Question

Wassily Leontief (1906-1999) was a Russian-born, American economist who, aside from developing highly sophisticated economic theories, also enjoyed trout fishing, ballet and fine wines. He won the 1973 Nobel Prize in economics for his work in creating mathematical models to describe various economic phenomena. In the remainder of this lab we will look at a very simple special case of his work called a closed exchange model. Here is the premise: Suppose in a far-away land of Eigenbazistan, in a small country town called Matrixville, there lived a Farmer, a Tailor, a Carpenter, a Coal Miner and Slacker Bob. The Farmer produced food; the Tailor, clothes; the Carpenter, housing; the Coal Miner supplied energy; and Slacker Bob made High Quality 100 Proof Moonshine, half of which he drank himself. Let us make the following assumptions:

Everyone buys from and sells to the central pool (i.e. there is no outside supply and demand). Everything produced is consumed. For these reasons this is called a closed exchange model. Next we must specify what fraction of each of the goods is consumed by each person in our town. Here is a table containing this information:

Food Clothes Housing Energy High Quality 100 Proof Moonshine
Farmer 0.25 0.15 0.25 0.18 0.2
Tailor 0.15 0.28 0.18 0.17 0.05
Carpenter 0.22 0.19 0.22 0.22 0.1
Coal Miner 0.2 0.15 0.2 0.28 0.15
Slacker Bob 0.18 0.23 0.15 0.15 0.5

So for example, the Carpenter consumes 22% of all food, 19% of all clothes, 22% of all housing, 22% of all energy and 10% of all High Quality 100 Proof Moonshin. The columns in this table all add up to 1. Explain why this happens.

Answer 1

The columns sum up to 1 as they indicate the entirety of goods consumed within the closed exchange model, allocating all produced items among the town's inhabitants based on their consumption.

Step-by-step explanation:

In a closed exchange model like the one presented in Matrixville, the sum of each column in the consumption fractions table equals 1 due to the principle of complete utilization within the system. The values in each column represent the percentage of each specific good consumed by the Farmer, Tailor, Carpenter, Coal Miner, and Slacker Bob, respectively. Because all goods produced in the closed economy are consumed within the town and there is no external input or output, the entire production of goods is divided among the residents based on their consumption patterns.

The fractions assigned to each individual in the consumption matrix indicate the proportion of each good they consume relative to the total production. For instance, the entry "0.22" in the Carpenter's row and the "Food" column signifies that the Carpenter consumes 22% of all the food produced in Matrixville.

The sum of these consumption fractions across all residents for a particular good must equal 1 because it accounts for the entire production of that good, leaving no surplus or deficit within the closed economic system. Therefore, the columns in the consumption fractions table add up to 1, depicting complete utilization and allocation of goods among the inhabitants based on their consumption patterns.

Answer 2

The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed. There is no leftover.

When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.

Step-by-step explanation:

a) Data and Calculations:

Food Clothes Housing Energy High Quality 100

Proof Moonshine

Farmer 0.25 0.15 0.25 0.18 0.20

Tailor 0.15 0.28 0.18 0.17 0.05

Carpenter 0.22 0.19 0.22 0.22 0.10

Coal Miner 0.20 0.15 0.20 0.28 0.15

Slacker Bob 0.18 0.23 0.15 0.15 0.50

Total 1.00 1.00 1.00 1.00 1.00