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.     

Idiosyncratic Uncertainty and Firm Investment

We test the impact of idiosyncratic demand uncertainty on investment using a panel of 82 Dutch listed manufacturing firms in the period 1984–1995. The measure of uncertainty is constructed by estimating a state space model at the firm level to isolate idiosyncratic uncertainty from other unobserved components. Generalised Method of Moments estimators show that demand uncertainty, which is specific to the firm, depresses firm investment. More interestingly, we find that idiosyncratic uncertainty is more important in explaining firm investment than total uncertainty that mixes idiosyncratic uncertainty with other sources of uncertainty.     

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.     

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.     

Labour Hoarding, Price Rigidity and the Theory of Imperfect Competition under Uncertain Demand

It is shown that a monopolistic firm under uncertainty may be inclined to keep some of its output unsold when demand is low. This gives rise to changes in conventional results. Under uncertainty, a risk-neutral monopolistic firm produces more than in a deterministic environment and it refuses to sell its total output when demand is low, because the marginal revenue could become negative or lower than the cost of selling the product. Moreover, in this framework, prices are shown to be more rigid downwards than upwards. The model also provides a new explanation for labour hoarding.
JEL classification : D 24; D 42     

Imperfect Forward Markets and Hedging

This paper considers a hedging model of a risk-averse competitive firm facing output price uncertainty. Imperfections exist in forward transactions in that the firm faces a downward-sloping demand function for its forward sales. We show that the optimal output and hedge ratio of the firm are, in general, not separable, and are related in a deterministic manner. We also derive some economic implications of production and hedging decisions when firms differ in their attitudes towards risk. A more risk-averse firm is shown to produce less and hedge more than a less risk-averse firm.
(J.E.L.: D21, D81).     

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.     

Costs,prices and profitablity in UK manufacturing

The 1984 input–output tables make it possible to estimate directly the cost structure of any industrial sector. The results of this calculation are presented for the non-food manufacturing sector for the period 1970–87. This cost estimate is found to be part of a co-integrating set with output prices, in contrast to the specification implied by a Cobb–Douglas production function. The other elements of the equilibrium vector are an index of capacity utilization, positively related to the mark-up, and the variance of inflation (proxying inflation uncertainty), which is negatively related. Import prices have an indirect effect on the mark-up, via demand.     

Uncertainty Resolution and Strategic Trade Policy in Oligopolistic Industries

This paper investigates a government's choice of strategic trade policy when the domestic firm observes a private noisy signal about the stochastic market demand while in competition with a rival firm. The government chooses between quantity controls and subsidies to maximize profits of the domestic firm. Assuming that firms compete à la Cournot in a third country, it is shown that the optimal trade policy depends not only on demand uncertainty but also on the predictability of the true market demand by the firms.     

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.     

Risk sharing and export performance with firm heterogeneity

We investigate how market uncertainty affects the export performance of a firm through financial frictions. We first extend Melitz's (2003) heterogeneous firm trade model by incorporating demand shocks, linking the demand uncertainties to the financing costs of firms. In this extension, the default probability is endogenously determined by a firm's productivity and demand uncertainty. Hence, firms with higher productivity or lower market uncertainty are offered lower interest rates and thus show better export performance. As an application, we also show that a risk-sharing mechanism, that pools default risk for a certain group of firms, lowers the default risk. This mechanism allows banks to charge lower interest rates to the member firms and therefore ultimately improves their export performance in both extensive and intensive margins. We find a real-world example of such a mechanism from business groups in Korea. Using Korean firm-level data, we show that the more diversified the business group, the greater the likelihood that its member firms export and the bigger their export revenues. We also show that our results are robust to alternative explanations for Korean business groups’ export competitiveness.     

FIRM AND INDUSTRY OUTPUT WHEN PRODUCT DEMAND IS UNCERTAIN

Previous work has established the partial equilibrium response to product demand uncertainty by a single firm in a competitive industry, but for many purposes the aggregate output response of the whole industry is more important. The paper shows that this depends in a simple and intuitive way upon the attitudes to risk of the industry's constituent firms.     

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.     

THE EFFECT OF FORWARD MARKETS ON MULTINATIONAL FIRMS

This paper presents a model of a risk averse multinational firm under exchange rate risk. The firm, which owns and controls assets in two countries, is engaged in production, sales and forward contracting whenever forward markets exist. First, we investigate the effects of exchange rate uncertainty without any risk sharing markets. It is shown that the firm internalizes missing hedging markets by increasing foreign production and lowering foreign sales. Therefore the firm hedges by repatriating foreign profits in the form of goods. Second, the implications of the existence of forward markets of global market decisions are discussed. It is shown that a separation theorem holds. This does not imply that the multinational firm shifts all the risk into the forward exchange market.     

On the comparison of price and quantity competition under endogenous timing

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with linear demand, and asymmetric constant marginal cost under endogenous timing. It shows that endogenous timing leads to two sequential play with both leader–follower configurations in Bertrand, but simultaneous play in Cournot. Moreover, every firm’s mark-up/output ratio and the two firms’ weighted ‘average’ price are all lower, but the two firms’ weighted ‘average’ output is higher in either of the two sequential Bertrand equilibria than in the simultaneous-move Cournot equilibrium.     

Currency Hedging For Export-Flexible Firms *

This paper examines the production and hedging decisions of a competitive exporting firm under exchange rate uncertainty. The firm possesses export flexibility in that it can distribute its output to either the domestic market or a foreign market, after observing the true realization of the exchange rate. It is shown that the separation theorem does not hold under export flexibility, i.e., the firm's optimal output depends on the firm's preference and on the underlying exchange rate uncertainty. Furthermore, the export- flexible firm underhedges its exchange rate risk exposure in a currency forward market where in the forward exchange rate contains a non-positive risk premium. [D21, F31]     

Export-Flexible Firms and Forward Markets

This paper examines the production and hedging decisions of an exporting firm under exchange rate uncertainty. The firm is export flexible in that it can distribute its output to either the domestic market or a foreign market, after observing the realized spot exchange rate. The firm is a monopoly in the domestic market but a price-taker in the foreign market. It is shown that the separation theorem holds if selling exclusively in the domestic market is suboptimal even under the most unfavorable sport exchange rate. Otherwise, the firm's optimal output depends on its preference and on the underlying exchange rate uncertainty. Furthermore, the export-flexible firm underhedges its exchange rate risk exposure in a currency forward market wherein the forward exchange rate contains a non-positive risk premium. [D21, F31]     

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.     

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.     

Endogenous Co-Leadership When Demand is Uncertain

Consider an oligopolistic industry where production is time-consuming, so that each firm needs to make quantity commitment by producing before the market opens. If demand uncertainty resolves some time before the market arrives, then those firms who produce early behave as simultaneous leaders (co-leaders), whilst those who wait until demand becomes observable will be followers. We discover that, in an n -firm oligopoly, the equilibrium number of co-leaders tends to be in excess of their socially optimal number, albeit both numbers monotonically decrease in the magnitude of demand uncertainty relative to the expected level of demand. We also find that, with demand uncertainty and the possibility of Stackelberg behaviour, whether the excess entry theorem applies depends upon the number of existing followers.