ECON 201 (Fall 2016)

Department of Economics, SFU

Prof. Christoph L¨ulfesmann


Midterm Exam


Please solve ALL of the problems below. Allow all consumption choices to be continuous.


I. Short Problems - Explain! No credit will be given without a justification of your answer (8 pts each)

    1. What is a monotonic transformation (MT) of a utility function? Is it possible for indifference curves of utility functions that are MTs to cross each other? Why or why not? Explain briefly but precisely, using a graph.

    2. Tom is an optimizing consumer. Last week, he consumed a bundle X when another bundle Y was also affordable to him. This week, he buys bundle Y when another bundle Z is affordable to him. (a) Illustrate this situation in a graph. (b) What do we know about the preference relations between X, Y and Z when (i) Tom’s preferences are transitive; (ii) Tom’s preferences are not necessarily transitive. Explain your answers!

    3. Discuss three important properties of consumer demand with Cobb-Douglas preferences. Explain precisely.

    4. Amanda consumes blue (good 1) and red (good 2) pencils. Initially, each of these goods costs 1 dollar but for some unknown reason, the price of blue pencils (good 1) increases by 50 cents. Does the price increase make Amanda worse off when her preferences are described as (a) U = min? Argue carefully!

    5. In College town, 3 apartments are currently available. Moreover, 4 students are interested in renting them: Ana (who has a Reservation price of RP = 600), Berta (RP = 500), Clara (RP = 400), and Dora (RP = 300). (a) Which market outcome would we expect under Perfect competition? Instead, which outcome would we expect when all apartments are owned by a price discriminating monopolist? (b) Which of the outcomes in (a) – if any – is Pareto efficient, and why? (c) Assume that for some reason, the 3 apartments are rented out to Ana, Berta, and Clara at a price of p = 300. Is this outcome Pareto efficient? Why or why not?


Long Problem (24 pts.) (Explain your answers!)

Kathryn likes fitness courses (good 1) and Lalilemon yoga pants (good 2). Her preferences can be described as . Prices are , respectively.

a) Compute Kathryn’s optimal consumption of Fitness classes and Yoga pants when her annual budget is (a) m = 1200, and (b) m = 1800. Illustrate both choices in a diagram. (Label carefully, including slopes and intercepts).

b) Find Kathryn’s demand functions for each good (explain what you are doing). Then, graph the Income offer curve and both Engel curves (label them carefully, including slopes). Explain your findings. Are Kathryn’s preferences homothetic? Ex-plain why or why not.

c) Let m = 1200. In a sale, Lalilemon offers each customer the first 8 yoga pants (this is good 2!) at half-price. (a) graph Kathryn’s new budget line with this sale (label everything), and explain briefly. (b) find the mathematical formula for this new budget line (describe your steps); (c) find Kathryn’s new optimal consumption bundle and graph it in your diagram in (a).