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ECON 30010: Intermediate Microeconomic Theory HW3, Cronin Assignment Overview: This assignment is designed to enhance your understanding of constrained optimization, using a graphical approach or a calculus-based approach. Required Research: Microeconomics , Chapter 3; Perloff Class Notes/Slides Assumptions and Agreements: 1. See Canvas/Assignments for the due date and time. 2. You will enter your multiple-choice answers in Canvas under Assignments/ Homework 3 MC. Long-form answers will also be submitted in Canvas, but under Assignments/ Homework 3 LF. No hard copies will be accepted. The assignment will be graded automatically in Canvas. Please plan accordingly and submit your assignment early. If you experience severe technological difficulties using Canvas, you may e-mail me your solutions in a PDF file BEFORE the due date/time but try to work the problem out with Canvas first. See syllabus for rules regarding late submissions. 3. Note the directions for long-form submissions in Section 4 below. 4. You may re-submit your assignment as many times as you would like. Canvas will grade your last submission. 5. Individuals can discuss the assignment with any other member(s) of the class. 6. For all problems, assume that it is possible to purchase fractional quantities of the goods. 7. For all problems, assume only non-negative quantities of the goods can be purchased. 8. Funny-looking answers don’t necessarily mean you did something wrong. In some cases, the answer is completely right. In other cases (for instance, if you find the optimal bundle has negative units of one of the goods), it might mean an interior solution does not exist. 9. Unless explicitly stated, assume preferences are rational, monotonic, continuous, and strictly convex.
ECON 30010: Intermediate Microeconomic Theory HW3, Cronin Section 1: Budget Lines (2 points each) For questions 1-4, consider the market for coffee and donuts. Coffee costs $3, while a donut costs $2. Assume you have $18 to spend on coffee and donuts. 1. (coffee/donuts) Which of the following accurately portrays your budget line?
ECON 30010: Intermediate Microeconomic Theory HW3, Cronin 2. (coffee/donuts) What is the marginal rate of transformation between coffee and donuts? A. B. C. D. 3. (coffee/donuts) What is the marginal rate of transformation between donuts and coffee? A. B. C. D. = coffee,donuts 2 MRT 3 = coffee,donuts MRT 3 2 = coffee,donuts MRT 6 = coffee,donuts MRT 1 6 = donuts,coffee 2 MRT 3 = donuts,coffee MRT 3 2 = donuts,coffee MRT 6 = donuts,coffee MRT 1 6
ECON 30010: Intermediate Microeconomic Theory HW3, Cronin 4. (coffee/donuts) Now assume the particular brand of coffee you enjoy implements a new pricing policy. In particular, if you want to purchase any of their coffee you must pay $3 to become a “Premiere Delectable Coffee Member”. Once you pay the $3, you can purchase as much coffee as you would like for $2 per cup. If you do not purchase the membership, you cannot purchase their coffee. Donuts still cost $2 and you still have $18. Which of the following accurately portrays your budget line?
ECON 30010: Intermediate Microeconomic Theory HW3, Cronin 5. Oftentimes, we reduce a complex economy to a two-good economy by specifying one particular good and combining all other goods into a “numeraire” good that can be interpreted as “everything else” on which the individual spends money. Let us consider the market for Netflix streaming-movies and “everything else”. Netflix costs a fixed $8 per month after which an individual can stream as many movies as she would like for free. Assume a unit of “everything else” costs $4 and an individual has $24 to spend on Netflix movies and everything else. Which of the following accurately portrays her budget line if she signs up for Netflix?
ECON 30010: Intermediate Microeconomic Theory HW3, Cronin 6. You purchase food and clothing and you have $100 to spend. Clothing costs $25 per unit, and food costs $10/unit. However, your local boutique is currently running a bulk special. Specifically, your first 2 units of clothing costs $25/unit. After that, clothing only costs $20 per unit. Which of the following accurately portrays your budget line?
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