Economics 411 Public Sector Economics Assignment 3 Due at 3 30pm on Wednesday October 2 2024 5 Points ASSIGNMENT POLICY Please read carefully and follow these instructions EXACTLY You may work with up to two other students i e co workers Each student submits their own unique assignment NO copying Co workers may receive different grades Write you name in the upper right corner of the first page and CIRCLE it Write Assignment X in the top middle of the page where X is the assignment number STAPLE your pages together Non stapled assignments are not accepted Dog eared assignments will be burned DO NOT put this printed sheet on the front If you have co workers write CO WORKERS ad their names not circled beneath your name PAPERCLIP your assignment with your co workers assignments in alphabetical list by LAST name Submit them together i ii iii iv v vi 1 Don Draper and Roger Sterling consume whiskey x and cigars y Don is person 1 and Roger is person 2 They have Cobb Douglas utility functions a What are Don s gross demand functions for whisky and cigars Where x1 is Don s consumption of whiskey etc The exponents in these Cobb Douglas utility function describe each person s expenditure share on whiskey Roger always spends at least three times as much on whiskey as on cigars while Don divides his expenditures evenly 1 1 1 1 1 2 1 1 2 2 2 2 2 3 4 2 1 4 Don has an endowment 1 1 4 0 of whiskey and cigars while Roger has an endowment 2 2 0 4 The relative price of whiskey to cigars is p 1 and 1 What are Roger s gross demand functions 2 and 2 c Take the derivative of with respect to p i e Does Don s utility increase or decrease people in the economy What price will clear the market 1 2 d Say Don and Roger are both price takers in the market for cigars despite being the only two with the relative price of whiskey What about Roger s b What are Don and Roger s indirect utility functions e Draw an Edgeworth Box with the correct dimensions and the following elements i ii iii iv The endowments The equilibrium consumption The budget sets for Don and Roger The indifference curves PLEASE be precise Use a graphing calculator online graph utility to make sure everything is correct f Peggy the Planner ends what she saws are foolish games Don and Roger are playing with Instead she forces both gentlemen to consume the same bundle 2 2 Is this allocation efficient Are either Don or Roger better off with this allocation 2 Robinson Crusoe and Friday live on an island Crusoe can climb a coconut tree to produce coconuts y according to the production function 1 2 1 2 1 1 1 2 1 1 2 where L is Crusoe s labor time and K is the number of coconut trees Crusoe faces a time constraint so that time on labor and leisure l add up to one i e He maximizes utility Friday is incapable of climbing trees and so does not work at all He owns all of the coconut trees on the island That number is K 1 Friday s utility is simply 2 2 1 2 where 2 is his consumption of coconuts Begin by assuming that Crusoe and Friday set up a competitive market where the price of coconuts is 1 and the wage for labor is w Crusoe s only source of income is his labor a Taking the wage as given determine Crusoe s budget constraint incorporating his time constraint Then maximize his utility to solve for his labor supply coconut demand and indirect utility functions 1 1 tree Profits are given by b Friday is the sole owner of CoCo Corp which hires labor to produce coconuts on the island s 1 1 2 Solve CoCo Corp s profit maximization problem to solve for its labor demand coconut supply and profit functions c With all of CoCo Corp s profits going to Friday solve for his coconut demand 2 and indirect utility function 2 d Draw the labor demand and supply curves on a graph Using the labor market clearing condition find the equilibrium wage e What are the equilibrium coconut and labor allocations 1 2 and resulting utility levels 1 2 f Jeremy Bentham arrives shipwrecked on the island He quickly takes control and imposes a benevolent dictatorship with a planned economy His goal is to maximize the sum of utilities Show that his problems can be given by max 1 1 2 1 1 2 1 1 2 1 1 2 And take the first order conditions g Solve for the Benthamite allocations 1 2 and resulting utility levels 1 2 Are these the same allocations as under a competitive equilibrium