For the given sets A and B, find A∩ B, A∪ B, and Ac (the complement of A). A and B are subsets of the set S={0, 1, 2, 3, 4, 5}. A={0, 1, 2} and B={0, 2, 4, 5}.
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For the given sets A and B, find A∩ B, A∪ B, and Ac (the complement of A). A and B are subsets of the set S={0, 1, 2, 3, 4, 5}. A={0, 1, 2} and B={0, 2, 4, 5}.
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- Consider a hypothetical consumer named Hayden who is shopping for bread and brie. The graph with bread and brie on the axes presents the utility‑maximizing combinations of bread and brie that Hayden chooses when the price of bread is $1.00$1.00 per loaf and the price of brie is $4.00$4.00 and $6.00$6.00 per wheel, respectively. The other graph shows Hayden's demand curve for brie. The two points and associated values in the graph for bread and brie combinations correspond to points A and B in the graph of the demand curve for brie. What are the specific prices and quantities of brie associated with points A and B on Hayden's demand curve? price of brie at point A: $$ quantity demanded at point A: price of brie at point B: $$ quantity demanded at point B:According to Kahneman and Tversky, what is the major problem they find with the basic tenets of utility theory?Economists use a preference map to illustrate that A. preferences are complete. B. preferences are transitive. C. more is better than less. D. All of the above.
- 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.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 Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).For the case of two goods, give examples of different two utility functions that satisfy all of the following properties: (i) one utility is strictly concave in good 1 and the other is strictly convex in good 2; (ii) they represent the same preferences; and (iii) one utility function is homogeneous of degree 2.
- Consider two individuals whose utility functions are given byAssuming the two good case. When a person is attempting to maximize utility and income increases, then: a. The budget constraint expands, shifting the budget line outward indicating more choices are now affordable and a higher utility level is now possible. b. The budget constraint contracts, shifting the budget line outward indicating more choices are now affordable and a higher utility level is now possible. c. The budget constraint expands, shifting the budget line inward indicating more choices are now affordable and a lower utility level is now possible. d. The budget constraint contracts, shifting the budget line outward indicating more choices are now affordable and a lower utility level is now possible.There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(c, m) = min{c, m} + c + m, where c is the quantity of coffee (in grams) and m is the quantity of mineral water (in liters). The consumer has wealth in Dirhams of w > 0. The price of coffee is p > 0 (in grams/Dirham) and the price of mineral water q > 0 (in liters/Dirham). Now assume that w = 100, p = 10 and q = 10. In addition to the monetarybudget constraint, the consumer has a time constraint. The consumer hasonly 100 minutes available for the consumption of both goods. It takes5 minutes/liter to consume water and and 20 minutes/gram to consumecoffee. The government wants the consumer to consume an equal quantity of coffee and water. To achieve this policy objective, the government implements a tax of τ > 0 Dirhams/gram for coffee. This tax…
- There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(c, m) = min{c, m} + c + m, where c is the quantity of coffee (in grams) and m is the quantity of mineral water (in liters). The consumer has wealth in Dirhams of w > 0. The price of coffee is p > 0 (in grams/Dirham) and the price of mineral water q > 0 (in liters/Dirham). (a) In an appropriate diagram, illustrate the consumers map of indifference curves. Make sure you label the diagram clearly, and include as part of your answer any calculations about the slopes of the indifference curves. (b) Formulate and solve the consumer’s utility maximization problem. Your final answer should describe the consumer’s demand for coffee and mineral water as a function of the wealth w and the prices p and q, as well as the consumer’s indirect utility…There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function: u(c, m) = min{c, m} + c + m, where c is the quantity of coffee (in grams) and m is the quantity of mineral water (in liters). The consumer has wealth in Dirhams of w > 0. The price of coffee is p > 0 (in grams/Dirham) and the price of mineral water q > 0 (in liters/Dirham). Now assume that w = 100, p = 10 and q = 10. In addition to the monetarybudget constraint, the consumer has a time constraint. The consumer hasonly 100 minutes available for the consumption of both goods. It takes5 minutes/liter to consume water and and 20 minutes/gram to consumecoffee. (a) In an appropriate diagram, illustrate the consumer’s constraint set. Your diagram should illustrate the monetary budget constraint, the time constraint, and indicate the consumer’s overall…If (X, τX) and (Y, τY) are two topological spaces, then G ⊂ (X × Y ) is open in the product topology iff for all (x, y) ∈ G, there exists Gx ∈ τX and Gy ∈ τY such that (x, y) ∈ (Gx × Gy) ⊂ (X × Y )