Let there be two goods 1 and 2. Let x1 and x2 denote their respective quantities. x = (x1, x2) represents a bundle. Milton's preferences over bundles in R? can be described as follows: Between any two bundles x = (x1,x2) and y = (yı, Y2), Milton prefers the bundle that has %3D more of good 1. If two bundles have the same amount of good 1, he prefers the bundle that has more of good 2. (Obviously, bundles with the same amount of goods 1 and 2 are the same bundle). Do Milton's preferences satisfy the strong monotonicity assumption? Prove or provide a counterexample. (4) а. b. Draw the upper contour set for a bundle x. Note: it must be hand drawn on your answer paper. As such, do not worry about accuracy or scale. But label your axes and be clear which bundles are in the upper contour set for a bundle x. (4)

Let there be two goods 1 and 2. Let x1 and x2 denote their respective quantities. x = (x1, x2) represents a bundle. Milton's preferences over bundles in R? can be described as follows: Between any two bundles x = (x1,x2) and y = (yı, Y2), Milton prefers the bundle that has %3D more of good 1. If two bundles have the same amount of good 1, he prefers the bundle that has more of good 2. (Obviously, bundles with the same amount of goods 1 and 2 are the same bundle). Do Milton's preferences satisfy the strong monotonicity assumption? Prove or provide a counterexample. (4) а. b. Draw the upper contour set for a bundle x. Note: it must be hand drawn on your answer paper. As such, do not worry about accuracy or scale. But label your axes and be clear which bundles are in the upper contour set for a bundle x. (4)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Napoleon has preferences on bundles of two goods (x,y). Napoleon finds (x,y) is at least as good as (x’,y’) whenever the following is true: either x>x’, or x=x’ and y≥y’. Do Napoleon’s preferences violate transitivity?
For example (bb, cc) = (3,6) is a bundle with 3 units of baklava and 6 units of corn. All bundles where the amount of corn and baklava are greater than or equal to zero are allowed. The utility is uu(bb, cc) = \bb + cc. For each of the following different utility functions, argue whether or not they represent the same preferences as uu(bb, cc).
U1, U2 and U3 represent Ariadne's indifference curves at different levels of utility. Suppose she prefers any bundle on curve U3 to any bundle on U2 and prefers any bundle on U2 to any bundle on U1. Select the correct answer from the options below: Y U1 U2 U3 X If Ariadne's preferences satisfy completeness, then she prefers any bundle on curve U3 to any bundle on curve U1. If Ariadne's preferences satisfy transitivity, then she prefers any bundle on curve U3 to any bundle on curve U1. O If Ariadne's preferences satisfy transitivity, then she prefers a bundle on curve U1 to any bundle on curve U3. If Ariadne's preferences satisfy completeness, then she is indifferent between bundles on curve U3 and bundles on curve U1.
Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?
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1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.
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12 There are two goods and John's preferences can be represented by u: R²0 R given by u(x) = x₁³x2³. His income and price of the two goods are given by (M, P1, 20 P2) = (12, 1, 2). Which 2 of the following 8 options are false: In John's optimal bundle, he consumes the same amount of good 1 as good 2. If we change John's utility function to u(x) = x + then John's optimal bundle remains unchanged. At John's optimal bundle, the slope of the budget constraint equals the slope of the indifference curve. In John's optimal bundle, he spends the same amount on good 1 as good 2. John's preferences satisfy local non-satiation. At John's optimal bundle, his bang per buck of good 1 equals his bang per buck of good If we change John's utility function to u(x) = In (17 +x₁x₂) then John's optimal bundle remains unchanged. If we change the budget set to (M, P1, P2) = (24, 2, 4) then John's optimal bundle remains unchanged.
please only do: if you can teach explain steps of how to know of each cases? of the x