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- 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…ASAP DECİSİON RULE FOR UTİLİTY MAXİMİZATİON As I understand we choose the good which has higher marginal utility per dollar . BUT MY QUESTİON İs that What if our budget is not end up and the marginal utility per dollar is same for both good What should we do at that point? PLEASE ANSWER MY QUESTİON DONT GİVE CLLASİC DEFİNİTİON18. Declining MRSXY implies that:(a) The total utility is decreasing along an indifference curve(b) The consumer’s preferences do not satisfy the more-is-better principle(c) The consumer is willing to give up more and more X for additional Y as the consumption of X increases along an indifference curve(d) The consumer is willing to give up less and less X for additional Y as the consumptionof X increases along an indifference curve
- 3. What are the benefits to make rational decision?ADDED 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…10. Utility is a type of function that occurs in economics. When a consumer receives x unils of a certain product, a certain amount of pleasure, or utility U, is derived The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1 , from 1 to 2 , from 2 to 3 , from 3 to 4 b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is (Type an integer or a decimal.)
- 1. Enumerate and explain the properties of Consumer Preference. 2. Illustrate and explain the Utility Maximization1- If Isabelle's marginal utility for pizza is 10 and her marginal utility for salads is 2, then Isabelle will choose to eat five times more (a) salads than pizzas . (b) Isabelle will be ready to exchange five salads for a pizza. (c) Both of the above answers are correct. (d) None of the answers above is not correct. 2- Consider a consumer who consumes two goods, good 1 and good2. We denote by p1 the price of the good1 and by p2 the price of the good2. We denote by Um1 the marginal utility of good 1 for the consumer and by Um2 its marginal utility of good 2. The quantity of good 1 that the consumer must give up in order to be able to consume an additional unit of good 2 is equal to: (a) -p1 / p2 (b) -p2 / p1 (c) -um1/ um2 -Um2 / Um1. 3- Consider a consumer who consumes two goods, good 1 and good 2. We denote by q1 his consumption of good 1 and by q2 his consumption of good 2. Graphically, we measure the quantity of good 1 on the abscissa and the quantity of good 2 on the order. Suppose…What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing
- Anastasia, Emma, and Greta are deciding what to do on a weekend getaway. They each suggest a first, second, and third choice and then vote on the options. Table 18.2 shows their first, second, and third choice preferences. Explain why they will have a hard time teaching a decision. Does the group prefer mountain biking to canoeing? What about canoeing compared to the beach? What about the beach compared to the original choice of mountain biking?Would you expect marginal utility to rise or fall with additional consumption of a good? Why?. (b) Suppose there are two Bohemian roommates with identical preferences who derive utility from the number of paintings hung on their hotel's walls (X) and the number of granola bars (Y) that they eat. The specific utility function underlying their preferences is given by: U₁ (X,Y)= X1¹³ Y₁23 (for i=1.2) mes Given that each roommate has $300 to spend and P=$100, Py = $ 0.20, explore the consequences of various expenditure allocations. In particular provide a detailed analysis of the possibility leading to free ridership Will that solution be efficient? If so or if not, why? Calculate the efficient allocation. What arrangement for cost sharing would be Pareto superior?