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) = AªBB = 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 by the following utility function: U(A,B) = AªBB = A0.40 B0.60

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 by the following utility function: U(A,B) = AªBB = A0.40 B0.60

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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