Question

1. 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) = X0.5Y0.5, 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

A) Dawit’s income $= 100 \;units \times \$100 = \$10000$

Price of good y Py $= \frac{\$10000}{50 \;units}= \$200$

B) Dawit’s budget line equation = 100x+200y

C) U(X; Y) = X0.5Y0.5

Dawit need equal number of good X and Y.

So,

Px+Py=$100+$200 =$300

The number of units (x or y) $= \frac{10000}{300} ≈ 33$

X=Y=33 units