Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

Intermediated surge pricing

Although Uber and Lyft are known for their flexible “surge pricing,” they are surprisingly rigid in another way: each firm takes a constant percentage of passenger fare whether or not there is a surge. In this paper, I investigate the possible reasons for, and the impact of, this rigidity. I study a market in which a profit‐maximizing intermediary facilitates trade between buyers and sellers. The intermediary sets prices for buyers and sellers, and keeps the difference as her fee. Optimal prices increase when demand increases, that is, shifts right. If a demand increase is due to an increase in the number of ex ante symmetric buyers, then the intermediary's optimal percent fee decreases. If, instead, a demand increase is due to a reduction in the elasticity of demand, then the intermediary's optimal percent fee increases. In either case, if the intermediary keeps a constant percent fee regardless of shifts in demand, as is the case with Uber and Lyft, then surge pricing (i.e., the ratio of price during high demand to price during low demand) is amplified on one side of the market and diminished on the other side.     

Decentralized Supply Chain Decisions on Lead Time Quote and Pricing with a Risk‐averse Supplier

We consider a decentralized supply chain containing a risk‐averse supplier and a risk‐neutral retailer with lead time‐sensitive and price‐sensitive demands. A Stackelberg game is employed to model the lead time quote and pricing decision process between the two members under the conditional value‐at‐risk criterion. A unique equilibrium is obtained. Using the corresponding centralized mode as a benchmark, we find that a less risk‐averse supplier is better to cooperate and share risk with the retailer to improve the entire supply chain's efficiency. With a uniformly distributed realized lead time, the impact of the supplier's risk aversion on the decisions can be characterized by a few threshold values of the late delivery penalty cost. In particular, when the unit delay penalty cost exceeds a certain level, a more risk‐averse supplier will counter‐intuitively quote a shorter lead time by risking a higher delay penalty cost. Copyright © 2016 John Wiley & Sons, Ltd.     

Inventory management under uncertainty: A financial theory for the transactions motive

This paper examines the effects of risk aversion and output market uncertainty on optimal inventory policy decisions for a transactions demand for inventory using the capital asset pricing theory. The paper shows that (1) the optimal order quantity of the risk-adjusted value-maximizing firm is smaller than that of the expected-profit-maximizing one and (2) the greater the firm's output market uncertainty, the smaller its optimal order quantity, where the output market uncertainty is defined as the relative volatility of the demand for the firm's output.     

Comment: further sufficient conditions for an inverse relationship between productivity and employment

Extant empirical studies document that productivity gains due to technological progress often lead to reductions in employment. This paper rationalizes the stated empirical finding within the context of the theory of the competitive firm under price uncertainty. We show that technological progress affects employment adversely if the firm’s coefficient of relative risk aversion is no less than unity and its production technology exhibits non-decreasing returns to scale. On the other hand, technological progress unambiguously increases output if the firm’s preference has non-increasing absolute risk aversion.     

Disclosure Policy in a Mixed Market

This paper investigates the optimal disclosure strategy for private information in a mixed duopoly market, where a state-owned enterprise (SOE) and a joint-stock company compete to supply products. I construct a model where the two firms compete in either quantity or price, and uncertainty is associated with either marginal cost or market demand. The model identifies the optimal disclosure strategies that constitute a perfect Bayesian equilibrium by type of competition and uncertainty. In Cournot competition, both firms disclose information under cost uncertainty, while only the SOE or neither firm discloses information under demand uncertainty. Alternatively, in Bertrand competition, only the joint-stock company discloses information under cost uncertainty or demand uncertainty. Recently, developed countries have required the same level of disclosure standards for SOEs as for ordinary joint-stock companies. The findings described in this paper warn that such mandatory disclosure by SOEs can trigger a reaction by joint-stock companies, putting the economy at risk of a reduction in welfare.     

The market for crash risk

This paper examines the equilibrium when stock market crashes can occur and investors have heterogeneous attitudes towards crash risk. The less crash averse insure the more crash averse through options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth [Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433–451] implicit pricing kernel puzzle, and the stochastic evolution of option prices. Crash aversion is compatible with some static option pricing puzzles, while heterogeneity partially explains dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.     

Financial contracts as coordination device

We study the use of financial contracts as bid‐coordinating device in multi‐unit uniform price auctions. Coordination is required whenever firms face a volunteer's dilemma in pricing strategies: one firm (the “volunteer") is needed to increase the market clearing price. Volunteering, however, is costly, as inframarginal suppliers sell their entire capacity whereas the volunteer only sells residual demand. We identify conditions under which signing financial contracts solves this dilemma. We test our framework exploiting data on contract positions by large producers in the New York power market. Using a Monte Carlo simulation, we show that the contracting strategy is payoff dominant and provide estimates of the benefits of such strategy.     

Risk aversion,forward markets and the competitive labor-managed firm under price uncertainty

This paper examines the behavior of a labor-managed co-operative firm which can sell its output in both spot and forward markets, where the random spot price varies between a price floor and a price ceiling but the forward price is a known parameter. We demonstrate that a risk-averse labor-managed firm will base its production decision on the forward market price, and that risk aversion is sufficient to give the direct relationship between a change in uncertainty and the amount hedged in the forward market.     

Production theory,uncertain prices and investment portfolios

This paper examines the allocative decisions of a competitive firm where input and output prices are uncertain and where the capital asset pricing model prevails. The firm behaves much as a profit maximizer under certainty, except that certainty equivalent prices formally replace the known prices. These certainty equivalent prices are composed of the expected price, the covariance of the price with the market (a measure of systematic risk) and a measure of risk aversion in the economy. Both static and comparative static propositions emerge in a natural way as extensions of standard, competitive and profit maximizing behavior. In addition, the model contains both the certainty case and the risk-neutral case as limiting examples.     

International tenders and futures hedging

This paper examines the optimal bidding and hedging decisions of a risk‐averse firm that takes part in an international tender. The firm faces multiple sources of uncertainty: exchange rate risk, risk of an unsuccessful tender, and business risk. The firm is allowed to trade unbiased currency futures contracts to imperfectly hedge its contingent foreign exchange risk exposure. We show that the firm shorts less (more) of the unbiased futures contracts when its marginal utility function is convex (concave) as compared with the case that the marginal utility function is linear. We further show that the curvature of the marginal utility function plays a decisive role in determining the impact of currency futures hedging on the firm's bidding behavior. Sufficient conditions that ensure the firm bids more or less aggressively than in the case without hedging opportunities are derived. Copyright © 2006 John Wiley & Sons, Ltd.     

How Do Alphas and Betas Move? Uncertainty,Learning and Time Variation in Risk Loadings*

I employ a parsimonious model with learning, but without conditioning information, to extract time‐varying measures of market‐risk sensitivities, pricing errors and pricing uncertainty. The evolution of these quantities has interesting implications for macroeconomic dynamics. Parameters estimated for US equity portfolios display significant low‐frequency fluctuations, along patterns that change across size and book‐to‐market stocks. Time‐varying betas display superior predictive accuracy for returns against constant and rolling‐window OLS estimates. As to the relationship of betas with business‐cycle variables, value stocks’ betas move pro‐cyclically, unlike those of growth stocks. Investment growth, rather than consumption, predicts the betas of value and small‐firm portfolios.     

Location-scale portfolio selection with factor-recentered skew normal asset returns

This paper analyzes the single period portfolio selection problem on the location-scale return family. The skew normal distribution, after recentering and reparameterization, is shown to be in this family. The recentered and reparameterized distribution, called factor-recentered skew normal, can be expressed as a skew factor model which is characterized by a location parameter and two scale parameters. Risk preference on scale parameter is non-monotonic and risk averse investors prefer larger (smaller) scale when the scale is negative (positive). The three-parameter efficient set is a part of conical surface bounded by two lines. Positive-skewness portfolios and negative-skewness portfolios do not coexist in the efficient set. Numerical cases under constant absolute risk aversion are analyzed with its closed-form certainty equivalent. An asset pricing formula which nests the CAPM is obtained.     

Peak load pricing with spatial diffusion

The demand for public utility service varies not only temporally but spatially as well. The analysis of the problem of meeting these variations in system load with optimum plant capacity within the framework of a price determination structure is the objective of this paper. No simple cost-based solution proves possible. The solution presented, under a social welfare-maximization criterion, is similar to the joint product pricing discussed by Marshall. The characteristics of peak load pricing developed apply to the profit-maximizing firm as well as to the welfare-maximizing firm. With a profit-maximization objective, price will exceed rather than equal marginal cost. When regulation is imposed, whatever its form, normally there will be a price reduction as the output of the firm is moved closer to the welfare-maximizing level.     

Two remarks on the uniqueness of equilibria in the CAPM

In the standard ‘capital asset pricing model’ (CAPM) with a riskless asset we give a sufficient condition for uniqueness. This condition is a joint restriction on the agents’ endowments and their preferences which is compatible with non-increasing absolute risk aversion and which is in particular satisfied with constant absolute risk aversion. Moreover, in the CAPM without a riskless asset we give an example for multiple equilibria even though all agents have constant absolute risk aversion.     

Cost-based decision rules for output,quality, and price

The present paper develops a theoretical model to address the relationship between a firm's pricing policy and its cost of increasing product quality. The model expresses both firm costs and firm revenues as functions of the quantity of a firm's output and overall product quality, where quality is expressed as quantity times quality per unit. The model starts with a generic good that measures output, and models quality as priced quality enhancement for each unit of the generic good. The model leads to decision rules by which the price of quality is a mark-up over the marginal cost of increasing product quality. The relationship between the price of quality and revenues from increasing output is also determined, and is conditioned by the sign and magnitude of the elasticity of demand for quality.     

The effects of uncertainty on investment and the expected long-run capital stock

This paper examines the effects of output price uncertainty on the optimal investment behavior of a risk-neutral competitive firm with a constant returns to scale production function. In the presence of convex costs of adjustment, investment is an increasing function of q, the shadow price of capital. Given the current price of output, we find that increased uncertainty will raise the current rate of investment. Increased uncertainty will also increase the expected long-run capital stock if the price of output is serially uncorrelated. However, if the price of output is serially correlated, then the direction of the effect of increased uncertainty on the expected long-run capital stock depends on the curvature of the marginal adjustment cost function. In this case, we obtain results which are directly opposite of the results in the literature and we locate the flaw in the existing analysis.     

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.     

Optimal advance selling discount strategy with future-oriented consumers

This paper examines the advance selling decisions over two periods and considers future-oriented consumers who are more concerned about the product quality than price discounts. We find that the advance selling strategy is not always best, and its merits are contingent on parameters of the market and consumers. Moreover, there is no need to set a deep advance selling discount for the retailer if consumers are highly risk averse. Next, we analyze the feasible advance selling pricing strategies for the retailer. Finally, we observe that the retailer can announce a higher advance selling price if consumers are moderately risk averse.     

Attitude towards risk,uncertainty, and fixed investment

We explore the relevance of the risk attitude of managers to the investment-uncertainty relation. Higher moments of the distribution of net profits are used to measure the risk premium of the firm, from which we derive a proxy for the risk aversion of managers. Using an unbalanced panel of Dutch listed firms, we find that in general a low degree of risk aversion coincides with a positive impact of demand uncertainty on investment. More specifically, we find that risk-averse firms respond to demand uncertainty by cutting investment, while the investment undertaken by risk-taking firms responds to demand uncertainty positively.