Regret theory and the competitive firm

This paper examines the production decision of the competitive firm under uncertainty when the firm is not only risk averse but also regret averse. Regret-averse preferences are characterized by a modified utility function that includes disutility from having chosen ex-post suboptimal alternatives. The extent of regret depends on the difference between the actual profit and the maximum profit attained by making the optimal production decision had the firm observed the true realization of the random output price. If the firm is not too regret averse, we show that the conventional result that the optimal output level under uncertainty is less than that under certainty holds. Using a simple binary model wherein the random output price can take on either a low value or a high value with positive probability, we show the possibility that the firm may optimally produce more, not less, under uncertainty than under certainty, particularly when the firm is sufficiently regret averse and the low output price is very likely to prevail.     

Regret theory and the competitive firm: A comment

In a recent paper, Wong [Wong, K. P. (2014), Regret theory and the competitive firm. Economic Modelling, 36, 172–175.] develops a model to examine the production behavior of a regret averse competitive firm. Wong discusses the sufficient condition to ensure the conventional result that the optimal output level under uncertainty is less than that under certainty hold. Our contributions in this note are two-fold. Firstly, we point out that Wong's condition in terms of the first order derivatives of the utility function and the regret function is actually not sufficient. Secondly and more importantly, we show that a sufficient condition should be in terms of the relatively increase rate of the first order derivatives of the two functions. That's, it's the ratio of the risk aversion and regret aversion degree that matters. Our proposed condition requests that the firm should be not too regret averse.     

The Impact of Regret on Exports

We examine optimal production and export decisions of a firm facing exchange rate uncertainty, where the firm's management is not only risk averse but also regret averse, i.e., is characterized by a utility function that includes disutility from having chosen ex post suboptimal alternatives. Experimental and empirical results support the view that managers tend to be regret averse. Under regret aversion a negative risk premium need not preclude the firm from exporting which would be the case if the firm were only risk averse. Exporting creates an implicit hedge against the possibility of regret when the realized spot exchange rate turns out to be high. The regret‐averse firm as such has a greater ex ante incentive to export than the purely risk averse firm. Finally, we use a two‐state example to illustrate that the firm optimally exports more (less) to the foreign country than in the case of pure risk aversion if the low (high) spot exchange rate is more likely to prevail. Regret aversion as such plays a crucial role in determining the firm's optimal allocation between domestic sales and foreign exports.     

Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.     

Regulating a Monopolist with Unknown Demand: Costly Public Funds and the Value of Private Information

In this paper, we analyze the optimal regulation policy when the regulated firm has better information concerning the market demand than the regulator. We show that introducing a cost on public funds into the Planner's objective function does not lead to qualitative results similar to those obtained by introducing distributional considerations. In particular we show that under constant marginal cost the full information policy is not implementable and that the optimal regulatory policy results in informational rents. The social value of private information and the firm's informational rents are both increasing functions of the cost of the public funds.     

RISKY PRODUCTION WITH EX-ANTE PRICES UNDER MONOPOLY ANALYTICAL AND SIMULATION RESULTS

This paper concerns the case of a monopolist facing multiplicative uncertainty in demand. Karlin and Carr (1962), henceforth KC, show that, when price and production are both chosen ex ante , the uncertainty price exceeds the certainty price. They also give a sufficient condition under which the firm locates above the certainty demand curve, but they do not consider the effect on the output level. In this note we replicate the KC results and then go further. In the special case that the price elasticity of certainty demand is constant, and the probability distribution for the uncertainty parameter in the demand function is uniform, output is unambiguously lower under uncertainty, and KC's condition for the firm to locate above the certainty demand curve can be strengthened to one that is both necessary and sufficient. The robustness of these results is tested under less stringent assumptions on demand, abandoning symmetry for a lognormal distribution of the uncertainty parameter. Simulation confirms that the results hold up, and also determines the effects upon the firm's decisions of an increase in demand uncertainty.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Make vs buy in a monopoly with demand or cost uncertainty

The issue of technical progress under uncertainty is nested into the debate on vertical integration versus outsourcing, to show that, in general, the former is preferable to the latter in terms of both expected profits and technological efficiency. It is then shown that there exist (i) an optimal two part tariff where the unit price set by the upstream firm is conditional upon its R&D effort, and (ii) an optimal contract specifying the input price in terms of the initial capabilities of the sub-contractor, whereby the industry replicates the same performance as the vertically integrated firm as for both profits and R&D efforts.     

Operational and financial hedging for exporting firms

This paper examines the interaction between operational and financial hedging in the context of an internationally competitive but domestically monopolistic firm under exchange rate uncertainty. Operational hedging is modeled by letting the firm make its export decision after it has observed the true realization of the then prevailing spot exchange rate. Financial hedging, on the other hand, is modeled by allowing the firm to trade fairly priced exotic derivatives that are tailor-made for the firm's hedging need. We show that both operational and financial hedging unambiguously entice the firm into producing more. We further derive sufficient conditions under which operational hedging dominates (is dominated by) financial hedging in terms of promoting the firm's optimal output.     

Imported inputs and privatization in downstream mixed oligopoly with foreign ownership

This paper examines welfare implications of privatization in a mixed oligopoly with vertically related markets, where an upstream foreign monopolist sells an essential input to public and private firms located downstream in the domestic country. The impact on domestic welfare of privatizing the downstream public firm is shown to contain three effects. The first is an output distortion effect, which negatively affects welfare since privatization decreases the production of final good for consumption. The second is an input price lowering effect resulting from a decrease in derived demand for the input. When the level of privatization increases, a decrease in final good production lowers input demand, causing input price to decline and domestic welfare to increase. The third is a rent‐leaking effect associated with foreign ownership in the downstream private firm. The rival domestic firm strategically increases its final good production, causing profits accrued to foreign investors to increase and domestic welfare to decline. Without foreign ownership in the downstream private firm, the optimal policy toward the public firm is complete privatization as the output distortion effect is dominated by the input price lowering effect. With foreign ownership, however, complete privatization can never be socially optimal due to the additional negative impact on domestic welfare of the rent‐leaking effect. We further discuss implications for domestic welfare under different privatization schemes (e.g., selling the privatization shares to the upstream foreign monopolist or to the rival domestic firm).     

Price or quantity setting under uncertain demand and capacity constraints: An examination of the profits

This article considers price formation and quantity setting of a capacity-constrained risk-neutral firm facing uncertain demand. It is shown that the optimal price of a price-setting risk-neutral monopolist decreases with demand uncertainty. With a strictly convex demand function expected profits increase with uncertainty for a quantity-setting monopolist whereas expected profits decrease for a price-setting monopolist. Furthermore, similar results on the effect of uncertainty are derived for a differentiated goods industry.     

Should refusal to sell be illegal?

We analyse a private firm's decision of whether to refuse to sell to a particular group of consumers whose interaction with other consumers generates negative externalities. The literature has rarely incorporated this motive directly into the firm's profit-maximisation problem. Discriminatory refusal-to-sell policies can increase profits and consumer utility among those affected by the negative externality. Of course it also reduces utility among consumers who are refused, raising the possibility of an indeterminate effect on social welfare. We obtain a stark and rather surprising result: The refusal-to-sell policy is socially optimal whenever it is individually optimal for a profit-maximising firm to adopt such a policy. No legislation or regulation is required from a social-welfare perspective (under the assumptions used in the specification of the social welfare function). We prove this result analytically for the case of linear demand functions. Numerical simulations show that the result also holds for constant-price-elasticity demand functions.     

Testing expected utility maximization under price and quantity risk with a heterogeneous panel

Refutable implications based on the curvature properties of the indirect utility function for the competitive firm operating under uncertainty are extended to the case of both price and quantity uncertainty. Using unit roots and cointegration tests for heterogeneous panels, a model of US agricultural production is developed based on the time-series properties of a panel of state-level data. Most refutable hypotheses under output price and output quantity risk are not rejected, but symmetry conditions implied by a twice-continuously-differentiable indirect utility function are rejected. The same test conclusions are obtained from a traditional model that presumes stationarity in all variables.     

Export Flexibility And Currency Hedging*

This article studies the behavior of an export‐flexible firm under exchange rate uncertainty. We show that the separation theorem holds if selling exclusively in the domestic market is suboptimal even under the most unfavorable spot exchange rate. Otherwise, the firm's optimal output depends on its preferences and on the underlying uncertainty. We further show that the full‐hedging theorem holds only when the firm always finds it optimal to sell its entire output in the foreign market. Otherwise, export flexibility introduces a convexity into the firm's foreign exchange risk exposure, which calls for the use of currency options for hedging purposes.     

Forward Markets and the Behaviour of the Competitive Firm with Production Flexibility

This paper examines the production and hedging decisions of the competitive firm under output price uncertainty when a forward market for its output is available. The firm possesses production flexibility in that it makes its production decision after the resolution of the output price uncertainty, albeit subject to a capacity constraint on production. We show that the firm optimally acquires a higher level of capacity investment than an otherwise identical firm with no production flexibility. We further show that production flexibility allows the firm to implicitly hedge against its output price risk exposure by the ex post production decision. The firm as such under‐hedges its output price risk exposure in the forward market wherein the forward price contains a non‐positive risk premium.     

Corporate finance side of the Q theory of investment

This paper presents a model of a firm under uncertainty in which the financial and investment decisions are simultaneously determined. If profits are small relative to investment, the firm finances a constant fraction of incremental investment by debt and the rest by retentions. If profits are large relative to investment, a constant fraction of marginal finance comes from debt and the rest from new shares. In these two financing regimes a one-to-one relationship between optimal investment and Q can be derived. No such relation exists in the third and intermediate regime in which incremental investment is entirely debt-financed.     

Price Caps and Output Floors: A Comparison of Simple Regulatory Rules

We study in this paper a simple alternative to price cap regulation. The mechanism, which we label 'output floor' regulation, requires the regulated firm to supply a given level of output. This rule is as simple as price cap regulation, and performs identically when the regulated firm is a natural monopoly; however, we show that, in the presence of a competitive fringe, output floor regulation yields lower prices and stronger incentives for cost reduction. Its introduction, however, is likely to be resisted by the industry, since it lowers managerial utility and shareholders' profits.     

The response to incentives and contractual efficiency: Evidence from a field experiment

We use data from a field experiment to estimate worker reaction to incentives and the optimality of piece-rate contracts. Our estimate of the elasticity of output with respect to piece rates is 0.39. Regression methods cannot predict performance under hypothetical contracts. Therefore, we apply structural econometric methods (without imposing profit maximization) to evaluate observed-contract optimality. Using profit as a metric, we estimate the distance between observed and profit-maximizing contracts to be negligible. This suggests that observed contracts closely approximate optimal contracts under asymmetric information about worker ability. Under complete information, the firm could increase expected profits by 14 percent keeping workers indifferent to the observed piece-rate contract. Profits could increase between 44 and 49 percent if the firm exploited information about ability to reduce worker utility to the outside alternative.     

Currency Options and Export-Flexible Firms

This paper examines the production and hedging decisions of a globally competitive firm under exchange rate uncertainty. The firm is risk averse and possesses export flexibility in that it can distribute its output to either the domestic market or a foreign market after observing the realized spot exchange rate. To hedge against its exchange rate risk exposure, the firm can trade fairly priced currency call options of an arbitrary strike price. We show that both the separation and the full‐hedging results hold if the strike price of the currency call options is set equal to the ratio of the domestic and foreign selling prices. Otherwise, neither result holds. Specifically, we show that the optimal level of output is always less than that of an otherwise identical firm that is risk neutral. Furthermore, an under‐hedge (over‐hedge) is optimal whenever the strike price of the currency call options is below (above) the ratio of the domestic and foreign selling prices.     

Preference for output price uncertainty by the non-renewable resource extracting firm

We establish a general preference for price uncertainty by the price-taking, risk-neutral, non-renewable resource extracting firm with orthodox convex extraction costs. We prove that the relevant value function for profits over an interval is convex in output price.