor and 140 acres of (homogeneous) land.
In short, this economy uses two primary factors, labor and land, to produce a net output of two consumption goods, ale and corn. This example differs from misleading introductory textbook models of comparative advantage in that the use of produced capital goods is shown explicitly.
A technique consists of the ale-producing process and exactly one of the corn-producing processes. The technique in which the first corn-producing process is used is called the Alpha technique. The other technique is called the Beta technique. Given the technique and the required consumption goods, one can calculate the levels at which each process in the technique must operate to produce these consumption goods in a stationary state. The amount of labor and land constrains the maximum net output in a stationary state. Economies in a stationary state with this technology and these endowments can consume more ale if they consume less corn. In other words, ale and corn can be traded off in this sense. How would you construct the Production Possibilities Frontier from the above data on technology and endowments to show this trade-off? Does your construction show a linear combination of the two techniques along the frontier?
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3 comments:
ummm ... think ... think
No is the answer. I don't think it can be.
Ale is more land-intensive and less labour intensive than either corn A or corn B. Corn B is much more labour intensive than corn A and more land intensive, though not all that much more land intensive when you include the land "embodied" in the ale input. So ... when you are producing a lot of ale, you will have surplus labour and land will be the constraint, so you will use technique B exclusively. Similarly when you are producing a lot of corn, you will have surplus land and labour will be the constraint and you will use technique A exclusively.
When you are in the middle of the PPF, then both constraints will be binding, and you will use both technologies because they convert land and labour into outputs at different rates, so the solution will have some of both.
I have not a clue in hell how to calculate the actual PPF though ... oh dammit, it just involves doing the bloody linear algebra doesn't it? Well I'm not going to do it then as this has basically atrophied within me, but I think I can follow it nonetheless.
(further to the above; I suspect you could have picked the input endowments such that there always was a linear combination of the two technologies used but since this is meant to be a switching example I'm guessing that you didn't)
dsquared, I assure you I had already written the next post in the series (expect for the concluding questions about prices) before looking at your comment. I don't think you need do the arithmetic if you can just see the answer.
I actually learned about matrices in high school. I might have even seen a linear program somewhere about then.
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