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.