Self-Promoting Investments

When human capital skills differ in their ability to attract offers from alternative employers, a potential inefficiency in human capital investment arises. If a worker's output is observed by the labour market only when the worker invests in self-promoting activities, then high-ability workers overinvest in self-promotion. No bond is posted in the contract that both attains efficient investment and minimizes the bond subject to individual rationality constraints and the zero profit condition. The contract is one in which the firm (i) offers to match outside offers strategically and (ii) guarantees a minimum wage. The model predicts that, under both the spot market contract and the efficient contract, wage declines with seniority even when conditioning on high ability. This prediction is consistent with the stylized fact regarding the decline of wages with seniority in academia. The model can also explain how the seniority wage premium may vary across disciplines, time, and schools.negative seniority wage premium, spot market contract, efficient contract, general human capital

Budget-Constrained Sequential Auctions with Incomplete Information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder\\'s type. Parameters permit the existence of multiple equilibrium symmetric bidding functions that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α is higher when good α is sold first.sequential auctions, budget constraints, efficiency, revenue, price, sequence.

Self-Promoting Investments

When human capital skills differ in their ability to attract offers from alternative employers, a potential inefficiency in human capital investment arises. If a worker's ability and investments are observed by the labour market only when the worker invests in self-promoting activities, then high-ability workers overinvest in self-promotion. No bond is posted in the contract that both attains efficient investment and minimizes the bond subject to individual rationality constraints and the zero profit condition. The contract is one in which the firm (i) offers to match outside offers strategically and (ii) guarantees a minimum wage. The model predicts that, under both the spot market contract and the efficient contract, wage declines with seniority even when conditioning on high ability. This prediction is consistent with the stylized fact regarding the decline of wages with seniority in academia. The model can also explain how the seniority wage premium may vary across disciplines, time, and schools.microeconomic theory, negative seniority wage premium, spot market contract, efficient contract, general human capital, multi-tasking

Budget-Constrained Sequential Auctions with Incomplete Information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.sequential auctions, budget constraints, efficiency, revenue, price, sequence

Self-Promoting Investments

What is the impact on human capital investment when a worker's ability and investments are observed by the labour market only when the worker invests in self-promoting activities? When firms pay spot market wages, high ability workers overinvest in self- promotion. There is no employment contract that attains full efficiency. Constrained efficiency is attained when employment bonds are feasible. \ The contract that both attains constrained efficiency and minimizes the bond posted offers (i) severance payments, (ii) strategically matching outside offers and (iii) a minimum wage.

Equilibria of a Two-Person Non-Zero Sum Noisy Game of Timing

Necessary and sufficient conditions are obtained for the existence of an equilibrium point (as well as for the existence of a dominating equilibrium point) in a two-person non-zero sum game of timing

Profit-Sharing in a Collusive Industry

We study a model in which collusive duopolists divide up the monopoly profit according to their relative bargaining power. We are particularly interested in how the negotiated profit shares depend on the sizes of the firms. If each can produce at the same constant unit cost up to its capacity, we show that the profit per unit of capacity of the small firm is higher than that of the large one. We also study how the ratio of the negotiated profits depends on the size of demand relative to industry capacity, and how this ratio changes with variations in demand

Equilibria for a Three-Person Location Problem

We find all the mixed strategy equilibria, within a certain class, of the simplified three-firm location model of Hotelling (in which the price variable is ignored)