Market Power

Abstract

In previous chapters, we discussed the static efficiency of markets from a theoretical perspective. We learned that a market is allocatively efficient when total (consumer plus producer) surplus is maximized and price equals marginal cost. A firm is said to have monopoly or market power when it can profitably raise price above marginal cost. Theory tells us that market power will be present in unregulated monopoly but not perfectly competitive markets. The extent of market power in oligopoly markets will depend on the specific characteristics of the market.

Appendices

Appendix A: Monopsony Power

As we saw in Sect. 12.1.1, there is a single buyer of an input in a monopsony market. Lack of competition for an input enables the firm to lower the price of the input without completely eliminating supply. Instead of being an input price taker, where the input supply function is perfectly elastic, the firm is an input price maker. Similar to a monopolist that earns greater profit by raising the output price above its competitive level, a monopsonist earns greater profit by lowering the input price below the competitive level.³⁰

In this case, the index of input market power for input x is I _x  ≡ (VMP − w)/VMP, where VMP is the value of the marginal product of input x ³¹ and w is the price of the input. When the input market is perfectly competitive, w = VMP and the index equals 0. Market power is present when I _x  > 0. A “bilateral monopoly” exists when there is a monopoly supplier and a monopoly buyer.³² In this case, Chang and Tremblay (1991) showed that under certain conditions I _x  = (1/ε _S + 1/η)/(1 + 1/ε _S), where ε _S is the price elasticity of supply of input x and η is the absolute value of the price elasticity of demand. In this case, input market power increases as output demand becomes more inelastic (i.e., η falls) and input supply becomes more inelastic (i.e., ε _S falls). Notice that I _x  = 1/η, the Lerner index, when the firm is an input price taker (i.e., the input supply elasticity is infinite).

Azzam (1997) uses an approach that is similar to the NEIO method to estimate the degree of monopsony power in the US beef packing industry. The empirical specification derives from the first-order condition of profit maximization for the beef packing input. He found that higher concentration in beef packing led to greater monopsony power. He also found support for the hypothesis that higher concentration led to greater cost efficiency, with the cost-efficiency effect outweighing the market-power effect.

Appendix B: The Lerner Index in a Dynamic Setting

Here, we formalize our discussion of the measurement of market power in a dynamic market from Sect. 12.1.2. Assume that firm i competes in an oligopoly market where production today affects future profit, as with addictive commodities, learning-by-doing, or a durable good.

Problems such as these can be solved using dynamic programming methods, where the goal of the firm is to choose the level of output in each period that maximizes the present value of the stream of profits now and into the future, V.³³ In essence, this represents the market value of the firm. The firm’s problem can be described in period t by a Bellman equation

$$ {V_t} = { \max }\left[ {{p_t}\left( {{Q_t}} \right){q_t} - {\hbox{T}}{{\hbox{C}}_t}\left( {{q_t}} \right) + D \cdot {V_{{t + 1}}}} \right], $$

(B.1)

where V _t is the value function in period t, D is the discount factor as discussed in Chap. 2, and subscript i is suppressed for notational convenience. The goal is to choose q _t to maximize V _t . The general first-order condition that includes the behavioral parameter θ is

$$ \frac{{\partial {V_t}}}{{\partial {q_t}}} = {p_t} + \theta \frac{{\partial {p_t}}}{{\partial {Q_t}}}{q_t} - {\hbox{M}}{{\hbox{C}}_t} + \alpha = 0. $$

(B.2)

Note that α ≡ D · ∂V _t+1/∂q _t is an adjustment factor that represents the effect of a change in q _t on the present value of the stream of future profits beginning in period t + 1. In a static market with no future effects, α = 0 and (B.1) reduces to the first-order condition found in the static model found in (12.2). With addiction and learning-by-doing, this term will be positive. An increase in production today increases future demand with addiction and lowers future costs with learning-by-doing. In a durable goods problem, this term will be negative because an increase in sales today will lower future demand.

The α parameter plays a key role in identifying the degree of market power. After rearranging terms in (B.2), a dynamic Lerner index is defined as

$$ \mathcal{L} \equiv \frac{{{p_t} - {\text{M}}{{\text{C}}_t} + \alpha }}{{{p_t}}} = - \theta \frac{{\partial {p_t}}}{{\partial {Q_t}}}\frac{{{Q_t}}}{{{p_t}}}\frac{{{q_t}}}{{{Q_t}}} = \frac{{{\text{m}}{{\text{s}}_t}\theta }}{\eta }. $$

(B.3)

In this case, there is no market power when ℒ = 0, but ℒ need not equal 0 when price equals marginal cost. In a dynamic setting where α > 0, as with addiction, market power is present (ℒ > 0) even when price equals marginal cost.

The issue is even more complicated in a model with learning-by-doing (Pindyck 1985). For example, consider a monopolist whose marginal cost in period t is a negative function of learning and where learning is a positive function of the firm’s cumulative past production ($\Sigma Q_{{t - 1}}^{\rm{M}}$). Correctly estimating ℒ not only requires information on price and α but also requires an estimate of the marginal cost that would result if the industry had been perfectly competitive all along. Note that because cumulative output will be greater under competition ($\Sigma Q_{{t - {1}}}^{\rm{PC}}$) than under monopoly, MC($\Sigma Q_{{t - 1}}^{\rm{M}}$) > MC($\Sigma Q_{{t - {1}}}^{\rm{PC}}$). From society’s perspective, the correct measure of the Lerner index is

$$ \mathcal{L} \equiv \frac{{{p_t} - {\text{M}}{{\text{C}}_t}\left( {\Sigma Q_{{t - 1}}^{\rm{PC}}} \right) + \alpha }}{{{p_t}}}. $$

(B.4)

Note that only MC($\Sigma Q_{{t - 1}}^{\rm{M}}$) is observable from firm data, however. If MC($\Sigma Q_{{t - 1}}^{\rm{M}}$) is used instead of MC($\Sigma Q_{{t - {1}}}^{\rm{PC}}$) to estimate ℒ, this will underestimate the degree of market power. This illustrates how difficult it can be to accurately estimate market power in the presence of learning-by-doing.

Appendix C: Estimating Game Theoretic Strategies

In this appendix, we provide an overview of the Gasmi and Vuong (1991) and Gasmi et al. (1992) method of estimating market power and the particular game being played by firms. Because applying this technique is complicated when there are many strategic possibilities, we illustrate the main idea by considering only nested games of output or price competition and ignore advertising. We consider differentiated Bertrand, Cournot, and cartel games only. The goal is to find a first-order condition that is general enough to nest each of these three possible outcomes. This is different from the NEIO approach, because this technique constrains the market-power parameter to take a discrete value that corresponds to Bertrand, Cournot, or cartel behavior.

We begin with Cournot. Assume that two firms, Coke and Pespi, compete in a static game where the choice variable is output and products are differentiated. Inverse demand, cost, and profit equations are the same as those found in Chap. 10, Sect. 10.2.1:

$${p_i} = a - {q_i} - d{q_j}, $$

$${\hbox{T}}{{\hbox{C}}_i} = c{q_i}, $$

$${\pi_i} = {\hbox{T}}{{\hbox{R}}_i} - {\hbox{T}}{{\hbox{C}}_i} = \left( {a{q_i} - q_i^2 - d{q_j}{q_i}} \right) - c{q_i}, $$

(C.1)

where subscript i represents Coke or Pepsi and subscript j refers to the other firm. The first-order condition for firm i is

$$ \begin{array}{lll} \frac{{\partial {\pi_i}}}{{\partial {q_i}}} &= {\hbox{M}}{{\hbox{R}}_i} - {\hbox{M}}{{\hbox{C}}_i}, \\ &= \left( {a - 2{q_i} - d{q_j}} \right) - (c) = 0, \\\end{array} $$

(C.2)

where MR _i is marginal revenue and MC _i is marginal cost.

Next, we consider the case where Coke and Pepsi form an effective cartel. The goal now is to maximize joint profits (Π), which is

$$ \begin{array}{lll} \Pi &= {\pi_i} + {\pi_j} \\ &= \left( {a{q_i} - q_i^2 - d{q_j}{q_i} - c{q_i}} \right) + \left( {a{q_j} - q_j^2 - d{q_i}{q_j} - c{q_j}} \right). \\\end{array} $$

(C.3)

The first-order condition for firm i is

$$ \begin{array}{lll} \frac{{\partial \Pi }}{{\partial {q_i}}} &= \left( {a - 2{q_i} - d{q_j} - c} \right) + \left( {d{q_j}} \right) \\& = a - c - 2{q_i} - 2d{q_j} = 0. \end{array} $$

(C.4)

In the Bertrand case, recall that we must reorganize demand so that quantity is a function of the choice variables, p _i and p _j . From (10.35) and (10.36), we saw that the demand structure from the Cournot game above produces the following demand function in prices:

$$ {q_i} = \alpha - \beta {p_i} + \delta {p_j}, $$

(C.5)

where α ≡ a(1 − d)/x, β ≡ 1/x, δ ≡ d/x, and x ≡ (1 − d ²). This yields the following profit equation for firm i:

$$ \begin{array}{lll} {\pi_i} &= {\hbox{T}}{{\hbox{R}}_i} - {\hbox{T}}{{\hbox{C}}_i} = {p_i}\left( {\alpha - \beta {p_i} + \delta {p_j}} \right) - c\left( {\alpha + \beta {p_i} - \delta {p_j}} \right) \\ &= \alpha {p_i} - \beta p_i^2 + \delta {p_j}{p_i} - \alpha c + \beta {p_i}c - \delta {p_j}c. \end{array} $$

(C.6)

The first-order condition for firm i is

$$ \begin{array}{lll} \frac{{\partial {\pi_i}}}{{\partial {p_i}}} &= {\hbox{MR}}{p_i} - {\hbox{MC}}{p_i} \cr &= \alpha - 2\beta {p_i} + \delta {p_j} + \beta c = 0. \end{array} $$

(C.7)

where MRp _i is firm i’s marginal revenue with respect to a change in p _i and MCp _i is firm i’s marginal cost with respect to a change in p _i .

The next step is to solve the first-order conditions in each of the three cases for q _i . This produces firm i’s best-reply function in q _i for the Cournot, cartel, and Bertrand cases.³⁴

$$\begin{array}{lll} {{\hbox{Cournot}}:}\ {{q_i} = + \frac{a}{2} - \frac{1}{2}c - \frac{d}{2}{q_j},} \\{{\hbox{Cartel}}:}\ {{q_i} = + \frac{a}{2} - \frac{1}{2}c - d{q_j},} \\{{\hbox{Bertrand}}:}\ {q_i} = - \frac{\alpha }{2} + \frac{\beta }{2}c - \frac{\delta }{2}{p_j}. \end{array}$$

(C.8)

The following equation nests each of these best-reply functions.

$$ {q_i} = {\psi_0} + {\psi_1}{q_j} + {\psi_2}{p_j}, $$

(C.9)

where ψ ₀ through ψ ₂ are parameters that take on different values for each of the three different models. That is,

$$ \begin{array}{lll} {{\hbox{Cournot}}}:\ {{\psi_0} = \frac{a}{2} - \frac{1}{2}c,\,\;\ \ \ {\psi_1} = - \frac{d}{2}, \,\;{\psi_2} = 0;} \\{{\hbox{Cartel}}:}\ {{\psi_0} = \frac{a}{2} - \frac{1}{2}c,\,\;\ \ \ {\psi_1} = - d,\,\;\ {\psi_2} = 0;} \\{{\hbox{Bertrand}}:}\ {\psi_0} = - \frac{\alpha }{2} + \frac{\beta }{2}c,\,\;{\psi_1} = 0,\,\;\ \ \ {\psi_2} = - \frac{\delta }{2}. \end{array} $$

(C.10)

The regression model to be estimated includes the system of demand, cost, and best-reply functions for each firm that are found in (C.1) and (C.9). The demand and cost regressions give estimates of parameters a, d, and c which relate directly to the parameters in (C.9). From the estimates of parameters and standard errors, hypothesis tests are conducted to determine which model is most consistent with the data. For example, the data support the Cournot model if the estimates indicate that ψ ₀ = [(a/2) − (1/2)c], ψ ₁ = –d/2, and ψ ₂ = 0.