A consumer has $100 to spend on two goods X and Y with prices $3 and $5

Question

respectively. Derive the equation of the budget line and sketch the graph.

Answer 1

The budget line equation can be derived by setting up the equation that represents the total expenditure within the given budget of $100.

Let's assume the consumer spends x amount of money on good X and y amount of money on good Y.

The total cost of good X would be 3x, and the total cost of good Y would be 5y.

According to the given information, the consumer has $100 to spend, so the equation representing the total expenditure is:

3x + 5y = 100

This equation represents the budget line. Now, let's sketch the graph based on this equation.

To plot the graph, we need to find two points on the line.

Point 1: When the consumer spends all the money on good X, y = 0
Substituting y = 0 into the equation:
3x + 5(0) = 100
3x = 100
x = 100/3

So, point 1 is (100/3, 0)

Point 2: When the consumer spends all the money on good Y, x = 0
Substituting x = 0 into the equation:
3(0) + 5y = 100
5y = 100
y = 100/5
y = 20

So, point 2 is (0, 20)

Now, let's plot these points and draw a line passing through them.

The graph of the budget line is as follows:

|
20 |
|
| .
| .
|
| .
10 | .
--------------------------------------------------
20 33.33 100


In this graph, the x-axis represents the quantity of good X, the y-axis represents the quantity of good Y, and the line represents the budget line. The line passes through points (100/3, 0) and (0, 20).

Note that the slope of the budget line is -3/5, which represents the rate at which good X can be exchanged for good Y while keeping the budget constant.