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?
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.
To draw the budget line (budget constraint) on a graph, you can indeed use the general formula of p1x1 + p2x2 = I. Here's how you can do it step-by-step:
1. Determine the values of price 1 (p1), price 2 (p2), and the income (I) given in the problem. Let's assume p1 = 5, p2 = 3, and I = 30 for demonstration purposes.
2. Rearrange the formula in terms of x2 (the quantity of good 2) to obtain: x2 = (I - p1x1) / p2. This equation gives you the relationship between the quantities of goods in terms of x2 when combining the given prices and income.
3. Choose a range of values for x1 (the quantity of good 1) that you want to plot on the graph. For example, let's take x1 values from 0 to 8.
4. Substitute the x1 values into the equation obtained in step 2 to find the corresponding x2 values. For example, when x1 = 0, x2 = (30 - 5*0) / 3 = 10. When x1 = 8, x2 = (30 - 5*8) / 3 = 2.
5. Plot the points (x1, x2) on a graph with x1 on the horizontal axis and x2 on the vertical axis. For example, the point (0, 10) represents 0 units of good 1 and 10 units of good 2, while the point (8, 2) represents 8 units of good 1 and 2 units of good 2.
6. Connect these points with a straight line to form the budget line. Make sure the line extends beyond the plotted points on both ends.
The resulting line represents all the combinations of x1 and x2 that can be purchased given the prices and income. Any point on or below the budget line is feasible, while points above the line are not affordable with the given resources.