George has a weekly income (I)of $50,which he uses to purchase doughnuts (D)and coffee (C).If the price of a doughnut is $1 and the price of coffee is $2.50,his budget constraint can be expressed as:
A)D $\leq$ 50 + 2.50C.
B)D $\leq$ 50 - 25C.
C)D $\leq$ 50 - 0.25C.
D)D $\leq$ 50 - 2.50C.

Question

Quizplus · Accepted Answer

The budget constraint can be expressed as:
D + 2.50C ≤ 50
This is because the total spending on doughnuts and coffee (D + 2.50C) cannot exceed the weekly income of $50.

To find the best choice, we need to consider the Marginal Rate of Substitution (MRS), which is the rate at which a person is willing to trade off one good for another while keeping the same level of satisfaction. In this case, the MRS can be calculated as the ratio of the prices of doughnuts and coffee, which is 1/2.50 or 0.4.

To maximize his satisfaction, George should choose the combination of doughnuts and coffee where the MRS is equal to the price ratio. This means that for every 1 doughnut he gives up, he should receive 2.50/1 or 2.5 cups of coffee to maintain the same level of satisfaction.

The optimal consumption of doughnuts and coffee can be found by solving for D and C in the budget constraint equation, subject to the MRS equation:

D + 2.50C = 50
MRS = 0.4 = -∆C/∆D

Solving these two equations simultaneously, we get:

D = 20
C = 12

Therefore, the optimal choice for George is to buy 20 doughnuts and 12 cups of coffee.

The correct answer is D, which is the option that represents the budget constraint equation correctly.

George Has a Weekly Income (I)of $50,which He Uses to Purchase