Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 4, Problem 4.3P
a)
To determine
To find: The number of cigars and brandy.
b)
To determine
To find: The number of brandy and number of cigar after doctor’sadvice.
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On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
EXERCISE 7
Aisha is considering how to allocate the next 6 hours of her free time. She could choose
between leisure (L) and helping her neighbour with the house chores. If she decides to
help her neighbour, she is going to get paid at £25 per hour, which she can then spend on
her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for
leisure and pizza are given by the following utility function: U(L, P) = 3L + P.
(MU₁ = 3, MUp = 1).
a) Write down Aisha's budget equation and draw the corresponding budget line.
Clearly label the axes and calculate the coordinates of the points of intersection of
the budget line with each axis.
b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain
the concept of MRS and interpret the figure obtained.
c) Find Aisha's optimal consumption bundle, both algebraically and graphically.
Explain your reasoning.
d) Would Aisha's optimal choice change if she could get a discount on her pizza
purchases so…
Suppose Ed's utility from the consumption of martinis (m) is proportional to the
number he drinks: U(m) = m. Further, Ed is particular about his martinis: He enjoys
them in exactly three parts of gin (g) to one part vermouth (v). So we can write the
utility as:
U(m) = U (g, v) = min (g, 3v).
(a) Provide a sketch of Ed's indifference curve in the (g, v)-space for various level of
utility.
(a) Let the prices be p, and p, and Ed's income be I. Find the demand functions
for 9 and v [Hint: Use the proportional rule and budget constraint. No need for
differential calculus]
(b) Using the results in (b), what is Ed's indirect utility function?
(c) Find the expenditure function; given a level of utility U, and prices pg and Pv.
Chapter 4 Solutions
Microeconomic Theory
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- Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?arrow_forwardConsider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils. a)Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b)Calculate the optimal weekly consumption bundle for this consumer. c)Does the consumer view C and S as complements or substitutes?arrow_forwardIf the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.arrow_forward
- Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2arrow_forward2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.arrow_forward3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…arrow_forward
- To help with his busy schedule, Joe drinks a lot of cappuccinos. In particular, his weekly demand for cappuccinos is: cap = 0.1 M-8 Pcap Where Xcap is the number of cappuccinos drunk per week, Mis Joe's weekly income and Pcap is the price of a cappuccino. (Note that Xcop is an average demand and need not be a whole number). (a) Suppose that income M = 240 euro, and the price is Pcap = 1.5 euro. How many Cappuccino, on average, will Joe drink per week? Suppose that the price increases to Pcap = 1.6 euro. (b) What is Joe's new demand for cappuccinos? What is his total change in demand due to the price change? (c) Given the new price (Pcap = 1.6), how much extra income would Joe need to allow him to continue buying the number of Cappuccinos calculated in part (a), without needing to reduce his demand other goods? (In other words, how much would Joe's expenditure on cappuccinos have gone up if he had continued to buy the number of cappuccinos calculated in part (a)?) (d) Compute the change…arrow_forwardAssume that a person's vitility function is given Assume by the following function. TU = 2x¹¹2,¹/2 also that the price of x is 22 and the price of is 26 and that the budget is 2240. what is the optimal amount of goods x and that should be purchused with this budget? of y уarrow_forward1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X+ 80Y – X² – 2Y?, where X is consumption of CDs, with a price of $1, and Y is consumption of movie videos, with a rental price of $2. Jae plans to spend $41 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize Jae's utility. а.arrow_forward
- 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? Suppose that 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? *use tables and/or graphs if possible, please original workarrow_forwardA consumer is choosing between magazines and books. His set of consumer optimums are shown on the graph to the right. 50 Consumer income allocated for these two goods is equal to $150. The price of 45 magazines (P,) is equal to $5.00. 40- How do these changes in the price of books affect the demand for magazines? 35- 30- 25 NN 20- demand remains constant 15- PCC demand increases 10- 5- demand decreases 0- Ó 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Books étv 21 MacBook Air 80 DII F5 F6 F7 F8 F9 F10 F1 F2 F3 ! @ $ & * 1 2 3 4 6. 7 Q W E T U A S F H. J K L C V M option command command op ...- * C0 Magazines Darrow_forwardExercise Suppose the utility function of a person consuming two commodities X and Ywith income Birr 600 is given by U = 2 X 06Y 04 If the per unit price of X is Birr 20 and per unit price of Y is Birr 40 a) What is the utility maximizing level of consumption of X & Y ? b) Find the MRSyy at the optimum ?arrow_forward
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