Question

Wobble’s Weebles is the only producer of weebles. It makes weebles at constant marginal cost c (where c > 0) and sells them at a price of p1 per weeble in market 1 and at a price of p2 per weeble in market 2. The demand curve for weebles in market 1 has a constant price elasticity of demand equal to –2. The demand curve for weebles in market 2 has a constant price elasticity equal to – 3/2. The ratio of the profit-maximizing price in market 1 to the profit-maximizing price in market 2 is?

Answer 1

Wobble's Weebles is a monopolist. So, it maximizes profit according to the rule: MR = MC.
where MR = P[1-(1/e)]; P is the price and e is the absolute value of elasticity of demand.
MC = c

In market 1, MR1 = MC gives,
P₁[1-(1/e₁)] = c
So, P₁[1-(1/2)] = c
So, P₁[1/2] = c
So, P₁ = 2c

In market 2, MR2 = MC gives,
P₂[1-(1/e₂)] = c
So, P₂[1-{1/(3/2)}] = c
So, P₂[1 - (2/3)] = c
So, P₂[1/3] = c
So, P₂ = 3c

Now dividing P1 by P2 we get,
So, P₁/P₂ = 2c/3c = 2/3

Thus, P₁/P₂ = 2/3