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https://learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5deff46c33361/18418963?X-Blackboard-Expiration=1632981600000&X-Blackboard-Signature=nR6QurAJbYFz1sZC5UEC5COz2yJbswmUGfY3OMPIS6g%3D&X-Blackboard-Client-Id=100902&response-cache-control=private%2C%20max-age%3D21600&response-content-disposition=inline%3B%20filename%2A%3DUTF-8%27%27EC201-Fall-2021-FirstProblemSet.pdf&response-content-type=application%2Fpdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20210930T000000Z&X-Amz-SignedHeaders=host&X-Amz-Expires=21600&X-Amz-Credential=AKIAZH6WM4PL5SJBSTP6%2F20210930%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=c4c699ef104bf9a1632bc0a26b4187a9abf13de3e6978c64b2795136a09cfd62 EC201-First Problem Set – Version A Chapter 4: Consumer Theory Due Date: 09/30/2020 1) (15 pts.) King has the following utility function of ! = 4√%& + 16%* where %&and %*are the two goods consumed by him. His income is Y= $4000 and the goods are sold at ,& = $8 and ,* = $640 at the market. a) (9 pts.) Compute his optimal choice? b) (6 pts.) Graph Albert’s optimal choice by marking x-axis as x& and y-axis by x*. Your graph should include: the budget line, the indifference curve and the optimal consumption point. 2) (30 pts) A city has three types of consumers, with different preferences about the use of bike and the subway. Let’s call B the number of rides in bike of each person per semester and S the number of rides in subway. Consumers of the first type have utility function ! = 1 + 2.52. Consumers of the second type use bike and subway in the fixed proportion 1:1, doing the same number or rides in bike and subway. And the third type of consumers have utility function! = 1 ∗ 2.Each consumer has a semester transportation budget of $420. Price per ride in bike is $1, and and the subway authority is considering a rise from is $ 2 to $ 3. The subway hires you to do some calculations. a) (8 pts.) How do we say that the goods rides in bike and subway are for consumers of the first type? Show in a diagram the equilibrium of one consumer of this type before and after the rise (Using the x-axis for 2 and the y-axis for 1). How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place. b) (8 pts.) How do we say that the goods rides in bike and subway are for consumers of the second type? Calculate and show in a diagram the equilibrium of one consumer of this type before and after the rise (Using the x-axis for 2 and the y-axis for 1). How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place? c) (8 pts.) How do we say that the goods rides in bike and subway are for consumers of the third type? Calculate and show in a diagram the equilibrium of one consumer of this type before and after the rise (Using the x-axis for 2 and the y-axis for 1). How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place? d) (6 pts.) Is the raise going to be worthy for the subway revenue? Would it be if there were no consumers of the first type? Why? To samoa i memo as as as as Part 2: chapter 4 - Consumer Theory 3) (15 pts.) Grace enjoys her cup of coffee with pieces chocolates. She always consumes 4 pieces of chocolate with one cup of coffee. a) (4 pts.) Using x& to represents pieces of chocolate, and x* to represents cups of coffee, write down the Graces’s utility function. Justify your answer b) (6 pts.) Grace spend $ 48 per week on her choice. When price of a piece of chocolate is $1 and price of a cup of coffee is $4, how many cups of coffee and pieces of chocolate will she consume? c) (5 pts.) Graph Graces’s optimal choice. Your graph should include: the budget line, the indifference curve and the optimal consumption point. d) 4) (15 pts.) Rafael has a utility function !(%&, %*) = %&8/:. %*&/:. The price of %& is $25 and the price of %* is $10. Rafael’s income is $1200. Use the Lagrangian method to find out Rafael’s optimum bundle (you should write down the first order conditions). 5) (15 pts.) Paul consumes only two goods, pizza (P) and hamburgers (H) and considers them to be perfect substitutes, as shown by his utility function: U(P, H) = 4P + H. The price of pizza is $4 and the price of hamburgers is $8, and Paul’s monthly income is $400. Knowing that he likes pizza, Paul’s grandmother gives him a birthday gift certificate of $80 redeemable only at Wild Willy’s Burger. Though Paul is happy to get this gift, his grandmother did not realize that she could have made him exactly as happy by spending far less than she did. How much would she have needed to give him in cash to make him just as well off as with the gift certificate? Represent his choice graphically (use x-axis for hamburger and the y-axis for pizza). 6) (10 pts.) Suppose a Canadian who lives equally close to gas stations in the US and Canada. Gasoline can be more expensive over time in one country than in the other due to taxes and, sometimes, prices are also the same. How do you expect to be the gasoline- purchasing behavior of this consumer? Answer using an indifference curve and a budget line diagram (x-axis for Canadian gasoline and y-axis for US gasoline). IMO