EC_308_Solutions_to_Problem Set 2_Fall_2023

True or false with reasoning: 1) _______When we claim that utility can be ordinally measured, we assume that the consumer is able to measure the total and marginal utility received when one extra unit of a commodity is consumed. 2)_______If MRS between two goods is constant, then having more of one good without having more of the other does not increase utility. 3)_______Marginal Utility increases until total utility is at a maximum and then marginal utility decreases.

RM2 1. Assume Good X and Good Y are perfect complements and both are normal goods. Suppose the price of X increases while the price of Y remains unchanged. On a preference map, a. demonstrate the change in the optimal consumption bundle. b. On a separate graph, decompose the substitution effect and the income effect.

10) Suppose that the utility function of an individual can be described as U(X,Y) = 4X +2Y. For this utility function the MRSA) is always X*YB) is always constantC) is always X/YD) is always X+YE) is always X-Y.

4 Assume that a person's utility over two goods is given by U(g1; g2) = g1 + ln g2. The price of good g1 is equal to p1 and the price of good g2 is p2. The total income of the individual is given by I. The marginal rate of substitution between g1 and g2 is given by 1/(1/g2). Then, the expressions for this person's (1) budget constraint, (2) budget line's slope (assume that, graphically, g1 is on the horizontal axis and g2 on the vertical axis), and (3) the person's demand function for g2 (that is, g2 as a function of price ratio) are respectively:

11) Stanley consumes only white and red wines and his utility function can be describedby U(R,W) = R0.40∙W0.60, where R is the number of bottles of red wine and W is the4number of bottles of white wine that he consumes per month. Suppose that his income is$500 and the price of a bottle of red wine $20 and the price of a bottle of white wine is$15. In this case, Stanley will purchase _____ bottles of red wine and _____ bottles ofwhite wine per month. Next, suppose that the price of red wine goes up to $35 per bottle.In this case, Stanley would consume ______ quantity of bottles of white wine comparedto the original situation.A) 10; 20; smallerB) 20; 10; smallerC) 10; 20; the sameD) 20; 10; the sameE) None of the above.

7) Suppose that upon solving for optimal bundles of hamburgers and french fries, we determine that when the price of hamburgers is $5 and the price of fries is $2, that we consume 2 hamburgers and 5 orders of fries. Suppose further that, upon changing the price of fries to $4, we only consume 3 orders of fries.  Draw out a demand curve for fries, labeling two points. This is not a trick question, this one is supposed to be easy.

27. If you have Marginal utility of 2 with a Total utility equals to 56, then when marginal utility is reduce to zero while Total utility remains the same, what does it mean? a. at 56 utils of MU equals zero, utility begins to gain momentum b. at 56 utils of MU equals zero, utility begins to diminish c. at 56 utils of MU equals zero. utility begins to increase d. at 56 utils of MU equals zero, utility begins to upswing

#10. Assume that Thomas can afford to buy as many candy bars and ice cream cones as he wants. He would continue to consume both candy bars and ice cream until the a. marginal utility of each decreases. b. marginal utility of each becomes negative. c. total utility of each becomes negative. d. marginal utility of candy bars and ice cream bars is equal. e. total utility of candy bars and ice cream bars is equal.

A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below.  Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend.   Product X   Product Y   Product Z     Quantity     Utility Marginal Utility per $       Quantity     Utility Marginal Utility per $       Quantity     Utility Marginal Utility per $ 1 42 NA   1 14 NA   1 32 NA 2 82 4   2 26 6   2 60 3.5 3 118 3.6   3 36 5   3 84 3 4 148 3   4 44 4   4 100 2 5 170 2.2   5 50 3   5 110 1.25 6 182 1.2   6 54 2   6 116 0.75 7 182 _0   7 56.4 _1.2   7 120 _0.5_ Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?

A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below.  Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend.   Product X   Product Y   Product Z     Quantity     Utility Marginal Utility per $       Quantity     Utility Marginal Utility per $       Quantity     Utility Marginal Utility per $ 1 42 NA   1 14 NA   1 32 ___NA__ 2 82 4   2 26 6   2 60 __3.5_ 3 118 3.6   3 36 5   3 84 __3___ 4 148 3   4 44 4   4 100 __2___ 5 170 2.2   5 50 3   5 110 _1.25___ 6 182 1.2   6 54 2   6 116 _0.75__ 7 182 0   7 56.4 1.2   7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…

6. MRS and utility maximization Suppose your classmate Bob loves to eat dessert—so much so that he allocates his entire weekly budget to apple crisp and pie. The price of one bowl of apple crisp is $1.25, and the price of a piece of blueberry pie is $3.75. At his current level of consumption, Bob's marginal rate of substitution (MRS) of apple crisp for pie is 2. In other words, Bob is willing to sacrifice two bowls of apple crisp for one piece of pie per week. Does Bob's current consumption bundle maximize his utility? That is, does it make him as well off as possible? If not, how should he change it to maximize his utility? Bob could increase his utility by buying more apple crisp and less pie per week.   Bob could increase his utility by buying less apple crisp and more pie per week.   Bob's current bundle maximizes his utility, and he should keep it unchanged.

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?