GM Rebates: The Intuition

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GM Rebates The Intuition

• What price, P, should GM post when it gives
  rebates of 1000 to old buyers and 500 to new
  buyers of its trucks? In addition,
• Old buyers receive rebate coupons which they can
  either use or sell to new buyers for price Q (
  200).
• In addition to the 200 they must pay to old
  buyers, new buyers must pay a brokerage fee of k
  (200) for each coupon they buy.
• If we present this question to Solver, we are
  told, Set P20,480.
• Lets make sense of this answer in five easy steps.

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GM Rebates The IntuitionStep 1) Base Case X
x Q k 0Optimal Price to each group
20,000 ? Profit 10bil
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GM Rebates The Intuition2) Imagine both old and
new buyers get 1,000 rebates and new buyers
dont have to pay anything for coupons.X x
1000 Q k 0

• Solution to this is a no - brainer
• GM does best when each group faces an effective
  price of 20,000.
• If each group gets the same rebate and there are
  no costs to transfer coupons from old buyers to
  new buyers, GM need only raise its posted price
  by the amount of the rebate.
• Everyone then continues to pay an effective price
  of 20,000.
• Raise price 1,000.

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GM Rebates The IntuitionStep 3) In fact, old
buyers do get a 1,000 rebate but new buyers only
get a 500 rebate. X 1000, x 500 Q k 0

• GM would like to keep the effective price to
  old-buyers at 20,000.
• It would like to raise the posted price to this
  group by 1,000.
• GM would like to keep the effective price to
  new-buyers at 20,000.
• It would like to raise the posted price to this
  group by 500.
• Solution Raise the posted price between 500 and
  1,000, weighted by the size of each group.
• The optimum ?P 650 (.7x500 .3x1,000)
• Raise price 650!

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GM Rebates The IntuitionStep 4) Next suppose
there are no rebates but new buyers must pay old
buyers 200 for a coupon while the brokerage fee
is zero.Q 200 X x k 0

• For each group, the effective price of a truck is
  now 200 above the posted price, P
• This is like a 200 tax on truck buyers
• Solution (explained on next slide)
• Reduce posted price by half of the tax
• Reduce price 100!

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GM Rebates The IntuitionStep 4 Explained Q
200 X x k 0

• For each group, the effective price of a truck is
  now 200 above posted price P
• Each groups demand curve shifts down by 200.
• Instead of letting demand fall, imagine GM
  reimburses buyers for the cost of the coupon.
• If ?MC 200, ?MR 200 at new optimum.
• Since MR rises twice as fast as P ( average
  revenue) for straight line demand curve, the
  effective price to buyers would need to rise only
  100 for MR to rise by 200, if indeed GM did
  bear the 200 cost.
• For effective price to rise only 100 when Q
  200 and buyers bear this cost, GM must lower its
  posted price by 100.
• GM meets its customers half-way on this tax.
• Reduce posted price 100!

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GM Rebates The Intuition Step 5) Now suppose
there are still no rebates but new buyers must
get a free coupon from old buyers and pay a 200
brokerage fee.k 200 X x Q 0

• GM would like to see the effective price to
  new-buyers rise by only half of this tax or
  100.
• GM would like to lower the posted price to new
  buyers by 100.
• GM would like to keep the effective price to
  old-buyers where it is, at 20,000.
• Solution Reduce the posted price between 100
  and zero dollars, weighted by the sizes of the
  two groups.
• The optimum ?P - 70 (.7x(-100) .3x0)
• Reduce posted price 70.

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GM Rebates The IntuitionGeneral Case X 1000,
x 500, Q 200, k 200

• From what weve learned
• Want to raise P by 650 because of the rebates
• The closer the rebates are to each other, the
  closer is this offset to the amount of the
  rebates
• Want to lower P by 100 (half of the coupons
  market value, Q) because of this equal tax on
  both old- and new-buyers.
• Want to lower P by an additional 70 because of
  the brokerage fee on new-buyers
• Ideally would lower P by 100 (half of k) to new
  buyers, except for effect on old buyers.
• Summarizing
• Optimal P 20,000 650 100 70 20,480