(a) Explain the differences between Cournot model of duopoly with similar product and differentiated product. (15 marks) (b) What…

(a) Cournot duopoly: similar versus differentiated product. With a similar (homogeneous) product, inverse demand is P = a − b(q₁ + q₂) and marginal cost c. Each firm maximises (a − b(q₁ + q₂) − c)q₁ taking the rival's output as given, so the reaction function is q₁ = (a − c − bq₂)/2b, and likewise for firm 2. The symmetric Nash equilibrium is q₁ = q₂ = (a − c)/3b, Q = 2(a − c)/3b and a single price P = (a + 2c)/3, above the competitive price c and below the monopoly price (a + c)/2; each firm earns (a − c)²/9b. With differentiated products, the goods are imperfect substitutes and each firm faces its own demand: p₁ = a − bq₁ − dq₂ and p₂ = a − bq₂ − dq₁, with 0 < d < b (d = b is the homogeneous case). The reaction function becomes q₁ = (a − c − dq₂)/2b, with slope −d/2b instead of −1/2, since the rival's output matters less. The symmetric equilibrium is q = (a − c)/(2b + d), p = [ab + (b + d)c]/(2b + d) and profit b(a − c)²/(2b + d)². Differentiation therefore softens competition: the price–cost margin b(a − c)/(2b + d) exceeds (a − c)/3, profits are higher, and prices differ if costs or demand intercepts differ.

(b)(i) The conjecture. The kinked demand curve (Sweezy, 1939; Hall–Hitch) rests on an asymmetric conjecture about rivals' price reactions. A firm believes that rivals will match a price cut (dp_j/dp_i = 1 downward, so demand is inelastic below the going price P₀) but will not follow a price rise (dp_j/dp_i = 0 upward, so demand is elastic above P₀). This gives a kink at P₀ and a vertical gap in the marginal revenue curve. It is a price conjecture, unlike the zero quantity-variation conjecture (dq_j/dq_i = 0) in Cournot.

(b)(ii) Is it a price-determination model? No; it explains price rigidity, not how price is determined. Because marginal cost can move within the vertical gap in MR without changing the profit-maximising output, price stays at P₀. But the model takes P₀ as given by history, convention or tacit collusion and says nothing about how it was reached; to determine the level, it must be supplemented by price leadership or cartel models. Stigler (1947) also found little evidence for it: in many industries rivals followed price rises, and prices were not especially sticky, while in slumps price wars occurred. Later game-theoretic work (Maskin–Tirole, 1988) shows kinked demand can arise in a dynamic game, but the level of price is still determined outside the kink. Hence it is a model of stickiness, not of price determination.

(c) Profit, wage and rent in the Ricardian system. As capital accumulates and population grows, national income and the demand for corn rise. Cultivation extends to inferior land (extensive margin) and to more doses of capital and labour on existing land (intensive margin), where returns diminish, so the corn price rises. Rent is the surplus of intra-marginal land over the marginal land, so it rises, both in total and as a share, as cultivation extends. The wage is fixed at the natural (subsistence) level in corn by the Malthusian population mechanism; the money wage rises with the corn price and the wage bill grows with employment, so wages rise in total but not in real terms per worker. Profit is the residual: on the marginal land, profit = output − wages, and since the rate of profit is equalised across land, it falls as the margin deteriorates. Example: lands A, B and C yield 100, 80 and 60 per dose, with wage 40 per dose. Cultivating A alone: rent 0, wage 40, profit 60 (rate 150%). Adding B: rent 20 (on A), wage 80, profit 80 (rate 100%). Adding C: rent 60 (40 on A, 20 on B), wage 120, profit 60 (rate 50%). Rent's share rises from 0 to 25%, the wage share from 40% to 50%, and the profit share falls from 60% to 25%. When the profit rate falls to zero, accumulation stops: the stationary state.