Using Lorenz curves to represent firm heterogeneity in Cournot games

We derive several comparative-static results for Cournot games when firms have nonconstant marginal-cost curves which shift exogenously. The results permit us to rank certain vectors of equilibrium marginal costs with the same component sum according to their associated social surplus or industry profit. We arrange the components of each vector in ascending order and then construct from the resulting ordered vector its associated Lorenz curve. We show that if two Lorenz curves do not cross, the one reflecting greater inequality is associated with higher social surplus and industry profit. A duality result permits a corresponding ranking of equilibrium output vectors. The same partial ordering is used in the literature on income inequality to rank certain distributions of income and in the literature on decision-making under uncertainty to compare the riskiness of certain probability distributions with the same mean.Lorenz curves, Herfindahl index, Cournot games

Strategic Rent: Full-Line Forcing, Maximum Resale Price Maintenance, Brand Discounts and Aggregate Rebates

This paper examines the implications of a retailer's shelf space stocking decisions on the optimal marketing strategy of an upstream multiproduct monopolist. When the retailer's opportunity cost of shelf space is known, full-line forcing, brand discounts, and maximum resale price maintenance are sufficient to achieve the monopolist manufacturer's first best profit. When these strategies are adopted, the retailer's profit is reduced to the scarcity rents obtainable on her shelf space. When the retailer's opportunity cost of shelf space is unknown, the use of aggregate rebates can act as a screening device to maximize channel profit.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100957/1/ECON401.pd

Slotting Allowances and Resale Price Maintenance: A Comparison of Facilitating Practices

Producers in a perfectly competitive industry compete to obtain shelf space at the retail level. Barring contract observability problems, slotting allowances are observed in equilibrium. Producers charge a high wholesale price, but give back their profits via up-front payments to retailers. However, if the individual supplier-retailer wholesale price terms are unobservable by competitors, then resale price maintenance will be seen, but the coverage will not be universal. The equilibria can be ranked by the usual social welfare criteria. Resale price maintenance, though worse than simple marginal cost wholesale pricing, yields greater surplus than the slotting allowance equilibrium.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100956/1/ECON400.pd

Mergers and Partial Ownership

In this paper we compare the profitability of a merger to the profitability of a partial ownership arrangement and find that partial ownership arrangements can be more profitable for the acquiring and acquired firm because they can result in a greater dampening of competition. We also derive comparative statics on the prices of the acquiring firm, the acquired firm, and the outside firms. In a dual context, we show that a cross-majority owner may have incentives to sell a fraction of the shares in one of the firms he controls to a silent investor who is outside the industry. Aggregate ex post operating profit in the two firms controlled by the cross-majority shareholder then increases, such that both the cross-majority shareholder and the silent investor will be better off with than without the partial divestiture.media economics, mergers, corporate control, financial control

Mergers and Partial Ownership.

In this paper we compare the profitability of a merger to the pro…tability of a partial ownership arrangement and …nd that partial ownership arrangements can be more profiable for the acquiring and acquired firm because they can result in a greater dampening of competition. We also derive comparative statics on the prices of the acquiring firm, the acquired firm, and the outside firms. In a dual context, we show that a cross-majority owner may have incentives to sell a fraction of the shares in one of the firms he controls to a silent investor who is outside the industry. Aggregate ex post operating profit in the two firms controlled by the cross-majority shareholder then increases, such that both the cross-majority shareholder and the silent investor will be better o¤ with than without the partial divestiture.Media economics; Mergers; Corporate Control; Financial Control

Mergers and Partial Ownership

In this paper we compare the profitability of a merger between two firms (one firm fully acquires another) and the profitability of a partial ownership arrangement between the same two firms in which the acquiring firm obtains corporate control over the pricing decisions of the acquired firm. We find that joint profit can be higher in the latter case because it may result in a greater dampening of competition with respect to an outside competitor. We also derive comparative statics on the prices of the acquiring firm, the acquired firm, and the outside firm and use them to explain puzzling features of the pay-TV markets in Norway and Sweden.Media economics; Mergers; Corporate Control; Financial Control

Do Low-Price Guarantees Facilitate Collusion?

We examine the role low-price guarantees allegedly play in supporting supracompetitive prices. We find that when firms can commit to matching or beating any lower price announced by a competitor, all Nash equilibria yield Bertrand selling prices. This result casts doubt on the robustness of the conclusions of models which restrict attention to meet-the-competition clauses only.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100775/1/ECON238.pd

Competitive Coupon Targeting

With the advent of panel data on household purchase behavior, and the development of statistical procedures to utilize this data, firms can now target coupons to selected households with increasing accuracy and cost effectiveness. As a consequence, new avenues of competition have opened up in which firms play an active role in market segmentation. In this article, we develop an analytical framework to examine the effect of targeting on firm profits, prices, coupon face values, and redemption rates. We also determine firms' optimal mix of offensive and defensive couponing. Among our findings: when rival firms can target their coupon promotions at brand switchers, the outcome will be a prisoner's dilemma in which the net effect of targeting is simply the cost of distribution plus the discount given to redeemers.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100959/1/ECON403.pd

The Welfare Effects of Forbidding Discriminatory Discounts: A Ssecondary Line Analysis of Robinson-Patman

We examine the welfare effects of forbidding price discrimination in intermediate goods markets when firms can bargain over terms of their nonlinear supply contracts. In particular, our focus is on secondary line injury to competition under three interpretations of what it means to forbid price discrimination. We find that in each case, forbidding discriminatory discounts renders retailer bargaining power useless in mitigating manufacturer market power. As a result, all retailers end up paying higher input prices, and all retail prices rise. We show by example that the welfare loss can be substantial.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100958/1/ECON402.pd

Optimal Asymmetric Strategies in Research Joint Ventures: Comment on the Literature

This paper identifies an overlooked implication of models of research joint ventures initiated by . Even though the aggregate R and D cost of identical firms in a research joint venture would be lowest if they invested equally to reduce subsequent production costs, nonetheless members may often enlarge their overall joint profit by making unequal investments. Such a strategy raises costs in the investment stage but may create more than offsetting benefits in the production stage since industry profits are larger there when the firms are of unequal size. When the consideration leading to asymmetry prevails, we find that, in contrast to previous work, a research joint venture can raise welfare even when there are no spillovers.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100941/1/ECON388.pd