Which of the following preference doesn't satisfy monotonicity? O Quasilinear preference O Perfect substitutes preference O Bads Cobb-Douglas Preference
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- T/F Explain If preference is strongly convex, the utility function will exhibit dimin- ishing marginal utility (MU).K Tiffany's constant elasticity of substitution (CES) utility function is U(91-92) = (a +92) Show that there is a positive monotonic transformation such that there is an equilivalent utility function (one with the same preferences ordering) U(91-92) =a +92 There is a positive monotonic transformation such that there is an equilivalent utility function because OA B. O C. OD. OE 1 (ai +92) * =q+ + 2 (af + a) (a² + a) ³ only wa+h+a+2> (a +² +a+g) ² af + a²>q* f+q* £ ony # (af +ah) ³ > (a •{• a•h) ² rif 2) (a +42 ) ² >9² +92.We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)
- Suppose that the price of good Y falls. How will this change the market rate of substitution between goods X and Y? Multiple Choice O It decreases. O It is not affected. O It increases. O It can increase or decrease depending on the preference of the individual.No written by hand solution Assume Fred has the following preference relation on [0, 1]: x ≿ y if and only if x ≤ y for all x ̸= 1 and y ̸= 1; and 1 ≻ z for all z ∈ (0, 1), 1 ∼ 1 and 0 ≻ 1. Does there exists a utility representation for this preference relation? If yes, provide a utility function. If no, explain. Show your work.I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?
- Suppose an indinidual has the following utility finction Urey)-2+2" writh a strictly ineveaseng morrginal rate of substitntion. and income of 3 The price of y is $4 CPpi ) The intial price of x is $lcre=) and then increases to 3 px=3). Find the chonge in the quantidy consumed of X.IHow much of the chonge is the income effect? How much by the Substitution effect? Evplan in Econ terms erplainedl byWhich form of utility is expressed on ranking the bundles According to preferences2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?
- If the MRS is an increasing function of which of the following must be true. a. Preferences are convex O b. None of the other answers O c. Utility is not homothetic O d. Demand will be a corner solutionWhich among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistentConsider the following utility function U (X,Y) = X÷Yi. What is the name for a utility function of this form? O Perfect substitutes O Fixed proportion O Cobb-Douglas O Negative exponential b. Fix a utility level U = 10. Fill in the blanks below. Instructions: Round your answers to 2 decimal places and enter your result for the MRS as a negative number. When X= 10, then Y= The corresponding marginal utility of X is , the marginal utility of Y is and the marginal rate of substitution for X with Y is
