1. 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%?
A. To draw the budget line, we need to plot the different combinations of goods X and Y that the person can afford with $100. The slope of the budget line is given by the ratio of the prices of the two goods.
Let's assume the quantity of good X is denoted by Qx and the quantity of good Y is denoted by Qy.
At the highest point on the budget line, the person spends all their money on one of the goods. Since the price of good X is $3 and the person has $100, they can afford 100/3 = 33.33 units of good X. Similarly, they can afford 100/5 = 20 units of good Y.
At the other extreme, the person spends all their money on the other good. They can afford 100/5 = 20 units of good Y and 100/3 = 33.33 units of good X.
Therefore, the budget line connecting these two extreme points is a straight line from (0, 33.33) to (20, 0) on a graph.
B. If the budget falls by 25%, the person will have 75% of the original budget, which is 0.75 * $100 = $75. This means the person can now afford the same quantities of goods X and Y but at lower prices.
Let's assume the new prices are pX and pY. Since the person can afford the same quantities, we have:
Qx * pX = Qy * pY
Since the person has $75, we can write:
Qx * pX + Qy * pY = $75
To simplify, let's assume the new prices are px = $3(1 - k) and py = $5(1 - k), where k represents the percentage reduction in price. Substituting these values into the equation, we get:
Qx * $3(1 - k) + Qy * $5(1 - k) = $75
Since we need to plot this new budget line, we can assume specific values for k and solve for Qx and Qy. For example, let's assume k = 0.25. Plugging this into the equation, we get:
Qx * $2.25 + Qy * $3.75 = $75
Solving for Qy, we get:
Qy * $3.75 = $75 - Qx * $2.25
Qy = ($75 - Qx * $2.25) / $3.75
Now we can plot the new budget line using this equation for different values of Qx.