Its economics......

Exercise 12 There are two sectors in the economy, A and B. The labor demands are: Sector A: w=50-5L, Sector B: w=80-7,5Lg a) Let the equilibrium wage be w= 5 . What is the total labor employed in each sector? b) Assume that there is a minimum wage of 7.5 only in sector A. i. What is the new level of employment in sector A? li. To absorb the excess labor supply, to which level must wage decrease in sector B? Exercise 13 The manufacturing sector in a certain country consists of 100 similar firms. Their product is sold in a perfectly competitive market where there is perfect mobility of labor among the firms in the sector. All this mobility among other sectors and countries is already reflected in the labor supply functions. The workers supply labor in a competitive market. The production function for each firm is given by X, =304-0.14, ". where X, is the output and & is the input. The labor supply functions for men and women are different, even though they are both equally productive: Ly =10ww +200 Ly =40WM -3200 Furthermore, the price of the output is 10. a) All markets are competitive. Find Ww . Wy . Ly . Ly and X. Compute the excess total revenue over the total variable cost of the manufacturing sector. b) Imagine now that the owners of the 100 firms constitute a union that acts as a monopsonist in the labor market. Compute the new values of the variables in the previous question. c) Even though the manufacturing firms have monopsony power, the law forbids sexual discrimination. Compute the new levels for the variable in question a). Exercise 14 There are 100 competitive firms acting in the market of output Q and using the labor (men and women) as an input. The price of output Q is El and the each firm's technology is given by: 0, = 25 , where The labor supply functions for men and women are given by Ly = 10wy and Ly =40 w . respectively. a) Consider a competitive market. Compute the equilibrium wage rate and the levels of labor for men and women. Find, for each firm, the level of labor used, production and profit. b) Assume that firms constitute a union with monopsony power in the labor market. Find the new equilibrium and discuss the possibility of discrimination. Compute each firm's profits in the new situation. C) Due to a technological improvement, the production function changes to O = 25L, + Ly - Considering a competitive labor market, find the new equilibrium and explain the differences to the one found in a).6. General Equilibrium Exercise 1 Consider an initial endowment inside the Edgeworth box. Can the negociated contracts coincide to any point in the contract curve if the result is Pareto optimal? Comment. Exercise 2 The contract curve has this name because it is the set of all possible contracts. Comment. Exercise 3 To get a Parcto optimum it is necessary that the marginal rate of substitution between any two goods be equal for any two people that buy them, Comment, Exercise 4 Represent graphically, and justify, the optimal Pareto allocations for two goods- tea (X) and coffee (Y) - consumed by two people, Mr. Lipton and Mr. Delta, in the following situations. Assume that the endowment of coffee and tea are A and L . respectively. a) Mr. Delta only likes coffee and Mr. Lipton only likes tea. b) They both like coffee and tea. The two goods are perfect substitutes for Mr. Delta. Mr. Lipton likes consuming a certain quantity of tea that equals L/ A of the quantity of coffee. c) Mr. Delta and Mr. Lipton have preferences given by: Up =XD+Lp and UL=2X, +Y, d) Mr. Delta and Mr. Lipton have strictly concave to the origin indifference curves. Exercise 5 Assume that a certain consumer type A has X units of X and a certain consumer B has Y units of Y. The utility functions of these two consumers are given by the expressions: U. =XAY, and U. =X Y. where X and Y are the quantities consumed. a) What is the equilibrium relative price of X in a competitive market? b) Is this equilibrium unique? c) Define the contract curve. Exercise 6 Two tribes, the Ocidentals and the Orientals, inhabit a certain island. They live in the respective sides of the island and meet only once a year in the annual market. No contact to the rest of the world is established. Both tribes collect com (Y) and hunt deers (X). In the annual market, the deers are exchanged for com in competitive conditions. There are 1000 ocidental families and each produces 30 deers and 200 tons of corn. The utility function of each ocidental family is Ude = Xoe . You . where Xoc is the number of deers and Yo, is the number of tons of corn consumed in a year. There are 2000 oriental families and each produces 25 deers and 300 tons of corn. The utility function of each oriental family is Uo = Xor Yor , where Xor is the number of deers and Yo, is the number of tons of corn consumed in a year. The annual market achieves a competitive equilibrium.Exercise 7 Consider an economy without production where there are two agents, A and B, with the following endowments: Xx =10, Y1 =20. X, =20 and YR =10 - Their utility functions are U, = X, - Y,"and Us = X,"-Y,"". a) Using the data find the relative price interval in which both agents are willing to trade. Determine the exchange pattern: who sells X and who sells Y- b) Check if P / Px = 2 is a competitive equilibrium. Explain why and, if not, describe how prices will evolve? c) How much is Y worth in terms of X in a competitive equilibrium? Represent the initial endowment and the competitive equilibrium in an appropriate diagram. d) Assume that agent A's preferences are now characterized by the following statement: "I must consume 2 units of X for each unit of Y" . i. Show that agent A's marginal rate of substitution is not always defined. ii. What is the shape of the contract curve? ili. Given the property in i., this economy has a continuum of competitive equilibria. Comment. Exercise 8 A certain economy produces only one consumption good (X) using only one input: labor (Y). Assume that there is only one type of families in this economy and consider each family's decisions with respect to consumption and hours of labor in a certain period of 24 hours. Each family's preferences can be represented by the utility function U = XO, where X measures the units of consumption good and O the hours of leasure. The profts in the production of X are totally distributed among the families in the same period. a) The current technology is represented by the production function X = VL and there is competitive equilibrium in the economy. The equilibrium real wage rate is v2/8- Find the production level, the total number of hours of work used in the production of X and the profit. Check the families' budget restriction. b) There is an alternative technology described by the production function X = L. Compute the equilibrium real wage rate and the pinfit if this technology is chosen. How much of good X will be consumed? Exercise 9 Mr. Crusoe's main problem when he was isolated in the island was to guarantee his subsistence. In the beinning he was able to survive eating fruits (X). The quantity of fruits he got depended on the time spent gathering them ( Ly ) according to the production function X = Ly . Unfortunately, fruits only last one day. Hence, Mr. Crusoe must gather fruits every day. Each day, his utility function is given by U = X(24-Ly ) . where Ly is the number of daily hours used gathering fruits. a) How much time must Mr. Crusoe spend gathering fruits each day? How many fruits will he get this way? After some time, Mr. Crusoe found out he was able to fish. If he uses Ly hours a day fishing, he gets the quantity Y = L." of fish Considering the possibility of fish consumption, his utility function is now U=(X +4Y )(24-L) , where L is the total quantity of time working. b) Find the new optimal allocation for Mr. Crusoe? How many fruits and fish will he consume?Exercise 15 Two goods, X and Y, are produced in a certain country, with CRS production functions. There are 2 inputs in fixed quantitites (K =100 and Z = 9 ). All markets are competitive and with perfect intersectorial mobility of inputs. The inhabitants' preferences for goods X and Y can be represented by tha marginal rate of substitution: MRS =- 4X Y a) In a certain period of time the equilibrium prices in this economy are: PX = 1. W =50 and R P =5. How much is produced of X and Y? b) Having the information that the production function of Y is given by the expression: Y = 10V10KL" and that the productive efficiency implies ky > Ky , represent graphically the transformation curve and compute the point of efficient production when only Y is produced. c) Imagine that the production function of X changes to one represented by the same algebraic expression of Y and that the quantities of inputs remain the same. Compute the general equilibrium quantities for X and Y. Exercise 16 Consider an economy with only two firms, X and Y, which use two inputs, capital (K) and labor (L), in the following way: - The production function of X is described by X = Ly Ky . - The production of Y uses fixed coefficients of inputs, i.e., always uses 10 units of labor for each unit of capital. Assume that the producers of X have 30 units of labor and 6 units of capital, and those of Y have 20 and 4, respectivelly. a) Represent, in an Edgeworth box in the space of the inputs, the contract curve for this economy. How does the relative wage ( w/ r ) change along the curve when sector X expands? b) Show that, starting with the initial endowments and in order to achieve a competitive equilibrium, sector X will expand its units of capital and tranfer labor to sector Y and the relative wage ( w/r ) will equal 0,3, i.e., ten workers will cost three units of capital. c) Assume now that labor is so specific to each production that it cannot be transferred between them. Starting at the initial endowment, and given the immobility of labor, what are the Pareto optimal allocations? Identify those allocations that would be efficient if labor was flexible. (Make a graphical analysis and justify it carefully)