Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy) g) Octopus income decreases to $35. Calculate new optimal bundle and graph it h) Repeat g) for income = 105. (ANSWER G/H)

Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy) g) Octopus income decreases to $35. Calculate new optimal bundle and graph it h) Repeat g) for income = 105. (ANSWER G/H)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

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Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy) 2. Right shoe price increases to $11 (Calc new optimal bundle and graph) 3. Right shoe price decreases to $0.5 (Calc new optimal bundle and graph) 4. Given answers to 1-3, draw Price consumption curve and the Octopus’ demand curve for RIGHT shoes ANSWER Q 4
Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy) 2. Octopus income decreases to $35. Calculate new optimal bundle and graph it 3. Repeat g) for income = 105. 4. Given answers to 1,2,3 Draw income consumption curve and engel curve for right shoes Are Right shoes normal or inferior good for Margot? What way is the engel curve sloping? ANSWER 4.
Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy) Right shoe price increases to $11 (Calc new optimal bundle and graph) Right shoe price decreases to $0.5 (Calc new optimal bundle and graph) ANSWER QUESTIONS 2,3
Octopus has 5RL (Right Legs) and 3LL (Left legs) Will only wear matching shoes on all 8 legs Utility Function U(q1,q2) = min[3q1,5q2] where: q1 = number of right shoes q2 = number of left shoes Octopus income is = $70 p1 = Price of right shoes = $4 p2 = Price of left shoes = $5 Find and graph budget line for the Octopus, and a few indifference curves. Display the optimal Bundle on the graph. Right shoes on X axis. Then Find the Optimal Bundle (How many of left/right shoes she will buy)
Michael does not like to mix peanut butter and jelly in the same sandwich. However, he will consume them separately; for him, a sandwich with 1 spoon of peanut butter is exactly the same as a sandwich with 2 spoons of jelly. Michael has an income of m = 50, and the prices per spoonful of peanut butter and jelly are pPB=5 and pJ=11. Please write down Michael’s utility function over peanut butter (PB) and jelly (J). 2. Please determine Michael’s Marshallian demands PB*m and J*m3. Please determine Michael’s new Marshallian demands PB*m and J*m, when the price of peanut butter falls to pPB = 1.4. What are the (Hicks) SE and IE? Draw a diagram to show your analysis, with peanut butter on thehorizontal axis, and jelly on the vertical axis. 5. Recall that there are two different types of substitution effects. For example, in Q2 we have used theHicks SE. Does your answer to the last part change if we use the Slutsky SE? Justify. 6. Nam likes his peanut butter and jelly sandwiches with exactly…
Which of the FF. statements is correct regarding the preference of the consumers when the income of the consumer can only be spent between apples and oranges? Assume that apples are written on the vertical axis while oranges are written on the horizontal axis A. when the consumer has few oranges, he is willing to trade more apple to get another orange B. when the consumer has so many oranges already, he will only exchange less apples for an orange C. the declining slope of the indifference curve shows the marginal value of oranges is declining D. all are correct E. none is correct
Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Suppose that now Reese loses almost his entire income, so that he is left with only one dollar, i.e. his new income is I0 = 1. If prices are still px = 2, py = 4, what is his new optimal consumption of x and y (Hint: Remember that consumption of both goods must be weakly positive, i.e. x∗ ≥ 0 and y∗ ≥ 0) (a) x∗ = 0.5, y∗ = 0(b) x∗ = 0.25, y∗ = 0(c) x∗ = 0.75, y∗ = 0.25(d) x∗ = 0.75, y∗ = 0(e) x∗ = 0.5, y∗ = 1
Solve part b and c. There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves. c) Are the consumer's preferences monotone? Provide an explanation foryour answer.
A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle(8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consumingbundle (4, 4). She is indifferent between these two bundles. Assuming that the utilityfunction is Cobb-Douglas of the form U(x,y)=xα yβ, where α and β are positiveconstants, what is the utility function for this consumer?
Suppose a consumer is indifferent between the bundles (x1, x2) = (20, 10) and (15, 16), and suppose that the same consumer prefers the bundle (19, 9) to both. Is there anything wrong about her preferences when evaluated against the standard assumptions of consumer preferences?
Heather and Jeremiah both enjoy sunflower butter (s) and jelly (j) sandwiches, but they have varying preferences regarding the optimal ratio of the two. Heather prefers her sandwiches to have 6 spoonfuls of sunflower butter for every 3 scoops of jelly, whereas Jeremiah prefers 3 scoops of sunflower butter for every 5 scoops of jelly. They both would prefer as many sandwiches as possible, but derive no utility from sandwiches without their preferred ratio of s and j. A) Write down a utility function for both Heather and Jeremiah regarding consumption of s and j (U(s,j)) B) On the same graph, draw a set of indifference curves for both Heather and Jeremiah, labeling which is which. C) In addition to s and j, Heather and Jeremiah now need bread, b, to make sandwiches. Heather prefers to separate her sunflower butter and jelly and therefore uses 3 slices of bread per sandwich. Write down Heather’s utility function Uh(s,j,b) as a function of the three inputs.
You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you’d be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. ( c) Forget about (b). In (a), just before going out for shopping with your backpack to buy the…