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

While oligopoly models analyze strategic firm behavior under imperfect competition, classical distribution theory examines functional factor shares during economic growth and accumulation.

Cournot Duopoly: Homogeneous vs Differentiated Product

In the homogeneous Cournot model, two firms produce identical goods facing a unified market inverse demand curve P = a - b(q₁ + q₂). With constant marginal cost c, each firm maximizes profit taking the rival’s output as given, yielding symmetric linear reaction functions q₁ = (a - c - bq₂)/2b and q₂ = (a - c - bq₁)/2b. The unique Nash equilibrium results in total output Q = 2(a - c)/3b and a single market-clearing price P = (a + 2c)/3, which settles strictly between the monopoly price and the perfectly competitive price (P = c).

Under product differentiation, firms produce imperfect substitutes facing distinct inverse demand curves: P₁ = a₁ - b₁ q₁ - d q₂ and P₂ = a₂ - b₂ q₂ - d q₁, where d measures product substitutability (cross-elasticity). The reaction function for firm 1 becomes q₁ = (a₁ - c₁ - d q₂)/2b₁. A single market price ceases to exist. Instead, the equilibrium generates price dispersion governed by cross-price effects and brand loyalty. If cost structures or consumer preferences diverge, the model yields asymmetric equilibrium prices and market shares.

Kinked Demand Curve and Price Stickiness

Paul Sweezy’s kinked demand model is founded on an asymmetric followership (or matching) conjecture: a firm assumes that if it raises its price above the prevailing level P₀, competitors will not follow (making demand elastic above P₀), but if it lowers its price, rivals will match the cut immediately to preserve market share (making demand inelastic below P₀).

This behavioral asymmetry produces a sharp kink at the current price and a corresponding vertical discontinuity (gap) in the marginal revenue (MR) curve. Consequently, the kinked demand curve is not a price determination model. It takes the benchmark price P₀ as exogenously given through historical precedent or collusion, without explaining how it was established. Its analytical value lies entirely in explaining price rigidity: any shift in marginal cost within the vertical gap of the MR curve leaves the equilibrium price and quantity unchanged.

Ricardian Distribution: Rent, Wage, and Profit

In the Ricardian system, economic expansion and capital accumulation raise national income, increasing the demand for food (corn). To feed an expanding population, cultivation extends to inferior soils (extensive margin) and applies successive doses of capital and labor to existing plots (intensive margin), encountering diminishing returns.

Income distribution shifts across factors as follows:

• Rent: Rent is a differential surplus arising on intra-marginal lands due to fertility differences. As the marginal cost of corn rises on the least fertile plot (where rent is zero), product price rises to cover that cost. Rent on superior lands rises continuously: Rent = Output - (Wages + Normal Profit on Marginal Land).
• Wages: Real wages are anchored at the physiological subsistence level by the Malthusian population mechanism. However, because producing corn on marginal land requires more labor, the value of the subsistence basket rises. Thus, the nominal wage bill absorbs a rising share of output.
• Profit: Profit is the residual surplus after paying wages on marginal land (Π = Y_margin - W). As rising corn costs elevate the wage bill, profits are progressively squeezed across all lands.

To illustrate mathematically, suppose successive grades of land A, B, and C yield 100, 80, and 60 units of corn per dose of capital-labor, with subsistence wages fixed at 40 units:

• Cultivating Land A only: Total Output = 100; Rent = 0; Wage = 40; Profit = 60.
• Expanding to Land B: Land A Rent = 20, Profit = 40; Land B Rent = 0, Profit = 40 (Wage = 40 on both).
• Expanding to Land C: Land A Rent = 40, Land B Rent = 20, Land C Rent = 0; Wage = 40; Profit falls to 20 across all plots.

As accumulation continues, the falling rate of profit eventually reaches zero, driving the economy into the Ricardian stationary state.

While modern oligopoly theory focuses on strategic price rigidities under imperfect competition, the Ricardian model unifies value and distribution into a macroeconomic dynamic, demonstrating that agricultural resource constraints inevitably redistribute income from productive capital to unproductive land, culminating in economic stagnation.