How to I draw the budget line (budget constraint) of a graph given the income, price 1, and price 2? Do I just plug it into the general formula of p1x1 + p2x2 = I?

Question

GPT 3.5 · Answer

Yes, you are correct. To draw the budget line or budget constraint on a graph, you can use the general formula:

p1x1 + p2x2 = I

Where:
p1 = price of good 1
x1 = quantity of good 1
p2 = price of good 2
x2 = quantity of good 2
I = income

To draw the budget line, you need to choose a range for x1 (quantity of good 1) and then solve for x2 using the given formula. Once you have the pairs (x1, x2), you can plot them on the graph to obtain the budget line.

Here are the steps to draw the budget line:

1. Determine a range for x1 (quantity of good 1) that you want to plot on the graph. For example, if you want to plot the range from 0 to 10, choose values like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 for x1.

2. Plug in the given values of p1, p2, and I into the formula p1x1 + p2x2 = I.

3. Solve the equation for x2 to get x2 = (I - p1x1) / p2.

4. Use the range of x1 values you selected in step 1 to find the corresponding x2 values by substituting x1 into the x2 equation from step 3.

5. Plot the (x1, x2) pairs on a graph, with x1 on the x-axis and x2 on the y-axis.

6. Connect the plotted points to form a straight line. This line represents the budget line or budget constraint.

Note: The slope of the budget line will be equal to -p1/p2, indicating the rate at which you can trade off one good for another while staying within your budget.