Answer to Question #290320 in Math for helenabebe

Question

A rational consumer spends all of her income on two goods: Apple and Banana. Suppose the last dollar spent on Apple increased her total utility from 60 utils to 68 utils and the last dollar spent on Banana increased her total utility from 25 utils to 29 utils. If the price of a unit of Apple is 2 Birr, what is the price of a unit of Banana at equilibrium?

Answer 1

Let $a$ denote Apple and $b$ denote Banana.

Increase in Apple utility divided by increase in Banana utility is equal to unit price of Apple divided by that of Banana at equilibrium

$$\dfrac{MU_a}{MU_b}=\dfrac{P_a}{P_b}$$

$$\dfrac{68-60}{29-25}=\dfrac{2}{P_b}$$

$$\dfrac{8}{4}=\dfrac{2}{P_b}$$

$$P_b=1$$

So the price of a unit of Banana at equilibrium is 1 Birr.