Any parts appreciated the more the better. 7. a. Consider an exchange economy with two goods and two individuals. Alice always requiresequal quantities of the two goods. Bob's expenditure on good 1 is always twice his expenditureon good 2. Suppose that Alice's endowment consists of 5 units of good 1 and no good 2 w4 =(5,0) and Bob's endowment consists of 1 unit of good 1 and 6 units of good 2, wB = (1,6).i. Suggest utility functions consistent with their behaviour and verify your answer. Drawa typical indifference curve for each individual.ii.Determine the contract curve. Illustrate it in an Edgeworth box.ii.Determine the competitive equilibrium price ratio and the consumptions. Illustrate theequilibrium in an Edgeworth box.iv.Now suppose that there is an additional individual named Cindy in the economy. Shenever consumes good 2. Her endowment consists of no good 1 and unit of good 2wB = (0,2). Suggest a utility function for Cindy and draw a typical indifference curve.Determine the competitive equilibrium price ratio. Determine the effect on equilibriumprice ratio and utilities if 4 units of good 1 were given to Cindy (NOT a transfer fromthe other two consumers)? Provide an intuitive explanation for your answer.b. Suppose each firm in a competitive industry has a production technology described by theproduction function f(l,k) = (min (I, 4k))'/2. The price of labour per unit is 2 and the price ofcapital per unit is 4, and each firm faces a recurring fixed cost of 300 (Firms incur fixed costs evenin the long run, however, not due to fixed labour or fixed capital).Suppose the market demand is given by Qd = 560 – P. Determine the long-runequilibrium price and number of firms in the industry.i.ii.Assume that the amount of capital is fixed at ko = 25 and that labour is variable.Derive the short run total cost function for each firm. Using the number of firms foundin part (b.i), derive and graph the short run market supply function.

*Hi there , as you have posted multiple sub parts , we are only allowed to solve first three .…

7. a. Consider an exchange economy with two goods and two individuals. Alice always requires equal quantities of the two goods. Bob's expenditure on good 1 is always twice his expenditure on good 2. Suppose that Alice's endowment consists of 5 units of good 1 and no good 2 wA = (5,0) and Bob's endowment consists of 1 unit of good 1 and 6 units of good 2, w® = (1,6). i. Suggest utility functions consistent with their behaviour and verify your answer. Draw a typical indifference curve for each individual.

7. a. Consider an exchange economy with two goods and two individuals. Alice always requires equal quantities of the two goods. Bob's expenditure on good 1 is always twice his expenditure on good 2. Suppose that Alice's endowment consists of 5 units of good 1 and no good 2 wA = (5,0) and Bob's endowment consists of 1 unit of good 1 and 6 units of good 2, w® = (1,6). i. Suggest utility functions consistent with their behaviour and verify your answer. Draw a typical indifference curve for each individual.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

5. Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = 1/3 x1³x2³. If we set good 1 as the numeraire (so that p₁ = $1), what will the equilibrium price of good 2 be?
4. Consider an exchange economy of two goods and two individuals. Consumer A has an endowment of 100 units of good 1 and 12 units of good 2 wA = (100,12), while consumer B has an endowment of 100 units of good 1 and 3 units of good 2 wB = (100, 3). The consumers' utility functions are given by: UA х,4 + Inx,A and UB x,B + 2lnx,B %3D Which of the following allocations is not efficient? a. (x,4,x24) = (100,5), (x,³, x2³) = (100,10) b. (x,4, x24) = (50,5), (x,®, x,³) = (150,10) c. (x,4, x24) = (0,4), (x,³, x,") = (200,11) d. (x,4, x24) = (100,0), (x1",x,") = (100,15) %3D
Let 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?
Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, ci) = c(ci)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
7) Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane's marginal rate of substitution ( MRS) of soft drinks for sandwiches is 4 and Bob's MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off?
3. Consider an Edgeworth Economy with two consumers A and B, and two goods 1 and 2. The initial endowments are E₁ = 10 and E2 = 10, and the initial endowments are e₁ = 10, e₁ = 0, e = 0, and e2 = 10. In words, A holds the entire endowment of good 1, and B holds the entire endowment of good 2. u(x1, x2)=x1x2, and the utility function of consumer B is uB (y1, y2) = √√√1 + √√√2- (a) Draw the Edgeworth Box that shows the initial endowments on it. (b) Verify that the price ratio ₁ = 1 and x₁ = x² = y₁ = y² = 5 is an equilibrium. P2 P2 Hint: You do not need to derive the equilibrium from scratch. You can just show that given the price ratio P₁ = 1, both consumers maximize utility when consuming 5 units of each good, and that this allocation is feasible. Alternatively, you can just show that the allocation satisfies the MRSA = MRSB and the feasibility conditions. (c) Solve for the equilibrium from scratch, instead of guessing and verifying.
4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
2. Assuming Bart and Homer barter (no pun intended), highlight the area of all post-trade allocations both of them prefer to their initial endowment. 3. What determines which particular post-trade allocation they end up with? Marge observes what is going on and intervenes. She (acting as the "Government' in our example) decides that Bart should not have any beer. She makes a lump-sum transfer leading to new initial endowments for Bart (0,21) and Homer (38,0). 4. In your Edgeworth box show the new initial endowments after the lumpsum transfer imposed by Marge. Label this poișt e2. (1 point) 5. After Marge's transfer mark one new possible post-trade allocation (Label this point f.) and draw the associated indifference curves for Bart and Homer. (1 point) 6. Did Marge succeed in her mission to not let Bart have any beer? Why or why not? 7. Add the contract curve to your Edgeworth box. 8. What do all points on the contract curve have in common?
5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear.…
Can you help me with this question. Im finding it quite difficult. In a two-good economy there are two equal-sized groups of people: type a have preferences given by 2 log(xa1) + log(xa2) and type b have preferenceslog(xb1)+2log(xb2) where xhi means consumption by a type h person of good i. The division of property is as follows: each a-person has an endowment of (30, k) units of the two goods; each b-person has an endowment of (60, 210−k) units, where k is some given number between 0 and 210. Assume that there is no production and that people can freely exchange goods to maximise their utility. If there is a competitive equilibrium, what are the individuals’ incomes (ya, yb) in equilibrium as a function of k?
3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.
Q. Consider two rational behaving consumers, A and B, in a two-good exchange economy. Their utility functions are defined as follows: 1A 2A X1/2X¹/3 X1/3 X2B 1B Their initial endowments are given by w₁ = (8,5) and wB = (4,3). a. Describe the initial condition that will lead to an exchange. After the exchange, how many units of Good 2 will Individual B end up receiving/offering in the final allocation? Elaborate in detail on the steps towards the solution and round up the final answer to two decimal places. UA UB - = b. Sketch an Edgeworth Box precisely showing the initial allocation and the final allocation on the vertical axis. You do not have to sketch the budget constraint and the indifference curves.