The condition for a gift to Tom increasing Ford's profit
is
b Edi > - Edp or
Edi > - Edp / b or
Edi > P / ((P - MC) b)
where
b is the fraction of Tom's income that Tom spends on Ford cars
Edi is the income elasticity of Tom's demand for Ford cars
Edp is the price elasticity of the market demand for Ford cars
P is the price of a Ford car
MC is the marginal cost of a Ford car (so (P-MC)/P is the profit
margin)
b is considerably less than 1, since people spend considerably
less than all their income on cars
-Edp is greater than 1, since a monopolist facing
inelastic demand would raise his price
the profit margin (P - MC) / P is less than 1 since
marginal costs are positive
Therefore, Edi would have to be considerably greater
than 1 for the gift to raise Ford's profit.
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