Mock End of Term Test 2012

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    ECO3041: Industrial Organisation.(Mock) End of term testAnswer all parts. Points will be awarded for your workings as well as your final answer.

    I advise you to use a calculator that works with fractions rather than decimals. You may also

    find it helps to work with letters rather than numbers for as long as possible.

    You have 90 minutes.

    Sainsburys and Tesco are located at both ends of a one mile long street. There are two types of

    shoppers (called high-value and low-value), with equal numbers of each type. High-value shoppers

    obtains a value of from buying a tub of Haagen-Dazs ice-cream, and an additional value of

    if they buy a bottle of Sainsburys Taste the Difference Maple Syrup as well, or an additional value of

    if they buy a bottle of Tesco Value Maple Syrup as well. Low-value shopper obtains a value of

    from buying a tub of Haagen-Dazs ice-cream, and an additional value of from buying either

    variety of maple syrup too. All shoppers only obtain any value from the first tub of ice-cream and the

    first bottle of maple syrup they buy (so they will not buy more than one). No shoppers get any value

    from buying maple syrup without ice-cream, but they do still get value from buying ice-cream without

    maple syrup.

    Shoppers of both kinds are uniformly distributed along this street. Both kinds have linear transport

    costs, so that walking miles costs them in lost value. However, once they have been to either

    Sainsburys or Tesco, they are laden down with shopping, so they wish to just walk home. (I.e. you

    may assume that the transport cost of visiting both Sainsburys and Tesco is infinite.)

    For both Sainsburys and Tesco, Haagen-Dazs has a constant marginal cost of. Sainsburys Taste the

    Difference Maple Syrup has a marginal cost offor Sainsburys, and Tesco Value Maple Syrup has a

    marginal cost of for Tesco. Sainsburys and Tesco cannot differentiate between the two types of

    shopper based on observable characteristics.

    Sainsburys charges for Haagen-Dazs and for their maple syrup. Tesco charges for Haagen-Dazs and for their maple syrup.

    You may assume the following parameter values. (These are the only things which will change in the

    actual test.) = 5, = 2, =

    , = 3, = 1, = 2, = 1, =

    , =

    .

    a) Assume that in equilibrium, all consumers buy both ice cream and maple syrup. How far from

    Sainsburys is the high-value shopper who is just indifferent between buying from Sainsburys and

    buying from Tescos? How far from Sainsburys is the low-value shopper who is just indifferent

    between buying from Sainsburys and buying from Tescos? (Your answers may be a function of firms

    prices.) (10%)

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    b) Given shoppers are visiting Sainsburys or Tesco anyway to buy ice cream, what must be true for

    them to want to buy maple syrup as well? (Your answer may differ across types of shopper.) Explain

    why this means that Sainsburys will price maple syrup at either or (rather than any other

    price), and why Tesco will price it at either or , (rather than any other price). In each case, you

    do not have to say which of the two options the supermarket would choose. (10%)

    c) Suppose that both shops sell their brands of maple syrup at . Write down each supermarkets

    profits as a function of prices. (Hint: be careful to include the revenue from selling both ice-cream and

    maple syrup, to both high-value and low-value customers. Dont forget costs either!) Then derive their

    optimal price for ice-cream. You should find that Sainsburys sell ice-cream at

    and Tesco sell it at

    9

    4. Explain intuitively why Sainsburys is charging a higher price for ice-cream despite having identical

    costs. (30%)

    d) Calculate both supermarkets profits at the prices you found in (c). (10%)

    e) Now suppose that Sainsburys deviates to selling maple syrup at , with Tesco still selling their

    maple syrup at . Which types of consumers would buy maple syrup from Sainsburys, given they

    were visiting the store anyway? Which types would buy maple syrup from Tescos, given they were

    visiting the store anyway? (5%)

    f) Under the set-up of (e), how far from Sainsburys is the high-value shopper who is just indifferent

    between buying from Sainsburys and buying from Tesco? how far from Sainsburys is the low-value

    consumer that is just indifferent between buying from Sainsburys and buying from Tesco? Your

    answers should be a function of and , not the solution found in (c). (5%)

    g) Under the set-up of (e), write down an expression for each supermarkets profits as a function of

    prices. (Again, be careful to include the revenue from selling both ice-cream and maple syrup, to both

    high-value and low-value customers.) You do not need to attempt to maximise this expression for

    profits. (5%)

    h) A kindly mathematician tells you that when you hold at the value you found in (c), under the

    set-up of (e), by choosing optimally Sainsburys will make profits of

    96. They go on to tell you that

    if you repeat the exercise of parts (e) to (g) assuming that Tesco instead deviate to charging for

    syrup, then with held at the value you found in (c), and chosen optimally, Tesco will make

    profits of

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    8. Using your answer to part (d), and the calculations of this friendly mathematician,explain why both firms selling syrup at must be a Nash equilibrium. (5%)

    i) Now, suppose that Sainsburys decide to introduce a Brand Match Guarantee, as they have done

    in real life. This is effectively a commitment to never price branded goods higher than Tesco does.

    Since both firms only sell non-branded maple syrup, here this promise just applies to the Haagen-Dazs

    ice-cream. Given this guarantee (and assuming that Sainsburys can react instantly), what effect does

    a cut in Tescos ice-cream price have on Tescos profits? As a result, assuming each firm still sells maple

    syrup at , what price will each firm set for ice-cream in equilibrium? What are profits? (20%)

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    BONUS QUESTIONS IF YOU HAVE SPARE TIME: YOUR MARK CANNOT GO OVER 100%

    SCORES GIVEN HERE ARE ONLY ILLUSTRATIVE, AND EVEN A PERFECT ANSWER MAY ATTRACT EITHER

    HIGHER OR LOWER POINTS AT MY DISCRETION. THUS I DO NOT ADVISE YOU TO SKIP PARTS ABOVE

    IN ORDER TO ANSWER THESE PARTS.

    j) Find the Nash equilibrium for maple syrup prices in the set-up of part (i). (10%)

    k) Prove the results of the friendly mathematician from part (h). (40%)