Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each and a consumer has $10 en total. Let us denote the cake and coke by x and Y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10. It could be either 10 pieces of cake and no coke or 10 bottles of coke and no cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the total number of items is less than 10. Assume that the consumer's happiness (utility) function is one of the following and find its maximum: a). u (x, y) = x² + y? b). u (x, y) = 2x² + y? c). u (x, y) = x² – y?

Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each and a consumer has $10 en total. Let us denote the cake and coke by x and Y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10. It could be either 10 pieces of cake and no coke or 10 bottles of coke and no cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the total number of items is less than 10. Assume that the consumer's happiness (utility) function is one of the following and find its maximum: a). u (x, y) = x² + y? b). u (x, y) = 2x² + y? c). u (x, y) = x² – y?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?
4. Suppose a person has $8 to spend only on apples and bananas. Apples 1 cost $0:4 each, and bananas cost $0:1 each. Furthermore, his preferences for apples (A) and bananas (B) can be represented by U = pAB. a) If A = 5 and B = 80, what will utility be?b) If A = 10, what value of for B will provide the same utility in part a? c) If A = 20, what value of for B will provide the same utility in parts a and b?d) Graph the indi§erence curve implied by parts a through c.e) Give the budget constraint, which of the points identiÖed in parts a through c can be bought by this person?f) show through some examples that every other way of allocating income provides less utility than does the point identiÖed in part b. graph this utility maximizing situation.
Suppose that you initially have $100 to spend on books or movie tickets. The books start off costing $25 each and the movie tickets start off costing $10 each. For each of the following situations, would the attainable set of combinations that you can afford increase or decrease? a. Your budget increases from $100 to $150 while the prices stay the same. b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20. c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.
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Assume that, a consumer has $1200 to spend on two goods, X and Y. If the price of a pair of good X is $20 per unit and the price of good Y is $15 each, which of the following combinations that the consumer can purchase from good X and Good Y?
please only do: if you can teach explain each What does it mean?there is no quantity of wine that he can convert to grapes. Thus, for example, if he purchases 4 units of grapes and 3 units of wine, he could consume any bundle (4-s, 3+ s) why the s ? What does mean? with s € [0,4] how to know what to look at: If p₁ < p2 or p1 ≥ p2, why these? Please how to solve: x(p, w) = (2w/3p1, w/3p1) (2w/3p1, w/3p2)
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2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
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