9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are u²(x,x)=(x²)(x²) u²(x²₁₁x²) = (x²)(x²)² In the following, use the normalization p2 = 1. e¹=(5,5) e²=(5,5) (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (c) Consider the allocation = (¹,²)= ((2,3), (8, 7)). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (e) conform with or violate this theorem.
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- 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?1) Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? Explain 2. Graphically show the effect of an increase in price of Coca Cola on the demand of PepsiCola 3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. Ifthe income of the consumer is 120 Birr, the y-intercept is 3, and the slope of the budget lineis -0.5 then determined the price of commodity…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.
- 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=243- Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions:UAhmet (XA,YA)= 5ln(XA)+ln(YA)UBerk (XB,YB)= XB0,5 YB0,5a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents.Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of good 1 and ₂ units of good 2, their utility is given by u(x₁, x2) = aln x₁ + ln x2, where a > 0 is a free parameter. (i) How does the parameter a affect the marginal rate of substitution between goods 1 and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter a increases.
- Suppose consumer consume two goods. Can both goods be inferior? Can one of the goods be inferior? Explain your reasoning clearly. 191. Hatfield and McCoy hate each other. The only good they both consume WH W2 40 Mand McCoy's is whiskey. Hatfield's utility function is UH utility function is UM = WM-W, where WHI is Hatfield's consumption 40' Η of whisky and WM is McCoy's consumption of whiskey. The sheriff has confiscated a total of 60 litres of whiskey which he could give back to them or throw in the creek. Say that the Sheriff wants them both to be as well off as possible and weighs their "happiness" equally. How much whiskey should the sheriff give to each of them? Should he throw any whiskey in the creek; if so how much? =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 A
- Explain 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…Let the following table represents the total utility of a given consumer, in the cardinal utility approach A) Calculate the MUx and MUy and fill the table in the 4th and 5th rows. B) If the two products (X&Y) are free goods how many of X and Y should the cons consumer take to maximize utility? C) What is the maximum utility of X and Y if they are free?. D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and YLet the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?