Question

Dawit plans to consume two goods (good x and good y) with a limited budget. If Dawit’s budget line has intercepts 100 units of good x and 50 units of good y and price of good x (Px) is $100. Then, answer the next three questions. A) What are Dawit’s income and Price of good y (Py) B) What is the simplified version of Dawit’s budget line equation? C) If Dawit’s utility function is given by U(X; Y) = X0.5Y 0.5, how many units of good X and good Y would he consume if he choose the bundle that maximize his utility subject to his budget constraint?

Answer 1

$$I=100\times100=10,000$$

$$P_Y=\frac{I}{Q_Y}=200$$

$$MU_X=0.5(\frac{y}{x})^{0.5}$$

$$MU_Y=0.5(\frac{x}{y})^{0.5}$$

$$\frac{MU_X}{p_X}=\frac{MU_Y}{p_Y}$$

$$x=2y$$

$$100x+200y=10,000$$

$$y=25$$

$$x=50$$