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?
To solve this problem, we need to use the concept of marginal utility and the principle of equimarginal utility.
First, let's calculate the marginal utility per dollar spent for each good. The marginal utility per dollar spent on Apple is (68 utils - 60 utils) / 1 Birr = 8 utils/Birr. The marginal utility per dollar spent on Banana is (29 utils - 25 utils) / (2 Birr * X) = 4 utils / (2 Birr * X), where X is the price of a unit of Banana.
According to the principle of equimarginal utility, a rational consumer will allocate their income in such a way that the marginal utility per dollar spent is equal for both goods.
Therefore, we can equate the marginal utility per dollar spent for Apple and Banana:
8 utils/Birr = 4 utils / (2 Birr * X)
To simplify the equation, we can multiply both sides by (2 Birr * X):
8 utils * (2 Birr * X) = 4 utils
16 Birr * X = 4 utils
Solving for X, the price of a unit of Banana, we get:
X = 4 utils / 16 Birr
X = 0.25 Birr
Therefore, the price of a unit of Banana at equilibrium is 0.25 Birr.