Answer to Question #290319 in Operations Research for helenabebe

Question

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?

Answer 1

Solution:

A.

$$p_x=3, G_x=\frac {100}{3}=33\frac{1}{3}$$ $$p_y=5, G_y=\frac{100}{5}=20$$

B.

$$100-0.25\times 100=75$$ $$p_x=3, G_x=\frac {75}{3}=25$$ $$p_y=5, G_y=\frac{75}{5}=15$$

Its slope will remain same, but starting point, final point and all other points are lower by 25%.

C.

$$p_x=6, G_x=\frac {100}{6}=16\frac{2}{3}$$

Its slope is decreasing at a higher rate than previous. Starting point is same, but ending point will be different.

D.

$$p_y=5, G_y=\frac{100}{4}=25$$

Its slope is decreasing at a higher rate than previous. Starting point is different, but ending point will be same.