The equation of the budget line can be derived by the formula:
Px * X + Py * Y = I
where:
- Px is the price of good X
- Py is the price of good Y
- X is the quantity of good X
- Y is the quantity of good Y
- I is the available income or budget
In this case, Px = $3, Py = $5, and I = $100. Substituting these values into the equation, we get:
3X + 5Y = 100
To sketch the graph, we'll first solve the equation for Y:
5Y = 100 - 3X
Y = (100 - 3X)/5
Now we can create a table of values for X and Y:
| X | Y |
|---|---|
| 0 | 20 |
|10 | 14 |
|20 | 8 |
|30 | 2 |
|40 |-4 |
Now we can plot the points (0,20), (10,14), (20,8), (30,2), and (40,-4) on a graph with X on the x-axis and Y on the y-axis.
A consumer has $100 to spend on two goods X and Y with prices $3 and $5 respectively. Derive the equation of the budget line and sketch the graph.
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