Principles of Economics (12th Edition)
12th Edition
ISBN: 9780134078779
Author: Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher: PEARSON
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Chapter 6.A, Problem 1P
To determine
Violation of the basic assumptions in the indifference curve.
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QUESTION: Use the sheet 1( picture below) utility function and parameter values to find the optimal solution via analytical methods (calculus/lagrangean/algebra). Show your work. Note that x1<a/b, so we will use the first utility function given in the yellow box in the sheet.
Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a
foreign country (F), as given by the utility function U(D,F)= 10DF. In addition, the price of a day spent traveling
domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane's annual travel budget is
$4000.
An indifference curve associated with a level of utility equal to 800 and an indifference curve associated with utility of
1200 are illustrated in the figure to the right.
Using the line drawing tool, graph Jane's budget line. Label this line L,.
Carefully follow the instructions above, and only draw the required object.
Can Jane afford any of the bundles that give her a utility of 800?
Can Jane afford any of the utility bundles that give her a utility of 1200?
Find Jane's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country.
days of domestic travel and days of foreign travel. (Enter…
12) Melquiades is worried about his grades from the microeconomics course, according to the
rules for grading, the final grade is obtained as the minimum between the grade for the midterm
test (x) and the final test (y).
The utility function of Melquiades will depend on the grades obtained from those two tests
Now, Melquiades has researched that the average student needs to study 24 minutes
an additional point in each test (tests are graded from 0 to 100)
obtain
a) If Melquiades has 20 hours to study for both tests (x and y), how much time would he
employ for each test? Figure out the grade that Melquiades will obtain in each test and
his final grade in microeconomics. Elaborate a graph.
b) How much additional study time would Melquiades require to increase his final grade by
10 points. Elaborate a graph.
c) Suppose the difficulty of the final test increases in such a way that now each additional
point would require 26 minutes of study. What would be the total cost (in minutes)…
Chapter 6 Solutions
Principles of Economics (12th Edition)
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- UP this part). Question 4 Solving Consumer's Choice Problem under CD Utility, Numerical The consumer with income Y has a preference represented by CD utility function U(91,92) = 90.492.6. Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice problem following the steps below. (a) Write down the consumer's maximization problem, i.e be clear about (1) the choice variables, (2) the objective function and (3) the constraint. mand (b) Write down the Lagrangian for this optimization problem. (c) Derive the three first-order conditions. IM gaitaluste (d) Solve for the optimal consumption bundles q1,92. (e) Plugging optimal consumption bundles q,q into U(91,92) to get the expression for indirect utility function, i.e. utility as a function of Y, P₁, P2. (f) Now we analyze the properties of demand. How does q respond to changes in P₁, P2 and Y? Specifically, does q increase or decrease if 1. p₁ increases? 2. p2 increases? 3. Y increases? For simplicity, we only…arrow_forward(a). What kind of preferences are represented by a utility function of the form u(x₁, x₂) = √√x₁ + x₂? What about the utility function v(x₁, x₂) = 13x₁ + 13x₂? Compute the slope of the two indifference curves. Do their slopes depend on the bundle? (b). What kind of preferences are represented by a utility function of the form u(x1, x₂) = x₁ + √√x₂ ? Compute the slope of the indifference curve. Does it depend on the bundle? In which way? (c). Consider the utility function u(x₁, x₂) = √x₁x2. What kind of preferences does it represent? Is the function v(X₁, X2) = X₁X2 a monotonic transformation of u(x₁, x₂)? Compute the slope of the indifference curve. Does it depend on the bundle? In which way?arrow_forwardWhat do you think is more realistic approach between cardinal and ordinal approaches to consumer behavior? Explain why.arrow_forward
- Using graphical analysis show how the following demand curves can be derived from indifference curve approach to understanding consumer behavior: What are the main assumptions for each of these demand curves? a) Marshallian demand curve b)Hicksian demand curvearrow_forward: submit your pdf for part. X + u/courses/124336/quizzes/156962/take Question 1 Calculate the marginal rate of substitution (MRS12) for the following utility function: U(91, 92) = 74√9₁ +0.6(92)² What is the value of MRS12 at bundle (9, 3)? Please round your final answer to two decimal places if necessary.arrow_forwardSuppose 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.arrow_forward
- Text: Consider a consumer whose preferences are characterized by the utility function u(x1, X2) = In x1 + x2. This utility function is often used to represent the tastes of a consumer to whom good 1 is essential, while good 2 is not. Furthermore, the tastes represented by this utility function satisfy the five standard assumptions about tastes introduced in the lectures. Based on this information, answer the following questions Questions: Which of the following maps of indifference curves could be the one associated with the utility function above? X2 X2 b darrow_forwardEren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).arrow_forwardEren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.arrow_forward
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).arrow_forwardNext Question A utility function is given as U= MB Q 45- where B represents the quantity of books consumed and M represents magazines. This utility is shown via indifference curves in the diagram to the right. (Round all numeric responses to two decimal places.) 40- 35- E 30- The level of utility at point A is 25- The marginal utility of books at point A is 20- 15- 10- 5- 0- 10 15 40 45 20 25 30 Books (B) 35 50 Reactions 27 étv MacBook Air 80 DII DD F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 @ 2$ & 4 7 9 Q W E R T Y U S D F G J K L V N ion command command option * 00 Magazines (M) B # 3 **arrow_forwardAnswer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEarrow_forward
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