Cartel cheating:-
Suppose that a product has a demand curve p = A - aq and the marginal cost is zero. Suppose also that a cartel of two identical firms controls this product.
(a) If the two firms act together and divide the market equally, what is the maximum profit (ignoring fixed costs) that each firm can obtain, and the corresponding production quantities?
(b) Suppose that one firm faithfully produces the quantity of part (a). Show that the other firm has an incentive to break the agreement by producing more than agreed to. What is the maximum profit this second firm can obtain?