3. Prove that strict convexity of preferences guarantees that there can not be more than one...
4. We want to think about the role of convexity of preferences (along with strict monotonicity of preferences) in consumer choice (a). In the consumer's utility maximization problem, explain why if prefer- ences are strictly convex, the ordinary demand choices are unique. (b). Now, explain if they are just convex, the claim in part (a) is not neces- sarily true. (c). Per part (b), now explain why with convex preferences (also strictly monotone), the optimal set of demands at any...
A consumer’s preferences are said to be strictly monotonic if “more is better than less”, or equivalently, for a C 1 utility function u defined on R n , ∂u(x)/∂xi > 0 for all i = {1, . . . , n}. Consider a budget set with prices pi > 0 for all i defined by Xn i=1 pixi ≤ m and x1 ≥ 0, . . . , xn ≥ 0, for some income level m > 0. Prove...
8. Fats Dominio's preferences over food expenditures, (f) and expenditures on other goods (g) can be represented by the utility function: Fats 3/4 1/4 with Slim Picken's preferences can be represented by the utility function: Slim 1/4 3/4 with Slim Each has income of only $100.00 per month: the competition from the pop idols and hip hop has really urt sales. Prices are pf - Pg -1 (a) What are the optimal expenditures on food and other goods for both...
How to prove that the independence axiom must be true for a set of preferences that can be represented by expected utility function?
8. Fats Dominio's preferences over food expenditures, (f) and expenditures on other goods (9) can be represented by the utility function: with Slim Picken's preferences can be represented by the utility function: with Each has income of only $100.00 per month: the competition from the pop idols and hip hop has really hurt sales. Prices are PP9 1. a) What are the optimal expenditures on food and other goods for both Fats and Slim? b) On ONE diagram draw the...
5.38. A nail manufacturer guarantees that not more than one nail in a box of 100 nails is defcctive. If, in fact, the probability of each individ ual nail being defective is p = 0.005, compute the probability that: (a) The next box of nails violates the guarantee. Use the Poisson approximation, after assuming independence. (b) The guarantee is violated at least once in the next 25 boxes. 5.38. A nail manufacturer guarantees that not more than one nail in...
Can you prove it? But proof needs to be no more than 3 LINES. Danke schön! Give an example of a commutative ring with identity in which the union of any two ideals is again an ideal.
Sally the Sleek’s preferences can be described by the utility function U(x, y) = x^2y^3/1000. Prices are px = 4 and py = 3; she has an income of $80 to spend. (a) If Sally initially consumed 5 units of x and 20 units of y, how much additional utility does she get from spending one (small fraction of a) dollar more on good x? How much additional utility does she get from spending one (small fraction of a) dollar...
. Basket A contains 5 apples and 1 orange. Basket B contains 1 apple and 5 oranges. Basket C contains 3 apples and 3 oranges. Assume throughout that tastes are monotonic. On Monday, Anne is offered a choice between basket A and C, and she chooses A. On Tuesday, she is offered a choice between basket B and C, and she chooses B. a) Graph these baskets on a graph with apples on the horizontal and oranges on the vertical...
No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are ________________.