To find the price of a unit of Banana at equilibrium, we need to determine the marginal utility per dollar spent on each good.
The marginal utility per dollar spent on Apple is the change in total utility divided by the change in the amount spent on Apple. In this case, the change in total utility is 68 - 60 = 8 utils and the change in the amount spent on Apple is 1 Birr (since the price of a unit of Apple is 2 Birr and the last dollar spent on Apple increased utility by 8 utils), so the marginal utility per dollar spent on Apple is 8/1 = 8 utils per Birr.
Similarly, the marginal utility per dollar spent on Banana is the change in total utility divided by the change in the amount spent on Banana. In this case, the change in total utility is 29 - 25 = 4 utils and the change in the amount spent on Banana is 2 Birr (since the last dollar spent on Banana increased utility by 4 utils and the price of a unit of Apple is 2 Birr), so the marginal utility per dollar spent on Banana is 4/2 = 2 utils per Birr.
At equilibrium, the marginal utility per dollar spent on each good should be equal. So we can set up the following equation:
8 utils per Birr (marginal utility per dollar spent on Apple) = 2 utils per Birr (marginal utility per dollar spent on Banana)
Simplifying the equation, we get:
8 = 2
This equation is not true, so there is no equilibrium price for Banana that satisfies the conditions given in the problem.
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?
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