Pricing and Trade Policy

  1. Introduction

We want to investigate the economic and welfare implications of pricing and trade policies, including price instruments as well as quantity instruments. The analysis is presented under transaction costs. Transaction costs are those costs that arise whenever resources are used in the process of exchanging goods among agents. The introduction of transaction costs in the analysis exhibits several desirable characteristics. First, if transaction costs vary among agents (e.g., if they increase with the distance between trading agents), then transaction costs can be expected to be higher in international trade (when traders are in different countries) than in domestic markets (when market participants are from the same country). Second, the analysis provides an endogenous treatment of what are the traded versus non-traded goods, depending on the magnitude of exchange costs. This can help explain the existence of “local markets.” Third, in general equilibrium, the transaction costs are themselves endogenous and can be affected by changes in economic policy. For example, market liberalization may contribute to reducing the cost of resources used in exchange, which would further stimulate (beyond the effects of reducing tariffs/quotas) the development of markets and increase the benefits from trade. This suggests significant interactions between policy, transaction costs, market activities and welfare.

The analysis relies on the benefit function and its use in general equilibrium analysis. It considers price and quantity distortions, by investigating the associated distorted market equilibrium, and by studying the implications of domestic and trade policy for resource allocation and welfare under transaction costs.

A significant problem in market liberalization is that it is often part of a second-best strategy. In this context, the reduction or elimination of a subset of distortions in a competitive equilibrium may not be welfare improving. While free trade is efficient under competitive markets, in the presence of trade barriers, a partial move toward free trade may actually reduce welfare. This is of particular interest when domestic policy affects the distortionary effects of trade policy. For example, there are situations where domestic production quotas can help reduce the distortionary effects of export subsidies. This stresses the importance of an integrated analysis of the effects of domestic and trade policy.

  1. A Global Economy

Consider a global economy consisting of m commodities and n economic agents. We distinguish between two mutually exclusive groups of agents: consumers and production units. Let Nc be the set of consumers, and Ns the set of production units. The set of all agents is N = Nc Ns = {1, 2, …, n}. The i-th consumer chooses a consumption bundle xi = (xi1, …, xim)  Xi Rm, i  Nc. We assume that the feasible set Xi is closed, convex, has a lower bound and a non-empty interior, i  Nc. The i-th consumption unit has a preference relation represented by the utility function ui(xi), i  Nc. The utility function ui(xi) is assumed continuous, non-decreasing, and quasi-concave on Xi, i  N.

The allocation of m goods among the n agents also involves production and trading activities. For the i-th production unit, the production activities yi = (yi1, …, yim) are netputs (positive for outputs, and negative for inputs) chosen from the feasible set Yi Rm representing the underlying technology, with yi Yi, i  Ns. The set Yi is assumed non-empty and closed, i  Ns.

Note: The feasible set Yi being defined separately for each firm implicitly assumes no externality across firms. Introducing externalities would require appropriate modifications to the analysis presented below.

Trade involves the vector t = {tijk: i, j  N; k = 1, …, m} . For outputs, tijk is the quantity of the k-th commodity traded from agent i to agent j. When i  j, tijk is the quantity of the k-th commodity “sold” or “exported” by agent i to agent j, or equivalently the quantity “purchased” or “imported” by the j-th agent from the i-th agent. When i = j, this includes tiik, the quantity of the k-th commodity that the i-th agent trades with itself. We consider the case where trade can be costly and involves the use of resources. Let z = (z1, z2, …, zn), where zi = (zi1, …, zim)  Rm is the vector of commodities used by the i-th agent in trading activities, i  N. The trading activities (-z, t) are chosen from the transformation set Z  Rmn consisting of all feasible points involving trade t and the associated vector z. Thus, (-z, t)  Z, where the notation “-z” is used to reflect that the z’s are inputs in the trading process. We assume that the set Z is closed, and that (0, 0)  Z, i.e. that the absence of trade can take place without using any resources. Below, we will interpret the cost of z as “transaction costs” associated with exchange among the agents. Also, we make the following assumption.

Assumption A1: (free tiik distribution).

If (-z, t)  Z, then {(-z, t'): tijk' = tijk for i  j, tiik' = tiik + dik, k =1, …, m, i , j  N}  Z for all dik.

Assumption A1 states that the i-th agent can modify tiik, the quantity of commodity k not subject to trade, without affecting the use of resources z, for all k = 1, …, m, i  N. This means that no resources z are used when agents consume their own production. In other words, transaction costs are relevant only in the presence of exchange between different agents.

Since trade can exist between any two agents, each being either a production unit or a consumer, it will be convenient to treat all agents symmetrically. For that purpose, we let Xi = {0}  Rm be the consumption set of the i-th production unit, i  Ns, and Yi = {0}  Rm be the production set of the i-th consumption unit, i  Nc. This means that the only feasible production for a consumption unit is yi = 0, i  Nc, and that the only feasible consumption for a production unit is xi = 0, i  Ns. Note that, labor being one of the m commodities, consumers can trade labor with production units, which allows for joint production and consumption choices under a single decision-maker (e.g., the case of household production).

Let x = {xi, i  N}, y = {yi, i  N}, where x  X = X1X2…Xn, and y  Y = Y1Y2…Yn.

Definition 1: A feasible allocation is defined as a vector (x, y, z, t) satisfying

jN tij yi - zi, i  N,(1a)

and

xijN tji, i  N,(1b)

where tij = (tij1, tij2, …, tijm), xi Xi, yi Yi, i  N, and (-z, t)  Z.

Equation (1a) states that the i-th agent cannot export more than its production yi net of resources used in trade zi, i  N. And equation (1b) states that the i-th agent cannot consume more than it obtains either from itself (tiik) or from others (ji tjik). Note that summing (1a) and (1b) over i yields

iN xijNiN tijiN yi - iN zi,

which implies that aggregate consumption cannot exceed aggregate production, minus aggregate resources used for trading purpose. Next, we incorporate various domestic and trade policy instruments in the model and investigate their effects on market equilibrium and resource allocation.

  1. Policy Distortions and Market Equilibrium

We consider a market equilibrium where the i-th agent can face two prices for commodity k: piks when commodity k is treated as a production activity, and pikc when commodity k is treated as a consumption activity. The corresponding price vectors are ps = {piks: k = 1, …, m, i  N}  for "producer prices," and pc = {pikc: k = 1, …, m, i  N}  for "consumer prices." Although the case where ps = pc can be seen as an important special case, the distinction between ps and pc will prove important in policy analysis: ps and pc can differ in the presence of distortionary policy.

Consider policy distortions generated by domestic policy as well as trade policy. The policy instruments involve price instruments (i.e., taxes, tariffs and subsidies) as well as quantity instruments (i.e., production and trade quotas). Denote by rijk the unit tariff (unit subsidy if negative) imposed on tijk for commodity k exchanged from agent i to agent j, k = 1, …, m, i, j  N. We denote the unit tariffs/subsidies by the vectors rij = {rijk: k = 1, …, m}  Rm and r = {rij: i, j  N}  Rmn². Partition the set of agents into mutually exclusive groups: N = {D1, D2, …}, where Ds is the set of domestic agents in the s-th country. When i  Ds and j  Ds, then rijk represents an import tariff imposed on the k-th commodity by the s-th country. When i  Ds and j  Ds, then -rijk is an export subsidy imposed on the k-th commodity by the s-th country. As such, r measures price instruments used in trade policy. Alternatively, if (i, j)  Ds with i  Ns and j  Nc, then rijk represents a domestic tax (domestic subsidy if negative) on the k-th commodity, which creates a price wedge between producer price piks and consumer price pikc. As such, r would reflect domestic tax and pricing policy. Allowing for differences between domestic consumer and producer prices and thus price distortions in domestic markets, this conceptual framework provides a fairly general model of pricing policy. In general, taxes or tariffs (rijk > 0) tend to increase consumer prices, decrease producer prices and generate budgetary revenue. Alternatively, subsidies (rijk < 0) tend to increase producer price piks, decrease consumer price pikc and involve budgetary cost. The implications of these revenues/costs for welfare analysis are analyzed below.

Denote by qijk the quantity trade quota imposed on the trade flow tijk of the k-th commodity exchanged from agent i to agent j, k = 1, …, m, i, j  N. For simplicity, we focus the analysis on output quotas, with qijk 0. The quota qijk imposes an upper bound on the quantity traded tijk. Letting qij = (qij1, …., qijm), this gives

tij qij, i, j  N.(2a)

We also consider domestic production quotas qyi restricting the production of the i-th producer. The introduction of domestic production quotas is relevant as they can affect the distortionary effects of trade policy. Again, for simplicity, we focus the analysis on output quotas, with qyi 0 imposing an upper bound on the quantity produced by the i-th producer:

yi qyi, i  Ns.(2b)

We expect the quotas q = {qij: i, j  N; qyi, i  Ns} to generate quota rents to market participants. Denote by Qij the unit-quota rents associated with the quotas qij, and by Qyi the unit quota rents associated with the production quotas qyi. Then, the vector of quota rents is Q = {Qij: i, j,  N; Qyi: i  Ns}. The effects of quota rents on welfare will be discussed below. We are interested in evaluating the effects of the policy instruments  = (r, q) on resource allocation and trade, on the market prices (ps, pc) and on the quota rents Q.

We make the following additional assumption.

Assumption A2: (free g-distribution).

There exists a numeraire good that can be traded between any two agents without using any resource z. Let this good be the m-th commodity, which we call “money”. Throughout the paper, we consider monetary valuation that can be expressed in terms of units of the bundle g = (0, …, 0, 1) . We assume that:

a)if (-z, t)  Z, then {(-z', t): tijk' = tijk for all i, j  N, k = 1, …, m-1; tijm' = tijm + dijm for all i, j  N}  Z for all dijm satisfying tijm + dijm 0,

b)rijm = 0, qijm = + for i, j  N, and qym = +, meaning that neither tariff nor quota exists for the m-th commodity.

Note that condition a) in Assumption A2 states that money (i.e., commodity m) can be exchanged among agents without incurring any transaction cost. And condition b) reflects the fact that the analysis focuses on pricing and trade policy related to the first (m-1) commodities.

Next, consider the case where all agents are price-takers. We focus our analysis on the effects of the policy instruments (r, q) on market equilibrium. We call the associated equilibrium distorted market equilibrium. The objective is to investigate the nature of the distorted market equilibrium and the effects of (r, q) on production decisions y, consumption decisions x, trade activities (z, t), market prices (pc, ps), and quota rents Q.

Definition 2: An allocation (x*, y*, z*, t*) along with market prices ps* = {pis*: pis* g = 1, pis*, i  N}, pc* = {pic*: pic* g = 1, pic*, i  N} and the quota rents Q* 0 is a distorted market equilibrium if

a) (x*, y*, z*, t*) is a feasible allocation,

b) for each i  Nc and all xi Xi,

pic* xi pic* xi* implies that ui(xi)  ui(xi*),

c) for each i  Ns and all yi Yi,

(pis* - Qyi*)  yi* (pis* - Qyi*)  yi,

d) for all (-z, t)  Z,

iNjN (pjc* - pis* - rij - Qij*)  tij* - iN pis* zi*

iNjN (pjc* - pis* - rij - Qij*)  tij - iN pis* zi,

e) for each i  N, pis* 0, pic* 0, with pis* [yi* - zi* - jN tij*] = 0, and pic* [jN tji* - xi*] = 0,

f) for each i, j  N, tij* qij, Qij* 0, Qij* [qij - tij*] = 0, and for each i, yi* qyi, Qyi* 0, and Qyi* [qyi- yi*] = 0.

Condition a) requires feasibility. Condition b) represents economic rationality for consumption units. Condition c) is the profit maximization behavior for production units under production quotas. It considers that firms behave as if they were facing prices (pis* - Qyi*), showing that quota rents Qyi* 0 reduce the incentive to produce. Condition d) states that trade activities maximize profit under trade policy distortions. When i and j represent agents located in different countries, both the tariffs r and the quotas q act as trade barriers that reduce the profitability of trade. Condition e) states the budget constraint for each agent, whether it is treated as a producer (involving prices ps) or a consumer (involving prices pc). Finally, condition f) imposes the quota constraints (2a) and (2b), with the requirement that the quota rent Q* can be positive only if the corresponding quotas are binding.

Note 1: Condition d) has important implications for trade activities under policy distortions (r, q). To illustrate, consider the trade cost function C(t, ) = minz {iN pis* zi: (-z, t)  Z}. In the special case where C(t, ) is differentiable in t and the k-th commodity is an output (tijk 0), the maximization problem implied by condition d) yields the familiar Kuhn-Tucker conditions with respect to tijk:

pjkc* - piks* - C/tijk - rijk - Qijk* 0 for tijk* 0,(3a)

and

[pjkc* - piks* - C/tijk - rijk - Qijk*]  tijk* = 0.(3b)

Equations (3) show how trade policy generates price distortions through the tariffs/subsidies rijk and the quota rents Qijk*. In the context of a competitive market equilibrium, equation (3a) implies that (pjkc* - piks*) C/tijk + rijk + Qijk*, i.e. that the price difference for commodity k between agents i and j, pjkc* - piks*, cannot exceed the marginal transaction cost, C/tijk, plus the price distortion, rijk + Qijk*. And when exchange takes place from agent i to agent j for the k-th commodity (tijk > 0), then (3a) and (3b) imply that (pjkc* - piks*) = C/tijk + rijk + Qijk*. In this case, the price difference (pjkc* - piks*) must equal the marginal transaction cost C/tijk plus the price distortion (rijk + Qijk*). This can be interpreted as the first-order condition for profit maximizing trade under distortionary policy. For example, in the absence of transaction costs where C/tijk = 0, then (pjkc* - piks*) = rijk + Qijk*, showing that (rijk + Qijk*) acts as a “price wedge” between consumer price pjkc* and producer price piks*. Note that in the absence of price distortions (where rijk = 0, Qijk* = 0), this would generate the law of one price: pjkc* = piks* for all i, j  N. This shows that under competitive markets, the law of one price holds only in the absence of both transaction costs and distortionary policy. Alternatively, when C/tijk > 0, transaction costs in (3) create a price wedge between pjkc* and piks*. Thus either policy distortion (rijk 0 and/or Qijk* > 0) or the presence of transaction costs (C/tijk > 0) is sufficient to imply that the law of one price fails. Finally, when transaction costs and price distortions are “high enough” so that C/tijk + rijk + Qijk* > (pjkc* - piks*) for some i and j satisfying (pjkc* - piks*)  0, then the incentive to trade disappears as (3b) implies tijk* = 0. Then, the k-th commodity becomes non-traded between agents i and j. If this happened for all agents, this would imply the absence of market for the k-th commodity. This illustrates that our general approach treats the presence and development of markets as endogenous. It shows the adverse effects that transaction costs and policy distortions can have on trade and market activities. Alternatively, it stresses the role of low transaction costs and market liberalization policies in the creation and functioning of competitive markets.

Note 2: In the case where ps = pc = p, solving for the term (pi* tij*) in condition e) gives

pi* tij* = pi* yi* - pi* zi* - pi* (ji tij*) = pi* xi* - pi* (ji tji*), i  N,

or

pi* (ji tij*) - pi* (ji tji*) = pi* yi* - pi* zi* - pi* xi*, i  N.

This can be interpreted as a “balance of payment” constraint which states that, for any agent i  N, the value of net exports must equal profit, minus the cost of trade, minus consumer expenditures.

4.The Utility Frontier in Distorted Market Equilibrium

To analyze the efficiency effects of distortionary policy, we rely on the concept of utility frontier.

Definition 3: Under policy  = (r, q), U(x*) = {ui(xi*), i  Nc} is on the utility frontier of the economy if x* = {xi*: i  Nc} is feasible and if there does not exist another feasible x such that u(x)  u(x*), u(x)  u(x*).

Since domestic and trade policy  = (r, q) generate distortions that can adversely affect the efficiency of resource allocation, the utility frontier defined above is typically not the Pareto utility frontier (especially since we have assumed no externality). Our objective here is to assess the quantitative and qualitative effects of partial policy reforms (represented by changes in ) on this utility frontier. The following function will prove important in our analysis.

Definition 4: Given the reference bundle g  satisfying g  0, define the i-th agent’s benefit function as

bi(xi, Ui) = max{: (xi - g)  Xi, u(xi - g)  Ui} if (xi - g)  Xi and u(xi - g)  Ui for some ,

= - otherwise,

for i  Nc. The aggregate benefit function is then defined as

B(x, U) = iN bi(xi, Ui),

where x = {xi: i  Nc} and U = {Ui: i  Nc}.

The benefit function bi(xi, ui) measures individual consumer benefit (expressed in units of the commodity bundle g) the i-th consumer would be willing to give up while facing xi to reach the utility level ui. When the commodity bundle g has a unit price, the benefit function can be interpreted as an individual willingness-to-pay measure. And B(x, U) provides a corresponding measure of aggregate consumer benefit. Under the assumptions that the set Xi is convex for each i  N and the function ui(x) is quasi-concave, the benefit function bi(xi, ui) is concave in xi for i  Nc. Then, the aggregate benefit function B(x, U) is concave in x.