A person has $ 100 to spend on two goods X and Y whose respective prices are $3 and $5.
A. Draw the budget line.
B. What happens to the original budget line if the budget falls by 25%?
C. What happens to the original budget line if the price of X doubles?
D. What happens to the original budget line if the price of Y falls to $4?
A. To draw the budget line, we can represent the two goods on a graph, with X on the x-axis and Y on the y-axis. The budget line represents all the affordable combinations of X and Y for a given budget of $100.
Let's assume X is on the x-axis and Y is on the y-axis. Goods X and Y are priced at $3 and $5 respectively.
To find the different combinations of X and Y that can be purchased with $100, we can set up the following equation:
3X + 5Y = 100
Now, we can rearrange the equation to solve for Y:
5Y = 100 - 3X
Y = (100 - 3X) / 5
Now we can plot the budget line on the graph. Choose a few values for X and calculate the corresponding Y using the equation we derived.
For example, if X = 10, then Y = (100 - 3(10)) / 5 = 70 / 5 = 14. So, one point on the budget line is (10, 14).
Similarly, for X = 20, Y = (100 - 3(20)) / 5 = 40 / 5 = 8. So, another point on the budget line is (20, 8).
Connect these points and continue the line until it intersects with the axes. This will give you the budget line.
B. If the budget falls by 25%, then the new budget would be 75% of $100, which is $75. To redefine the budget line, substitute $75 for the budget in the original equation:
3X + 5Y = 75.
By solving for Y again, the new equation would be:
5Y = 75 - 3X
Y = (75 - 3X) / 5.
Follow the same steps as in part A to plot the new budget line. The new budget line will have a steeper slope than the original budget line, indicating that the consumer has less purchasing power.
C. If the price of X doubles, then the new price of X would be $6. The original equation for the budget line would now be:
6X + 5Y = 100.
By solving for Y, we get:
5Y = 100 - 6X
Y = (100 - 6X) / 5.
Follow the same steps as in part A to plot the new budget line. The new budget line will have a steeper slope than the original budget line, indicating that the consumer has less purchasing power.
D. If the price of Y falls to $4, the original equation for the budget line becomes:
3X + 4Y = 100.
By solving for Y, we get:
4Y = 100 - 3X
Y = (100 - 3X) / 4.
Follow the same steps as in part A to plot the new budget line. The new budget line will have a flatter slope than the original budget line, indicating that the consumer has more purchasing power.