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.     

On the theory of the competitive firm with a utility function defined on profits and regret

In this paper we analyze the optimal output determined by a competitive firm facing uncertain demand. We analyze the effect of introducing uncertainty and the effect of increasing uncertainty on the optimal output, under the assumption that the utility function of the firm depends both on profits and on regret. We show that if the firm is more risk averse to profits than to regret (in a sense described below), both effects tend to decrease the optimal output. Similar effects of introducing uncertainty and of increased uncertainty were previously shown by Sandmo (1971) to exist in the case where utility is defined on profits only. Thus, this paper provides conditions under which the above results hold true, even when utility is defined on regret and on profits.     

Multiple variable factors,demand uncertainty,and the cooperative firm

It has been shown that the risk averse, cooperative firm producing its output with labor as the only variable input and selling this output in a competitive market will produce more than the cooperative firm operating under condition of certainty. This letter proves that this result may not apply to the case of the cooperative firm facing a stochastic demand and/or employing more than one variable input.     

On the theory of the competitive labor-managed firm under price uncertainty

The short-run behavior of a labor-managed firm under competitive assumptions and price uncertainty is analyzed assuming risk aversion. It is compared with its behavior under certainty and the behavior of a capitalist-managed firm under price uncertainty. It is shown that a risk-averse labor-managed firm employs more labor than a risk-neutral labor-managed firm. Generally, uncertainty is seen to have greater impact on the behavior of a labor-managed firm than on the behavior of a capitalist-managed firm. Except under constant risk aversion, the behavior of a labor-managed firm under price uncertainty is less predictable than that of a capitalist-managed firm.     

Intertemporal price cap regulation under uncertainty

This paper examines the intertemporal price cap regulation of a firm that has market power. Under uncertainty, the unconstrained firm 'waits longer' before investing or adding to capacity and as a corollary, enjoys higher prices over time than would be observed in an equivalent competitive industry. In the certainty case, the imposition of an inter-temporal price cap can be used to realise the competitive market solution; by contrast, under uncertainty, it cannot. Even if the price cap is optimally chosen, under uncertainty, the monopoly firm will generally (a) under-invest and (b) impose quantity rationing on its customers.     

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.     

COMPETITIVE LONG RUN INDUSTRY EQUILIBRIUM AND FACTOR-PRICE UNCERTAINTY*

In this paper we have considered competitive long run industry equilibrium with factor-price uncertainty. We discussed the long run equilibrium output of firms with risk neutrality, output price and their responses to changes in uncertainty, factor price and industry demand. In the first part of this paper we have derived a result that, given risk neutrality, the firms operate at proper capacity, i.e. where expected long run marginal cost is equal to expected long run average cost, as shown in the case of output-price uncertainty. This result is, however, different from that obtained from Sheshinski and Dréze (1976). From the comparative static analysis we first discovered that even under risk neutrality factor-price uncertainty affects the long run industry equilibrium: that is, a mean preserving increase in uncertainty leads firm's to enter the industry, because they can decrease expected long run costs as the variability of factor price increases. Consequently, output price goes down. In contrast, firm size is kept invariable in response to its increase as long as the cost function is separable, i.e. the separability of the cost function holds when production functions are the Cobb-Douglas and CES types used commonly in empirical work, although firm size might, generally, be affected by the increase. It is an interesting fact that firm size and industry size will express different responses to a change in risk. The result that the long run industry equilibrium with cost uncertainty is explicitly affected is a sharp contrast to the result under output-price uncertainty and provides a new aspect for understanding about the behaviour of the industry with uncertainty. Secondly, increased factor-price causes the number of firms in the industry to decline and output price to rise. In addition, firm's size will expand with its increase if that factor is inferior, while the effect on firm size is ambiguous if it is normal. The firm's output, i.e. firm size, is, however, kept constant if the cost function is separable. Thirdly, the long run equilibrium output of the firm remains intact but the number of firms increases as industry demand rises. This result holds, regardless of the firm's attitude towards risk. Finally, we find throughout the paper that the functional form of the cost function plays a significant role in determining the behaviour of the industry with factor-price uncertainty.     

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.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

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.     

Monopolistic price setting and supply rigidities in a disequilibrium framework

Summary. A model of the firm with a delayed adjustment of prices and employment is analyzed. Prices and employment are determined under uncertainty about the location of the demand curve. Three models are distinguished: price setting with predetermined supply, employment determination with pre-determined prices, and a simultaneous price and employment determination. It is shown that many of the results of the deterministic case can be transfered to the stochastic set-up. The deterministic model is included as a special case. However, the model allows for supply rigidities and labour hoarding and permits the analysis of price adjustment.Received: May 17, 1995; revised version: October 13, 1996This revised version was published online in February 2005 with corrections to the cover date.     

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.     

PRICE CONSTRAINTS,FORWARD MARKETS AND THE COMPETITIVE FIRM UNDER PRICE UNCERTAINTY*

This article proposes a model of the competitive firm simultaneously facing price constraints and forward markets under price uncertainty. The incorporation of a forward market is shown to be very important because a risk-averse firm will set its production decision to the forward price regardless of its attitude toward risk. In addition, we show that risk aversion is a sufficient condition for a decrease in risk to reduce the amount hedged when risk is reduced through a mean-preserving price squeeze.     

The effects of abandonment options on operating leverage and forward hedging

This paper examines the behavior of the competitive firm under output price uncertainty when the firm is endowed with an abandonment option and has access to a forward market for its output. When the realized output price is less than its marginal cost, the firm optimally exercises its abandonment option and ceases production. The firm lets its abandonment option extinguish, thereby producing up to its capacity, only when the realized output price exceeds its marginal cost. The ex post exercising of the abandonment option as such convexifies the firm's ex ante profit with respect to the random output price. We show that neither the separation theorem nor the full-hedging theorem holds in the presence of the abandonment option. The firm under-hedges its output price risk exposure in the forward market wherein the forward price contains a nonpositive risk premium. When the set of hedging instruments is expanded to include options, we show that both the separation and full-hedging theorems are restored. We further show that the firm prefers options to forwards for hedging purposes when both types of contracts are fairly priced.     

Cyclical dumping and correlated business cycles in imperfect markets: empirical applications to the Canadian pulp and paper industry

This paper deals with theoretical and empirical aspects of firm behaviour under imperfect competition and uncertainty. It contains an analysis of the behaviour of a firm facing a stochastic demand curve for its output in the ordinary (home market), but in addition with access to a backstop (international) market. The theory is thus a variation of the theory of dumping. Since the expected volume in general differs from the volume at the expected price, a price-setting mode is not equal to a quantity mode. Cyclical dumping, in the sense of a negative correlation between domestic and foreign sales, would occur if the firm adhered to a pricing mode in the ordinary market, and was able to learn about the demand conditions in the ordinary market before it decided how much to sell in the international market. The expirical part of the paper is an illustration of how to test for different behavioural modes and cyclical dumping by applying the model to the CAnadian pulp and paper industry. In the empirical exercise the domestic markets are the North American market for pulp and newsprint, while the backstop market are the corresponding European markets. One of the main results of this exercise is that the Canadian industry seems to operate under pricing behaviour for both pulp and newsprint, while cyclical dumping on the European market applies only for pulp.     

A dynamic model of advertising by the regulated firm

A profit-maximizing firm subject to price regulation typically seeks alternative variables to control if the regulatory constraint is binding. Advertising may be one such variable. By shifting the demand curve inward or outward between rate hearings, the firm may increase its earnings above the allowed level. Here, a simple discrete-time optimal-control model is proposed to examine the dynamic implications of advertising by the regulated firm. Our results indicate that, in the long run, the combined effect of regulation and advertising leads to a steady-state equilibrium that is closer to the minimum point on the firm's long-run average-cost curve than the original output level. Thus, an invisible-hand property is established that pushes the regulated firm to shift its demand curve toward the minimum point on its long-run average-cost curve in the presence of regulation. As a result, the well-known allocative inefficiency created by rate-of-return regulation (PMC), on which so much has been written over the past 100 years, is reduced (and, under certain conditions, eliminated) if the regulated firm is allowed to advertise.     

The cost effect in third-degree price discrimination

In the presence of a non-constant marginal cost and demand uncertainty, we show that an output increase is no longer a necessary condition for welfare to increase following the introduction of third-degree price discrimination. We thus highlight the existence of an effect that might offset the well known output and misallocation effects of price discrimination. We propose a specific example where this is indeed the case.     

MONOPOLY POWER AND DOWNWARD PRICE RIGIDITY UNDER COSTLY PRICE ADJUSTMENT

A method of 'backward deduction' is used to analyse the decisions of a firm, setting price and quantity before demand observations are made, with the option to adjust price at a cost after demand is observed. It is shown for such a firm that the events of (1) downward price rigidity; (2) overproduction; and (3) a high degree of monopoly power are closely related. The paper distinguishes itself from the previous literature on costly price adjustment in its treatment of disequilibrium situations and focus on monopoly power in relation to price rigidity. The main results are obtained for a linear demand curve and a uniform demand distribution.     

RETAIL PRICE REGULATION AND THE OPTION TO DELAY

ABSTRACT ** :  This paper examines a two-period model of an investment decision in a network industry characterized by demand uncertainty, economies of scale and sunk costs. In the absence of regulation we identify the market conditions under which a monopolist decides to invest early as well as the underlying overall welfare output. In a regulated environment, we consider a monopolist who faces no downstream (final good) competition but is subject to retail price regulation. We identify the welfare-maximizing regulated prices when the unregulated market outcome is set as the benchmark. We show that if the regulator can commit to ex post regulation – that is, regulated prices that are contingent to future demand realization – then regulated prices that allow the firm to recover its total costs of production are welfare-maximizing. Thus, under ex post price regulation there is no need to compensate the regulated firm for the option to delay that it foregoes when investing today. We argue, however, that regulators cannot make this type of commitment and, therefore, price regulation is often ex ante – that is, regulated prices are not contingent to future demand. We show that the optimal ex ante regulation, and the extent to which regulated prices need to incorporate an option to delay, depend on the nature of demand uncertainty.     

Asymmetries in price and quantity adjustments by the competitive firm

Focusing on the crucial role of inventory carry-overs in the production and sales decision, we describe the profit maximizing behavior of a dynamic competitive firm facing random prices. Each firm's behavior is incorporated into a stochastic equilibrium model of the competitive industry with uncertain demand. The industry model exhibits asymmetric cyclical fluctuations of the “Keynesian” sort: when demand is weak, output contracts while price holds at a fixed floor; when demand is strong, price increases as output is constrained by a ceiling. Even in a pure world of constant returns, without increasing costs, the inability to instantaneously coordinate production and sales along with the existence of inventories is sufficient to yield a “backward L” shaped supply curve for the short run.