Suppose you go to Trader Joe's to buy fruit for the week. You only like apples (A) and bananas(B) and your weekly fruit budget is $11. When you arrive at Trader Joe's you notice that theprice of an apple is $1.00 and the price of a banana is $0.25.QUESTION #1: How many apples and bananas should you buy?QUESTION #2: When you have found the answer, draw a diagram that shows the outcome.Step #1. Determine your preferences. Let's suppose that your preferences can be representedby the following utility function: U(A, B) = AªBß = A0.40 B0.60FYI: This utility function is known as a Cobb-Douglas utility function. It is the most commonly used function used ineconomics! The reason we like it so much is that it has:1. Constant returns (double your consumption of A and B and your utility doubles); a + B = 12. Diminishing marginal utility (the extra utility gained from consuming A (or B) decreases as you consume more ofthe A good (or B good); a < 1, p<1.The way I described the utility function, you like bananas more than apples; that is, all things equal, eating a bananagives you more utility than eating an apple (0.60 > 0.40); B > a.Step #2: Determine your budget constraint (pÃª + PÂB = Y). Given your income and the pricesof the two goods, your budget constraint is: 1.A +0.25 B = 11FYI: The budget constraint shows that the amount spent on apples (1. A) and bananas (0.25 B) cannot add up tomore than $11. Clearly, more money spent on apples means less spent on bananas, and vice versa.Step #3: Set up the constrained utility maximization problem. That is, set up a problem thatshows that you need to maximize utility, given your budget constraint.max U(A, B) = A0.40 B0.60A,Bs. t. 1. A+0.25 · B = 11FYI: the two letters s. t. _ stands for "subject to"Step #4: Solve the constrained utility maximization problem. For this pre-problem, please usethe substitution method. *Substitution method: max U (A, B) = A⁰.4⁰ (44 – 4A)⁰.60AFYI: Substitution method - use the budget constraint to substitute away the B so that you maximize one equation inone unknown. That is, after removing the B, take the derivative with respect to A, set it equal to zero, and solve forA.*In general, there are two common ways to solve the constrained optimization problem: (1) the substitutionmethod, and (2) the Lagrangian method.

Preference is over apples and bananas.Income = $11Price of Apples = $1 Price of Bananas = 0.25 We…

Suppose you go to Trader Joe's to buy fruit for the week. You only like apples (A) and bananas (B) and your weekly fruit budget is $11. When you arrive at Trader Joe's you notice that the price of an apple is $1.00 and the price of a banana is $0.25. QUESTION #1: How many apples and bananas should you buy? QUESTION #2: When you have found the answer, draw a diagram that shows the outcome. Step #1. Determine your preferences. Let's suppose that your preferences can be represented

Suppose you go to Trader Joe's to buy fruit for the week. You only like apples (A) and bananas (B) and your weekly fruit budget is $11. When you arrive at Trader Joe's you notice that the price of an apple is $1.00 and the price of a banana is $0.25. QUESTION #1: How many apples and bananas should you buy? QUESTION #2: When you have found the answer, draw a diagram that shows the outcome. Step #1. Determine your preferences. Let's suppose that your preferences can be represented

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 10E

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