Question

Two firms, a and b, produce and sell wine. The demand for
a's wine is given by the equation,
Qa = 200 - Pa + Pb:
In this equation, the price of a's wine is Pa per bottle, and the price of b's wine is
Pb per bottle. a has a marginal cost of MCa = $20 per bottle, and a fixed
cost of FCa = $6000. The demand for b's wine is given by the equation,
Qb = 9000 - 100Pb + 40Pa:
b has a marginal cost of MCb = $10 per bottle, and a fixed cost of FCb =
$10;000. The two firms compete by simultaneously selecting prices.

1) Are the bottles of wine produced by a and b, homo-
geneous products or heterogeneous products? Your answer must reference the two firms
demand functions.

Answer 1

Qa = 200 - Pa + Pb
Qb = 9000 - 100Pb + 40Pa

Price elasticity of demand
Ea(a)=(-1)
Eb(b)=(-100)

Cross-price elasticity of demand
Ea(b)=(1)
Eb(a)=(40)

|Ea(a)|=|Ea(b)|, however |Eb(b)|>|Eb(a)|, so wine b has some distinctive characteristics (different from price),comparing with wine a, that influence its demand. Wine b cannot be totally replaced with wine a by price competition.

Answer
Heterogeneous