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    University of Canterbury

    Mid-Year Examinations 2010

Prescription Number(s): ECON 230W



Time Allowed: Three Hours

    Number of Pages: 5


     Answer all NINE questions

     Each Question is worth 10 points

     Standard Non-Programmable Calculators are permitted

     3 ECON 230W

    1. Memory-Dump Questions:

    a) Write down the Slutzky equation in elasticity form, and define each of the terms in the


    b) What is the general form of the utility function for Cobb-Douglas preferences (in exponent


    c) What does it mean for preferences to be “well behaved”?

    d) When is good i a complement to good j?

    e) What is an ordinary good?

    2. Cartman has a weekly allowance of 20 dollars which he can spend on ice creams and

    sweets. He has 168 hours which can be allocated to either leisure, or working delivering

    newspapers at a rate of 4 dollars per hour. He can choose how many hours to work subject

    to child-protection laws that restrict him to working no more than 10 hours per week. Ice

    creams cost 2 dollars each and sweets 4 dollars per bag.

    a) Write down mathematical expressions that completely describe Cartman‟s budget set over

    consumption of ice creams, sweets, and leisure.

    b) On a graph with leisure on the horizontal axis and sweets on the vertical axis, show all the

    bundles that Cartman could consume if he consumed exactly 5 ice creams every week.

    3. Jack Meridew has the following preferences over food and shelter: If he consumes less

    than 10 units of food, food is a bad; if he consumes more than 10 units, it is a good.

    Similarly, if he consumes less than 15 units of shelter, shelter is a bad; if he consumes

    more than 15 units, it is a good.

    a) On a graph with food on the horizontal axis and shelter on the vertical axis, draw some of

    Jack„s indifference curves and show the direction of increasing preferences.

    b) Are Jack„s preferences convex, not convex, or can you not tell? Explain your answer.

    4. Emma Woodhouse has perfect-substitute preferences over coffee and tea. Currently, she is

    at a corner solution in which she consumes only coffee and no tea. Now the price of tea

    falls and as a result she switches to consuming only tea and no coffee. For the Slutzky

    decomposition is this increase in the consumption of tea entirely due to the substitution

    effect, entirely due to the income effect, or a combination of the two? Similarly, for the

    Hicks decomposition is the increase due to the substitution effect, the income effect, or

    both? Explain your answers in words or on diagrams.


    x5. Yossarian‟s preferences over two goods, and x, are given by the utility function 12

    Uxxxxx(,)ln().;;; 12121

    The marginal utilities implied by this utility function are

    dUdU11 MUMU;;;;;1,.12dxxxdxxx;;112212

    ppYossarian faces prices for the two goods, and, and has an income of m. 12

    xxa) Find Yossarian‟s demand functions for and at interior solutions as a function of12

    pp, , and m. 12

    b) For each good, at interior solutions, state whether for Yossarian it is normal or inferior,

    ordinary or Giffen, and a substitute for or a complement to the other good.

    6. Tomáš has perfect-complement preferences over bowler hats and hat stands: For every 10

    hats he has, he needs 1 hat stand.

    a) On an indifference curve diagram, draw the indifference curve through the bundle

    consisting of 40 hats and 4 hat stands, and the indifference curve through the bundle

    consisting of 50 hats and 2 hat stands.

    b) Hats cost $20 each and hat stands $100 each. If Tomáš has $600, what is his optimal


    c) Now let the price of hat stands rise to $400. What is his new optimal bundle? Using the

    Slutzky decomposition, how much of the change is due to the income effect and how much

    to the substitution effect?

    7. Babe has an endowment of 15 acorns and 30 bones. His preferences over the two goods are

    given by the utility function


    p10p20.The prices of acorns and bones are, respectively, and AB

    a) What is Babe‟s optimal consumption of acorns and bones?

    b) Now imagine that the price of acorns changes, but you don‟t know if it rises or falls.

    Would babe be better off, worse off, of can you not tell? Explain your answer on a diagram

    or in words.

     5 ECON 230W

    8. Pierre Bezukhov can turn swords into ploughshares according to the production function,

    PS50 .

    The marginal product for this production function is

    25MP. SS

    He can sell any number of ploughshares at a price of p roubles each and can buy any

    number of swords at a price of w roubles each.

    a) Draw Pierres production function, and his isoprofit lines for profit=0 and profit=1,000 for the case where p=5 and w=2.

    b) Find Pierre‟s optimal output of ploughshares and optimal input of swords as functions of p

    and w.

    9. Ferris Bueller is taking a course in which half the course is theoretical and half is practical.

    He will receive a grade, T, on the theoretical half and a grade, P, on the practical half. The

    course instructor has stated that the overall mark in the course, M, will be the product of

    the two:


    Ferris‟ grade on each of the two halves of the course is an exact function of how much time

    he spends studying for each one. His production functions are


    llwhere and are the number of hours he spends studying for the theoretical and the TP

    practical halves of the course, respectively, and and are fixed parameters. Ferris TP

    has preferences over his overall mark in the course and the total number of hours he spends studying, L. He only cares about how much time he spends studying for each component to the extent that it affects M or L.

    Write down Ferris‟ optimisation problem. (Note: you do not need to solve the problem, just

    express it as a formal optimisation problem.)


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