(a) If we allow for the possibility of satiation, consumer's budget constraint takes the form px pw. Walras' Law then becomes pz(p) ≤0 for all p ≤0. Show that the standard proof of the existence of general equilibrium still applies for this generalized form of Walras' Law.
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- (c) If the preferences are concave, will the consumer ever consume both of the goods together?Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-3h¹+, where 3 > 0 and p > 0 are parameters. 1+pOn a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
- A 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)2 3) For each utility function, determine the marginal utility with respect to x, marginal utility with respect to y, and the MRS. (3pts each) a) U(x, y)-3x+2y b) U(x, y) 10x¹/5 y c) U(x, y)=x+ y²It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute four pounds of a generic store-brand sugar for two pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution between store-brand and producer-brand sugar? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?
- It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute four pounds of a generic store-brand sugar for two pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution between store-brand and producer-brand sugar? (Click to select) Yes No Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased?Producer-brand sugar: poundsStore-brand sugar: poundsIf prices change such that the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per…Ding Ding is a cat philosopher. He spends his time on two activities. Sleep and thinking. Both activities produce pleasure to Ding Ding. How effective Ding Ding is in each activity varies day by day. But on a given day, if he spend “s” effective hours in sleeping and “t” effective hours in thinking, his utility is u(s,t)=s^2+t. you can assume that time is continuous in answering the following question. (A) Let us first ignore that there are only 24 hours each day. Label “s” on the x-axis and “t” on the y-axis in a diagram. Draw two indifference curves u(s,t)=s^2+t=24^2=576, and u(s,t)= s^2+t=12^2=144. On each indifference curve, you have to mark at least the coordinates of four points to illustrate the shape of it. (B) Describe in words how these two indifference curves in (a) relate to each other.Question One ) Zabron has preferences > for Champagne (good 1) and Wine (good 2) defined by. (x1, x2) > (21, 22) e min (x, x2) 2 min (z1. z2) and max (x, x2) 2 max (z,, 2) Are Zabron's preferences complete? Transitive? Locally Non – satiable? Convex? Justify your answers and draw the No-worse-Than, No-Better-Than and the Indifference set of a representative bundle. (i) Suppose that Zabron's preferences > can be represented by a continuous utility function. Show that > satisfies Axioms 1 (Completeness), 2 (Transitivity) and 3 (Continuity).
- 3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?Q- Marginal utility can never be negative. True/FalseSolve all this question......you will not solve all questions then I will give you down?? upvote....... Convexity and optimization. Indicate which of the following graphs of various budget constraints (BC) have a nonconvex choice set by checking the box below the graph that satisfy this property. check all that apply