# Monopolies on Giffen Goods

I’m taking an intermediate microeconomics course in college and just got to the topic of monopolies. I know the concept of a Giffen good.

As always, Revenue is given by $$R= Pq$$. Since the monopoly has market power, $$P$$ is not constant. Therefore, the marginal revenue is $$MR = P + q \frac{dP}{dq} = P (1 + \frac{q}{p} \frac{dP}{dq}) = P (1 + \epsilon^{-1})$$ where $$\epsilon$$ is the own price elasticity of the demand.

My lecturer then showed these three cases:

• Elastic demand $$(\epsilon < -1)$$: $$MR>0$$
• Unit elasticity $$(\epsilon = -1)$$: $$MR=0$$
• Inelastic demand $$(-1<\epsilon<0)$$: $$MR<0$$

Therefore we would be more likely to encounter monopolies on elastic goods.

It made me think: Giffen good $$(\epsilon > 0)$$: $$MR>0$$. In fact $$MR>P$$.

The theory of monopolies says that since each extra unit of good produced would decrease $$P$$ (from the demand curve it follows that $$P$$ must decrease in order for those extra units to be demanded) the firm would have to find some optimal quantity that maximizes its profits. But in Giffen goods, for a higher quantity to be demanded $$P$$ must increase. This would mean $$P$$ would increase as they produce more units.

So wouldn’t a monopolistic firm want to produce even more and more units forever, for theoretically infinite profits?

I’m asking this since the Giffen good case was left out of my lecture and this Giffen good stuff awakens my curiosity. Maybe it was left out because there is some catch.