David Levhari

On Migration and Risk in LDCs

The authors develop the hypothesis that aversion to risk rather than expectations of higher income is the primary motivation for rural-urban migration in developing countries. This hypothesis maintains that an optimizing risk-averse small-farmer family will try to place a family member in the urban sector in order to diversify its income portfolio. An additional hypothesis related to risk is also considered at the individual rather than the family level. (ANNOTATION)

The Internal Organization of the Firm and the Shape of Average Costs

Do costs of coordination limit the size of firms? Do they lead to rising average costs at high output levels? A simple model of a firm which employs production and administrative labor, and where output is declining in coordination time by the latter, answers this question in two steps. First we derive a cost minimizing hierarchical structure for any given size of production labor. This structure shows similarity to that reported in the literature for both business and military organizations. Then we use the administrative technology that is developed to derive conditions under which average costs do eventually rise even in the presence of increasing returns to production labor. The presumption of a limit to the size of firms is shown to hold under reasonable, though not all, conditions

Savings and Consumption with an Uncertain Horizon

This paper studies the effect of lifetime uncertainty on optimal consumption decisions. It is shown that for risk averters changing the distribution of lifetime uncertainty decreases consumption due to the higher probability of having a longer life and increases consumption due to the desire for sure consumption in the present. The stronger of these effects determines the effect of lifetime uncertainty on optimal consumption decisions. The major result is that if the utility function is Cobb-Douglas and the rate of return is not too large relative to the amount of future discounting then lifetime uncertainty will always increase consumption.

Market Structure, Quality and Durability

This paper analyzes the effects of market structure -- monopoly versus competition -- on the quality and durability of goods. Also, it tries to find the impact of government regulation on these variables. The types of quality improvements discussed are: quality as pure substitute for quantity; quality which increases the demand for the good; and quality improvement which increases the durability of the good. In general, it is impossible to deduce that quality is independent of market structure. It depends on the cost structure. The paper shows that when quality is a substitute for quantity, both quality and quantity of the monopoly might fall short of those in the competitive market. Regulating only quality, or only quantity, may increase the monopoly misallocations of resources. In other types of quality improvements discussed, it may turn out that quality and durability may be better or worse in the monopolized industry than in the competitive one. Regulating only quality may improve the resource allocation but not eliminate the bias. Quantity regulation by itself may be sufficient for producing the optimal flow of services.

Uniqueness of the Internal Rate of Return with Variable Life of Investment

Attempts to prove that if, with a given constant rate of discount, we choose the truncation period so as to maximise the present value of the project, then the internal rate of return of the truncated project is unique.

The Pricing of Durable Exhaustible Resources

Partial or total durability characterizes a large class of exhaustible resources. We show that Hotellings r-percent rule will apply to a durable resource produced in a competitive market, but will not apply if the resource is produced in a monopolistic market. However, the r-percent rule does not mean that price is steadily rising. We show that in general the competitive market price will fall initially as the stock in circulation increases, and later will rise as the stock decreases and eventually depreciates toward zero after production ceases. Accounting for durability may thus help explain the U-shaped long-term price profiles observed for many resources.

Duopoly pricing and waiting lines

Abstract The paper deals with a model of duopoly pricing in the context of firms providing services to consumers. Each of the firms has a waiting line of customers arriving randomly. The service provided by both firms is identical and the service time of both firms is assumed to obey the same distribution. Different consumers have different time costs and have to decide whether or not to join one of the lines. It is shown that the Cournot-Nash equilibrium is such that the two firms charge in general different prices. One of the firms specializes in servicing individuals with high cost of time (and the other the rest). Moreover, some examples of non-existence of Cournot-Nash equilibrium and permanent oscillations of prices are shown.

Extensions of Arrow's “Learning by Doing”

In a recent paper1 Arrow discusses the behavior of an economic model in which technological change is related to cumulated gross investment, or to the serial number of the machines used in production. Arrow uses a model of fixed proportions, and for a machine of specified vintage and serial number there is a fixed labor requirement for production. In the following paper we shall show that most of Arrow’s results can be extended to any homogeneous production function of the first degree with the type of technological change discussed by him. The production function shows ordinary convexity. Here we shall distinguish two types of production function according to the properties of the marginal product of labor with zero labor input. In type I the marginal product of labor with zero input is. finite and it is impossible to produce without labor (as an example we have the CES production function with elasticity of substitution smaller than 1). In type II the marginal product of labor with zero labor input is infinite, or it is possible to produce without labor input (as an example we have CES with elasticity of substitution greater than or equal to 1; if it is 1, we have of course the known Cobb-Douglas case). As we shall see, in type I, as in the fixed proportion case, there is discarding of capital. Capital is used up to the time when it is scrapped. We shall ignore physical wear and tear and assume that the economic life of machinery is shorter than its physical life. There is no difficulty, and none of the results would change, if we include an exponential force of mortality. In type II, where marginal productivity is infinite with zero labor input, there is of course no complete discarding.

Decentralization, aggregation, control loss and costs in a hierarchical model of the firm

Abstract We study the multi-divisional firm with the help of a model which links organizational structure and performance. We add to our previous model an ability to delegate decisions at the cost of control loss, and study its effects on both the structure and the average costs of the firm. Our technique involves the aggregation of observations and disaggregation of commands: the aggregation, while simplifying the calculations by superiors and saving time, introduces error into their decisions. The tradeoff between time and error is taken into account in the construction of the hierarchy.

Consumption under Uncertainty

Publisher Summary This chapter presents some of the results in a convenient and integrated context through the use of dynamic programming techniques. It presents a model of consumer choice in which the consumers wealth is derived from earned income and from the return on investments (or savings). The chapter discusses a sequence of optimal policies as the horizon is increased. Under the assumption that no borrowing is allowed, consumption for each value of initial capital decreases as the horizon gets longer. If the random income stream is replaced by its mean, consumption decreases under the assumption that the marginal utility of consumption is convex. The chapter discusses the effect of possible boundary solutions on the optimal policies, for example, zero consumption or the consumption of the entire stock. The importance of these results can be seen from the work of Schechtman.