Provide step by step solutions to the following questions.
(Inverse) labor demand for low-skilled workers in Arizona is determined by w=32 -0.2E where E is the number of workers (in millions) and w is the hourly wage. There are 30 million native low-skilled workers in Arizona who supply labor inelastically. If the United States opened its borders to immigration from Mexico, 5 million low-skill immigrants would enter Arizona and supply labor inelastically. Assume that low-skilled immigrants are perfect substitutes for low-skilled native workers. a. Illustrate the effect of immigration in this labor market on a graph. b. What is the market-clearing wage if immigration is not allowed? C. What is the market-clearing wage with open borders? d. How much is the immigration surplus when the United States opens its borders? e. How much surplus is transferred from Arizona workers to Arizona firms? f. Now assume that low-skilled immigrants are complements to high-skilled (college educated) native workers. What do you expect to happen to equilibrium wages and employment for college educated native workers as a result of immigration? Why? Illustrate your explanation with a graph. 2. Debbie is about to choose a career path. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Debbie lives two periods. In the first, she gets an education. In the second, she works in the labor market. If Debbie becomes a marine biologist, she will spend $15,000 on education in the first period and earn $472,000 in the second period. If she becomes a concert pianist, she will spend $40,000 on education in the first period and then earn $500,000 in the second period. a. Suppose Debbie has a 5 percent discount rate between periods. Which career will she pursue? What if she had a 15 percent discount rate? Will she choose a different option? Why? b. Suppose musical conservatories raise their tuition so that it now costs Debbie $60,000 to become a concert pianist. What career will Debbie pursue if the discount rate is 5 percent?QUESTION 1: [worth15%] Consider an economy with two agents, Anna (A) and Bill [B], and two goods 2 and 3:, which are public and private goods, respectively. The utilities of two agents are i i UA =22$A2 1. U]; = zgmgz The economy is endowed with 15 units of the private good :c.The production technology in the economy is such that one unit of private good can be transformed into one unit of public good; that is, the MRT = E's/as = 1. (3.) Find a Pareto optimal allocation where Anna has a utility level [JrA = 5 . (b) Suppose that Anna is endowed with 7 units of private good (11,34) while Bill is endowed with 8 units of private good (3:3). What is the allocation obtained in this economy through private provision (voluntary contributions), where Anna's contribution (CA) plus Bob's contribution (c3) renders an amount of the public good (2) that they will both enjoy? (c) Is the allocation found in (b) Pareto efcient? Explain. (d) Graph Anna's indifference curve and the PPF [resembling the graphs for George's situa- tion in the \"Samuelson Condition\" lecture video). Graph them over values of z E [0, 15] on the horizontal axis. If you wish to make the graphing easier, for the indifference curve UA = 5, you may use integers for z = {1,2,3...,11}. E . E. E. AaBbCcDdEe AaBbCcDdEe AaBbCCDc AaBbCcDdEx A E E Normal No Spacing Heading 1 Hoading 2 Practice Problem 1: Nathalie decides how much to consume and save in each period by maximizing her lifetime utility given her lifetime resources. Her income in the first period is yr= 60,000 and in the second period yz = 33,000. Unfortunately, she holds no initiate wealth. However, she can borrow or lend at a real interest rate ofr = 10% Suppose that her lifetime utility is given by U (ci, ca) = U(cl) + PNU(cz). Where er is her current consumption, ca is her future consumption, and A is her discount factor with Be (0, 1). Further suppose that her marginal rate of intertemporal substitution is MRS12 = Cz BNC1 and that her optimal current-future consumption follows from the tangency and feasibility conditions with I MRS12 =- BNC "2 = 0CC2 =1+r - 62 = B"(1+r)c. which expresses the optimal relationship between future and current consumption given the real interest rate and her patience level. a) What would be her current consumption, her future consumption, and her saving if her consumption bundle would be right at the endowment point? b) Using the optimality condition from above and your previous answers, what would be the value of the discount factor, ", for which she would choose optimal consumption such that she would be neither a borrower or lender? Jakub has the same present value of lifetime resources and lifetime utility function. However, Jakub is less patient than Natalie. c) Is his discount factor smaller or greater than Natalie's - i.c., B 2 BN ? d) Wil Jakub consume today more or less than Natalie? e) Will Jakub be a borrower or lender? (Hint: Given the information above, you know Jakub's present value of lifetime resources - but do you know his endowment point?)Question 1 (40 pts) Consider the following model of a vertical market. In a market for a good, there exists a monop- olist manufacturer with a marginal cost of 5 who charges a wholesale price of Pm to a monopolist retailer. The retailer's only marginal cost if the manufacturer price; however, the retailer must pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts of his store.) The retailer charges a price to consumers of pr. Demand is linear with p, = 15 - Q. a. Write down the retailer's profit function. b. What is the price the retailer charges as a function of P.? c. Write down the manufacturer's profit function as a function of p.. What is the optimal pm set by the wholesaler? d. Given p., what is the retailer's profit? At what level of F will the retailer no longer be willing to purchase from the manufacturer? e. Consider the vertically integrated monopolist. At what level of F will the vertically inte- grated monopolist no longer be willing to stock the good in his retail division? At what values of F will the manufacturer carry the good if and only if it is vertically integrated with the retailer? Question 2 (35 pts) Suppose that two types of people exist, high (H) and low (L) productivity. Education is worthless other than to potential employers. Those workers that receive an education are identified as H- type and get a wage of wy = $9,000 while those that do not are identified as L-type and receive WL = $7,500. H-types can obtain an education at a cost of CH = $1,000, and L-types receive an education at a cost of GL = $3,000. Denote A as the probability that an individual is high productivity, A = P(H). a. Show a separating equilibrium exists. b. Does a pooling equilibrium exist at A =
