Consider a city with its boundary mapped onto quadrant I on the cartesian plane. Let x be distance from the central business district (CBD) where x € (0,x). Now consider two real estate user types, A and B. User A has a strong preference for proximity to the CBD while user B has stronger preference for open space. a. Which of the two user types has a more elastic demand for real estate with respect to distance from CBD? b. Let be the intersection point between demand from user A and B. Draw the demand curves for user A and B on the same graph and label the intersection point. Which user type has a higher willingness to pay for real estate at x € (0.£). Describe the location rule that assigns user types to the inner boundary of the city. c. d.
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- Consider the market for a single network good and suppose thatconsumers differ in their valuation of both the stand-alone and thenetwork benefits (it can indeed be argued that it is more plausiblethat a user who has a higher value for the stand-alone component of atechnology also assigns more importance to the size of its network.) Tocapture this idea, write the consumer’s utility function for joining thenetwork as U(θ) = θ(a + νne), where a is the stand-alone benefit, ν > 0measures the network effect, neis the expected number of users joiningthe network, and is uniformly distributed on the unit interval.a. What happens if p > a + νne? (Hint: Identify all consumer who buythe good for at price p and a given expected network size ne).b. What is the consumer’s willingness to pay for the nth unit of thegood when ne units are expected to be sold? Is the demand downwardsloping? Does the demand increase with the expected network size?c. Express the fulfilled-expectations demand curve…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…You are in the market for a new couch and havefound two advertisements for the kind of couchyou want to buy. One seller notes in her ad that sheis selling because she is moving to a smaller apartment, and the couch won’t fit in the new space.The other seller says he is selling because the couchdoesn’t match his other furniture. Which seller doyou expect to buy from? Why? ( Hint: Think whowould be the more motivated seller.)
- 1. 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? =a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?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.
- If the supply and demand functions for a commodity are 100 + 2(4+ Pa = - (Q.) P₁ = (Q + 2)² E plot each function on the same graph Estimate the quarum price and quarty aigebraicaty and graphicaly w▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪ ‒‒‒‒‒‒‒‒‒‒‒‒wwwwwwwwwSuppose that Bartolo and Emilio spend their incomes on two goods, food (F) and clothing (C). Bartolo's preferences are represented by the utility function: 16 15- U(F,C) 10FC 14- 13 while Emilio's preferences are represented by the utility function: U(F,C) 0.20F2C2 12 11 . 10- With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bartolo the same level of utility as bundle (10,5). Do the same for Emilio. Then, identify the set of bundles that give Bartolo and Emilio the same level of utility as bundle (15,8) 8- 1.) Using the three-point curved line drawing tool, graph an indifference curve for Bartolo that includes bundle (10,5) and that also contains bundles with 4 and 5 units of food. Label the curve U 6- 2.) Using the three-point curved line drawing tool, do the same for Emilio including bundle (10,5) and bundles with 4 and 5 units of food. Label the curve U1 3.) Using the three-point curved line drawing tool, graph an…goods, XandY per of good X is N$4 and the price of good Vis No10 Harrys unlity funchon is UCX,)==XY. Harry consumes 2 and he spend's Npbo month The price Find The values of gocal X and Y maximizes Harcys unly illustruate Hary's utlty maximizing.combinason clearly labelled on a graph. Suppose llustrate Harrys price & spod X increased to Ngb effects income and substitution ef the anel laballed graph.
- 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 AI like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.