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- NoneConsider the utility function uu(xx, yy) 10 for all bundles (xx, yy) (a) What are strict preferences? What are the indifferences? (b) Argue that the preferences represented by this utility function are strictly convex or that they are not. (c) Árgue that the preferences represented by this utility function are complete or that they are not. (d) Argue that the preferences represented by this utility function are strongly monotonic or they are not.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+p
- PROBLEM (2) A consumer has utility u(x,y) X y This time, I give you the marginal utilities (don't expect it in the midterm!) MUx = over bundles of food (x) and clothing (y). 1 and MUY x² (a) Does the consumer always prefer more food to less? (b) Does she exhibit diminishing marginal utility for food? (c) Does she exhibit diminishing MRS? (d) If she is indifferent between the bundles A = ( = = The more food she has, does she value food less relative to clothing? (That is, she is willing to give up fewer units of clothing for an additional unit of food) Circle: YES / NO Are her indifference curves bowed towards the origin? Circle: YES / NO ¹) and B = (¹,x), calculate x. , 3 4 1 y² (e) Does she value food -relative to clothing- the same at bundle A and B ? If not, at which bundle does she value food (relative to clothing) more? (f) Why should we not be worried about the fact that the utility function here always takes "negative values"? (g) (wait for the next class for us to cover utility…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+ y²While deriving consumer's equilibrium, what is given? (a) Income of the consumer (b) Price of the commodities (c) Both income and price (d) None of the above Qy|
- Consider the utility function U(x, y) = x^4 + y^2 (a) What happens to the marginal utility of x as y increases? (b) What happens to the marginal utility of x as x increases? (c) Solve for MRSx,y and test whether or not it is diminishing (d) What type of special utility function is this?(A) The unit in which the utility is calculated is ________ (B) Utility measures __________ of the consumercan you show how they got this answer
- Total utilityADDED DISCUSSION WITH QUESTIONS TOPIC: MARGINAL UTILITY 5 6 7 No. of Pieces Total Utility (Q) 1 2 3 4 (TU) 150 225 250 220 8 9 10 11 Marginal Utility is calculated using the formula given below 12 Marginal Utility (TU-TU)/(Q-Q) 13 14 D For 1 Piece For 2 Piece For 3d Piece (86-0)/(A6-0) -(87-86)/(A7-A6) 150 75 (88-87)/(AS-A7) 25 Marginal 15 Utility Formula 16 Marginal Utility 17 For 1st Piece of the Cake Marginal Utility1 = (150-0)/(1-0) Marginal Utility1 = 150 For 4th Piece (89-88)/(AS-AS) -30 For 2nd Piece of the Cake Marginal Utility2=(225-150)/(2-1) Marginal Utility2 = 75 For 3rd Piece of the Cake Marginal Utility3 = (250-225)/(3-2) Marginal Utility3 = 25 For 4th Piece of the Cake Marginal Utility4 = (220-250) / (4-3) Marginal Utility4 = -30 Therefore, here we can see how the marginal utility of a piece of cake declines after the consumption of the previous one. Here, the highest utility is reached at the consumption of the 3rd piece, beyond whichthe total declined. This is a…If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)