Suppose that an individual receives utility from two goods X and Y and his utility function is given by: u = -1/X -1/Y. a) Derive the Marshallian and Hicksian demand functions for X and Y. %3D b) How would you determine whether X and Y are gross substitutes or gross complements? c) How would you determine whether X and Y are net substitutes or net complements?
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- 4. a. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.) b. Conversely, demonstrate that it is possible they would choose to consume only x when theirincome is I but would choose to consume x and y when their income is I’ > I.c. Finally, show it is possible that they would choose to consume only y when their income is I butwould choose to consume only x when their income is I’ > I.Intialy mr. John is at equilibrium such that the last dollar spent on each of several products gives hi identical marginal utility i.e MUorange/porange=MUApple/pApple=...=MUn/pn where Mu orange =aditional utility derived from consuming one more unit of Apple ,pApple=price of a unit of Apple etc Q.how will Mr.Jhon react if the price of orange and other goods remain constant?and how can the equilibrium be restored?For normal goodsA) the substitution effect of a price decrease will decrease the quantity of the good demanded while theincome effect of a price decrease will increase the quantity of the good demanded.B) the substitution and income effects of a price decrease will both increase the quantity of the gooddemanded.C) the substitution and income effects of a price decrease will both decrease the quantity of the gooddemanded.D) the substitution effect of a price decrease will increase the quantity of the good demanded while theincome effect of a price decrease will decrease the quantity of the good demanded.
- 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?a. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1a. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1 instructions: answer d,e, and f only
- 7 Asen tries to minimize his cost of using two goods x subscript 1 end subscript and x subscript 2 end subscript. The price of the first good is BGN 12 and the second good BGN 8. His utility function is x subscript 1 superscript 3 divided by 5 end superscript x subscript 2 superscript 2 divided by 5 end superscript and the utility he will get from using both goods, is 32 units. Find the Hicks quantities demanded and what Assen's minimum budget must be to consume these quantities and obtain the above utility. e-412, h2=21, h1=21 e=416, h2=21, h1=21 e=640, h1=32, h2=32 e=422, h2=21, h1=21 e=378, h2=21, h1=21 e-378, h2=20, h1=20 another answer e-378, h2=24, h1=244) Assume Linda only buys two goods, chicken and rice with her income of M, and prices, Pc & PR. a) Graph her consumer choice model (with chicken on thex axis. Nowlet price of chicken fall, causing Linda to consume more chicken and more rice. Indicate the income and substitution effects on the graph. b) Based on your graph from part a, draw Linda’s ordinaly demand (do) and compensated demand (dc) curves for chicken c) (True/False) this chicken must be a nomal good. Explain how you know. d) (True/False) this rice must be a nomal good. Explain how you know.Answer the following short questions:a. Suppose that a consumer’s preferences between goods x andy are represented by the utility function u(x, y) = x^2 + 16xy + 64y^2. If these two goods have the same price, describe the optimal consumptionchoice of this consumer.b. Suppose that when the price of a good change, the incomeand substitution effects change the consumer’s demand for that goodin opposite directions.i. Is this good a normal or an inferior good? Explain.ii. Is this good a Giffen or an ordinary good? Explain.c. Is the following statement true or false? The differencebetween a monopolist’s marginal cost and its profit-maximizing price issmaller when the demand is more elastic.
- Guerdon always puts half a sliced banana, q, , on his bowl of cereal, q, The two 14 goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and mathematically. 12- 10- e, Guerdon's utility function (as a function of q, and q2) is 6- VA U= min/2q1.92} 4- O B. U=q, +92- 2- 0+ OC. U=29, + q92- 10 12 14 16 18 20 6 22 Bananas O D. U=0.5q1 + q2- OE. U=q, xq2- 5.00- 4.50- Guerdon's demand function for bananas (as a function of the price of bananas, P1. the price of a bowl of cereal, p2, and income, Y) is 4,00- 3.50- 91 = (p1 + 2p2) (Properly format your expression using the tools in the E 3.00 palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.) 2.50- * 2.00- P. 1.50- 1.00- 0.50- 0.00+ 10 12 14 Bananas tv 80 DI DD F1 F3 F4 F5 F6 F7 F8 F10 @ %23 $ & 1 3 4 7 Q W E Y U S F H. J く C V M option command command optic ーの * CO Cereal (bowls) p. S per banana B * * N AExplain the difference between a positive and a negative network externality. A network externality for a good is positive if O A. the substitution effect of a price change is larger than the income effect, but a network externality is negative if the income effect is larger than the substitution effect. B. consumption by others decreases a typical consumer's marginal utility from consuming the good, but a network extemality is negative if consumption by others increases a typical consumer's marginal utility from the good. c. the price is lower the more people own it, but a network externality is negative if the price is lower the fewer people own it. D. the quantity demanded is higher the more people own it, but a network externality is negative if the quantity demanded is lower the more people own it. O E. it has a complement, but a network effect is negative if it has a substitute. Give an example of each. An example of a positive network externality is the dermand for A. a work of…Which of the following statements are true? Instruction: you may choose more than one option. O. The Law of Demand is explained by the Slutsky-Hicks equationO. All statements are false.O. For well behaved preferences the income effect is positive.O. For well behaved preferences the substitution effect is non positive.O. if the demand foro good increases when income then the demand for that good must decrease when its price increases.O. A Giffen good cannot be explained by the Slutsky-Hicks equation.