...My post that crashed this afternoon was largely concerned with connecting individual subjective marginal utility to overall market demand. I'll try that again later in a separate post....
How the subjective values of individuals become total market demand -
The Austrian Subjective Theory of Value assigns values to economic goods and services according to the degree to which they can be utilized as means to satisfy the most urgent ends of a given individual at a given time, place, and in a given context. However, these utility values cannot be represented by numerical values that can be dealt with by mathematical operations, but rather can only be compared one to another or ranked in order of subjective utility as a group. Since overall market demand in either unit quantities of goods demanded or in money expended are subject to mathematical operations, it is not necessarily obvious how the immeasurable subjective values of individuals are combined and transformed into total market demand. This note attempts to demonstrate one possible explanation of this transformation.
Assume that multiple individuals exist in a simple market economy in which only three economic goods exist -- apples, oranges, and pears. Further assume for simplicity that no individual can possess more than 3 of any of the goods. Also assume that all of the goods are consumed in total each day, and must be purchased again the next day with the income earned today.
Every individual earns a particular amount of money each day, not necessarily the same from one individual to another, and must choose the combination of the 3 goods which maximize his subjective utility each day, subject to the amount of money he has earned and the market prices of each of the 3 goods.
On any given day, an individual must choose one of the 64 (4x4x4) possible different combinations of goods, as four unit quantity choices, 0,1,2, and 3, can be made independently for each of the 3 goods.
This choice is the result of an implicit rank ordering of the 64 different combinations of goods reflecting the subjective utilities of the combinations in serving as means to satisfy the given individual's most urgently desired ends.
For example, a combination of 0 apples, 0 oranges and 0 pears will be ranked number 64, as it has no utility at all. On the other hand, a combination of 3 apples, 3 oranges and 3 pears will be ranked number 1 simply because it can be utilized to serve the most urgent end or ends, given that the limit quantity of 3 was assumed for simplicity. We also can deduce that the combination ranked number 2 will consist of 2 goods of quantity 3, and 1 good of quantity 2, but we can't predict which goods will be which. Similarly, rank number 63 will consist of a single unit of a single good, but which good cannot be predicted, and will presumably vary from individual to individual, and possibly from time to time as well. Note that all 64 different rank numbers are implicitly assigned one to one to the 64 different possible combinations of goods by an individual entirely based on his subjective judgements. These rankings are entirely independent of the market prices for the 3 goods. The rankings are implicit in the sense that they are not made concrete until an actual choice is required for an economic exchange action.
Now that we have the subjective rankings from 1 to 64 for all the possible combinations of apples, oranges and pears for every individual, we now need only the daily income for every individual and the market prices for each of the three goods.
To determine the actual demand for each individual, we execute the following algorithm --
Starting with the rank 1 combination, use the market prices for each good to determine the total expenditure (cost) required to acquire that combination. Since rank 1 will consist of 3 each of apples, oranges and pears, the cost of the rank 1 combination will be the sum of 3 times the market price of apples, plus 3 times the market price of oranges, plus 3 times the market price of pears. Store the expenditures for each of the 3 goods, and the total sum for later use.
If this cost is greater than an individual's daily income, repeat the above for the next lower ranked combination until a combination is encountered which can be purchased with the daily income available for that individual.
Repeat all of the above for all of the individuals.
We now have, for every individual, how much he will purchase of each good, both in unit quantity and money expenditure, so as to maximize his utility of the goods acquired by expending his entire daily income at market prices. (For simplicity, assume that any of the income left over when the cost falls slightly below income can be distributed to charity).
If we then total the unit quantities and goods expenditures over all individuals, we have arrived at the total market demand in both units and money for all three goods. These are actual numbers, subject to mathematical operations, but have been derived from the immeasurable subjective utilities of individuals.
Note that if any market price or prices change, this doesn't mean that the ranking of the combinations of goods change, although they may do so for any reason at any time, as they are purely subjective. However, what must happen is that the algorithm above for determining actual demand for each individual must be completely re-evaluated and market demand may change as a result.
To investigate this, assume that the market price of apples declines and that the market prices of oranges and pears remain constant. What does this imply about the market unit demand for apples, oranges and pears?
Determine which of the following statements are true and which are false.
1. Nothing may happen. T/F
2. Nothing may happen except that larger amounts are donated to charity. T/F
3. The demand for apples must increase if there is any change in demand at all. T/F
4. The demand for apples, oranges and pears may all decrease. T/F
5. The demand for oranges may increase. T/F
6. The demand for apples, oranges, and pears may all increase. T/F
7. The demand for apples may decrease. T/F
Enough already!
Note that an entirely separate set of questions could be asked about the market money demand for the three goods as changes in the expenditures for a given good are not necessarily tied to changes in the unit demand for that good. (Remember the price elasticity of demand from previous posts).
Regards, Don |
