Uncertainty and the Theory of International Trade

E. Grinols

• Publisher: Taylor & Francis
• Year: 2013
• ISBN:
  9781136454721
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

This book considers the impact of uncertainty on traditional theories of international trade.

1.BASIC CONCEPTS

This chapter introduces the basic framework for discussing uncertainty and the theory of international trade. Three things are done. The elements of the model are presented, uncertainty is introduced, and the Heckscher-Ohlin-like production framework is given for the uncertain environment.

A. Elements of the economy

We will discuss the theory of international trade and uncertainty within the context of a Debreu-type economy as described, for example, in Theory of Value or in Arrow and Hahn, General Competitive Analysis. This framework is broad enough to incorporate virtually every major question of interest with the exception of questions requiring an infinite time horizon.

The following notation will be followed. Given a positive integer l, let R^l denote l-dimensional Euclidean space; and R^l₊ the nonnegative orthant of R^l. If x and y are vectors in R^l, let x . y denote the inner product of χ and y, Σ_hx_hy_h, where x_h and y_h represent the hth components of x and y, respectively.

The model of the world economy with l commodities, m consumers and nfirms can now be reviewed. From the point of view of the world a commodity bundle is a point x in R^l where x_h describes the quantity of commodity h. Commodities are distinguished by their type, location, date of delivery, and, in the case of uncertainty, by state of nature of delivery. Different commodities generally will have different market prices. Hence, an umbrella scheduled for delivery tomorrow if it rains will typically sell for a different contract price than the same umbrella scheduled for delivery tomorrow if it does not rain.

Producers are numbered j=1, . . ., n. The output of producer; is a vector y_j ∊ R^l whose positive components represent net output levels and whose negative components represent net input levels or use of factors. For each firm, output y_j must be chosen from the production set, Y_j, a set of feasible productions Y_j ⊂ R^l. With market prices for commodities given by p ɛ R^l, the market value of firm j is equal to the present value of its profit earned, p . y_j. if there is only one period and no uncertainty, this is the standard measure of current profit.

In the two industry case y₁(α) – F₁(K₁, L₁, α)≤ 0 and y₂(α) – F₂(K₂, L₂, α) ≤ 0 are the production sets of industries 1 and 2 where y_j(α) is output of good j in state of nature α and F_j(·) are production functions dependent on the state of nature α and factor inputs K_j and Lj.¹ Let p_j(α) represent the spot prices for good j in state of nature α, and let w and r be the wage rate for labor and the rental rate of capital, respectively. Deterministic values for w and r result in the case where factor services are contracted for at the beginning of the production period for the certain remunerations w, r. The future state-dependent profit of firm j is then,

π_j(α) ≡ p_j(α)F_j (K_j, L_j, α) – ρwL_j – ρrK_j,

where ρ represents the one period riskless interest rate.

Consumers are represented by their preference ordering ≲_i ⊂ R^l×R^l, and consumption set X_i ⊂ R^l. The preference ordering is interpreted in the following way. If x ∊ X_i, P ⊂ R^l then (x, P) ∊≳_i indicates that all points x’ in set P are preferred or indifferent to x. This is summarized by writing x’ ≳_ix. We assume that ≳_ig is complete and transitive meaning that all x, x’, x” in R^l can be ranked by ≳_i, relative to one another, and that x”≳_ix’, x’ ≳_ix implies x”≳_ix..

A country k consists of a set of producers (Y_j), consumers (X_i,,≳_i) and initial endowment of goods ω_k ∊ R^l, where the set of consumers i and producers j are a subset of world consumers i = 1,. .., m and j=1,....,n, respectively. Let i, j ∊ C_k refer to those i and j making up country k.

A world allocation is a set of consumptions and production choices ((xⁱ), (y_j)), xⁱ, y_j ∊ R^l. The trade vector of country k is equal to z_k ∊ R^l where Σ_iɛCk xⁱ - Σj∊C_k y_j -ω_k ≡ z_k. A world allocation is feasible if xⁱ ∊ X_i, y_j ∊ Y_j for all i and j, and Σ_kz_k = 0.

B. Uncertainty

Examination of the physical components of the world economy ((X_i, ≳_i), (Y_j), ω_k) reveals that the exogenous uncertainty enters the system through its effect on production, endowments, and preferences. For example, the production functions F_j (K_j, L_j, α) involve the random state of nature α, and endowments ω_k depend on the state of nature. Uncertainty also affects the structure of consumption sets X_i and preferences ≳_i, since goods are distinguished by the state of nature. For example, the list of alternative subsistence bundles i...

Table of contents

• Front Cover
• Half Title
• FUNDAMENTALS OF PURE AND APPLIED ECONOMICS
• Title Page
• Copyright
• Title Page
• Copyright
• Contents
• Introduction to the Series
• Introduction: Risk and Trade
• 1. Basic Concepts
• 2. Uncertainty and Security Markets: Demand
• 3. Uncertainty and Production: Supply
• 4. The Theorems of International Trade Theory
• 5. The Gains from Trade
• 6. Tariffs and Quotas
• 7. Commercial Policy
• Appendix
• References
• Index