How Would a Firm Which Produces a Giffen Good Maximize Profits?

I am curious as to how a firm which produces a giffen good would maximize profits? Having an upward sloping demand curve seems to imply that we cannot guarantee that there exists a quantity where marginal revenue is equal to marginal cost, and even if there is, would that point be the profit maximizing point?

My thoughts are the following:

There are two cases to look at:

(1) If the marginal revenue curve never crosses the marginal cost curve (i.e. they have the same slope and a different intercept). This yields two sub-cases:

$\qquad$(i) The marginal revenue curve lies above the marginal cost curve: This case would clearly $\qquad$lead to infinite production because the firm is always increasing profits.

$\qquad$(ii) The marginal revenue curve lies below the marginal cost curve: This case would lead to $\qquad$ the firm choosing not to produce because they will always make a negative profit.

(2) If the marginal revenue curve crosses the marginal cost curve. This also yields two sub-cases: $\qquad$(i) The marginal cost curve starts below the marginal revenue curve: This case seems to be$\qquad$ just like our classic case where we would see production up until the point where marginal $\qquad$ revenue is equal to marginal cost.

$\qquad$(ii) The marginal cost curve starts above the marginal revenue curve: This case is the one $\qquad$that I find most interesting. Would this case lead to infinite production? After marginal $\qquad$revenue crosses marginal cost, marginal revenue also grows at a faster rate than marginal $\qquad$cost, so my intuition tells me the firm could earn infinite profits.

• It might be worthile to post your thoughts in an answer so people can vote on them separately from the question. Then if you wish you can accept your answer. – Giskard Jun 20 '16 at 8:43
• It is implausible that the demand curve for a good would be upward sloping for all consumers and all prices: eventually each individual consumer would hit an overall budget constraint, forcing demand down as prices increase. So you are back to the more general case where the marginal revenue and marginal cost curves may cross several times: the monopolist will choose the best of the points similar to the classic case where the marginal profit, i.e. revenue minus cost, turns from positive to negative as quantity increases, providing this provides a net profit – Henry Apr 14 '18 at 22:41