1. Marginal is the change in one variable due to a unit change in another. For example, the change in the X value from 2 to 3 is 1 or a "unit change", which leads to an increase in Y from 12 to 21 or a "marginal increase" in the Y value of 9. The symbol Δ (the Greek letter delta) means change in.
2. In economics we say that the Total of Y is 21 when X is 3. The value of Y is the Total (or sum) of the Marginal values, or in this case the change in Y (ΔY).
X Y Δ X Δ Y Average
Y Value
1 5 1 5
2 12 1 7
3 21 1 9
4 31 1 10
5 46 1 15
3. Fill in the table below, finding the marginal changes or totals. Remember the change in X is always a unit change.
X Y Δ X Δ Y Average
Y Value
3 27 9
4 32
5 35
6 1
To fill in the table, we need to find the values of ΔY (the change in Y) and the average Y value.
1. Given the information provided, we know that when X changes from 2 to 3, Y changes from 12 to 21. So the ΔY for this change is 9.
2. Initially, we are told that when X is 3, the Total Y value is 21. To find the average Y value, we need to divide the Total Y value by the number of units by which X changes. In this case, the number of units by which X changes is 1. Therefore, the average Y value is 21/1 = 21.
Now let's fill in the remaining values in the table:
3. When X is 4, the change in Y is not given. We can find the change in Y by subtracting the Total Y value at X=3 (21) from the Total Y value at X=4 (31). Therefore, ΔY = 31 - 21 = 10.
4. To find the average Y value at X=4, we divide the Total Y value (31) by the number of units by which X changes (1). So the average Y value at X=4 is 31/1 = 31.
5. Similarly, when X is 5, the change in Y is not given. We can find ΔY by subtracting the Total Y value at X=4 (31) from the Total Y value at X=5 (46). Therefore, ΔY = 46 - 31 = 15.
6. To find the average Y value at X=5, we divide the Total Y value (46) by the number of units by which X changes (1). So the average Y value at X=5 is 46/1 = 46.
7. When X is 6, the change in X is given as 1 (unit change). However, the change in Y is not provided. We can fill in the remaining table by calculating the Total Y value at X=6. To do this, we can add the change in Y (1) to the Total Y value at X=5 (46). Therefore, the Total Y value at X=6 is 46 + 1 = 47.
Now, we can fill in the values in the table:
X Y ΔX ΔY Average Y Value
-----------------------------------
3 27 1 9 21
4 32 1 10 31
5 35 1 15 46
6 47 1 1 -