Gerhard Tintner, Note on the Problem of Bilateral Monopoly (1939)

Gerhard Tintner’s short theoretical journal note examines a market in which a monopolist selling a finished commodity also acts as the sole buyer of an input supplied by another monopolist. Steel and iron ore provide the running example. Following Bowley and Hicks, Tintner first reconstructs the alternative outcomes produced by buyer dominance, seller dominance, and joint profit maximization. His particular contribution is then to investigate when these outcomes coincide. The central conclusion is that static profit-maximizing analysis generally leaves the input price indeterminate: agreement among the solutions requires exceptional conditions, while bargaining power ordinarily decides the price within a range.

Tintner locates the disagreement between Cournot’s solution and the subsequent Edgeworth tradition in their assumptions about the exercise of monopoly power. In the Cournot case, the steel producer exercises monopoly power as a seller but does not exploit his position as a buyer. This distinction makes the allocation of price-setting authority integral to the analysis, rather than a detail added after an equilibrium has been calculated.

The model deliberately excludes changing consumer tastes, technological change, expectations, and anticipations. Demand and costs are fixed, and both producers maximize monetary profit. Tintner stresses the temporal boundary of this approach:

Time does not enter explicitly as a variable into static considerations; neither do expectations and anticipations, which are essentially problems of dynamic economics.

Quantities are nevertheless measured per unit of time. With production coefficients held constant, one unit of ore produces one unit of steel, so a single quantity, x, represents both input and output. Tintner notes that variable coefficients could be accommodated by using marginal value product instead of marginal revenue. In the simplified model, steel revenue is R(x) and ore production cost is C(x). The steel producer’s demand for ore, D(x), equals the marginal revenue from steel sales; the ore producer’s supply, S(x), equals marginal production cost. These are derived schedules whose economic meaning matters throughout the argument.

The exposition proceeds through three cases, each accompanied by a graph and conditions for profit maximization:

We distinguish three cases: (A) the producer of steel dictates the price of iron ore; (B) the producer of iron ore dictates the price of iron ore; (C) both combine and maximize their joint profit.

In Case A, the steel producer sets the ore price but remains constrained by the supplier’s supply function. Maximizing steel profits therefore equates marginal revenue with marginal expenditure on ore: D = S + xS′. The price itself lies on S. In Case B, the ore producer sets the price subject to the steel producer’s derived demand. His maximizing condition is S = D + xD′, and the price lies on D. Tintner identifies this second arrangement with Cournot’s treatment. In Case C, the producers maximize their combined profit, R − C, giving the condition D = S. The transfer payment between them cancels from combined profit, so the joint calculation compares revenue from steel directly with the cost of producing ore.

The first two cases generally yield incompatible outcomes. Tintner treats their prices as bounds on a bargaining range, rather than as rival predictions from which theory can simply select one:

This introduces an essential indeterminancy into the situation of bilateral monopoly under static conditions.

The point extends beyond the chosen industrial example. Replacing the ore monopolist with a trade union facing an employer in a monopolized industry turns the input price into a wage. The same framework then leaves wages undetermined within the indicated range. This application makes the note relevant to wage bargaining as well as to vertically related monopolies: economic optimization establishes constraints without necessarily fixing the distributive settlement.

Tintner’s distinctive analytical move is to examine the coincidence of the three solutions. For Cases A and C to give the same price and quantity, their first-order conditions require S′ = 0 and D = S: the supply curve must have a horizontal tangent where it meets demand. For Cases B and C to coincide, the corresponding requirements are D′ = 0 and D = S. He also supplies second-order inequalities to distinguish profit maxima from stationary points. His treatment of complete coincidence requires both schedules to have horizontal tangents at their common equilibrium; the ordinary and modified demand and supply curves all meet there. The further curvature restrictions he reports underline how special this configuration would be.

These geometric conditions support the substantive conclusion. Steel demand and ore production costs are independently determined, with no inherent reason to align in the precise fashion required by the proposed common solution. Tintner also clarifies that D is a marginal-revenue curve: its horizontal tangent does not mean that consumers’ demand for finished steel must be horizontal. The exceptional geometry concerns derived input demand, not the final-product demand curve.

The conclusion separates what static economics can determine from what determines the actual bargain:

Other noneconomic, especially political, forces will create the bargaining power of the two monopolists, which in turn determines the price within the range indicated.

Tintner suggests that dynamic conditions could often produce a stable result, referring to Hicks and Zeuthen, but leaves that investigation outside the note’s scope. The work’s lasting conceptual emphasis is thus the distinction between profit-maximizing conditions and a determinate market settlement. Its equations identify the consequences of alternative price-setting powers and the special circumstances of their agreement; they do not eliminate the conflict of interest that makes bargaining necessary.