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 find the equilibrium price of a unit of Banana, we need to compare the marginal utilities to the prices of the goods.
The marginal utility per dollar spent on Apple is calculated as the change in total utility divided by the change in the dollars spent on Apple.
ΔTU_apple = 68 utils - 60 utils = 8 utils
Δ$_apple = $2
Therefore, the marginal utility per dollar spent on Apple is 8 utils / $2 = 4 utils/$.
Similarly, the marginal utility per dollar spent on Banana is calculated as the change in total utility divided by the change in the dollars spent on Banana.
ΔTU_banana = 29 utils - 25 utils = 4 utils
Δ$_banana = $x
We know that the marginal utility per dollar spent on Apple is equal to the marginal utility per dollar spent on Banana for equilibrium.
4 utils/$ = 4 utils/$x
To find the price of a unit of Banana at equilibrium, we solve for x:
4/utils = 4/utils/$x
1 = 1/x
x = 1
Therefore, the price of a unit of Banana at equilibrium is $1.