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I: THEORETICAL BACKGROUND OF MARKET ANALYSES

Chapter 1 reviews the most important concepts employed in the traditional supply-demand market equilibrium model. Limited space and the many available textbook treatments of the topic dictate that the exposition be brief.1 However, the chapter provides a refresher for students who have had previous training in economics and is a ready reference for the spreadsheet exercises that follow.

The chapter is divided into four sections. The first reviews the derivation of the supply curve from the marginal cost curves of the firms in an industry. The notes on supply response also discuss the derivation and significance of producer surplus for policy analysis. Because the concept of the price elasticity of supply figures so prominently in the market level analysis, it too has been reviewed briefly.

The second section treats the demand curve in an analogous manner. First, the neo-classical derivation of the demand curve from an aggregation of consumer preferences is discussed, followed by a section on consumer surplus and its implications for judgments about the welfare effects of price policy. Subsequently, the final section on demand analysis makes some brief comments on demand elasticities and their origin.

The Chapter's third section brings together supply and demand curves for an illustration of market level policy analysis. It contains a brief discussion about the difference between the modeling of tradable and nontradable commodities, a topic that is taken up in detail in later chapters. (Tradables prices are assumed to be exogenous to the determination of market equilibria when the country's share of the world market is small. All quantity adjustments are reflected in trade. The prices of nontradables are determined in domestic markets.) 2

The final section in Chapter 1 relates the market level analysis to the concepts of the policy analysis matrix (PAM) presented in Volume I and provides a brief comparison between the two approaches. As the discussion makes clear, the most frequently cited PAM limitations are inherent in the budgeting methods that use average costs and returns as the basis for analysis rather than the marginal values that optimal resource allocation requires. In principle, there is nothing to keep analysts from arranging data on private and social profitability obtained from marginal analysis in the form of a policy analysis matrix. Admittedly, when output prices are permitted to influence the optimal combination of inputs used in production, some problems will arise with the interpretation of the “divergences” row. It will not be clear, for example, whether a divergence is due to a difference between private and social prices or between the changes in the PAMs technical coefficients that take place as relative input and output prices change.

Figure 1.1: Marginal and Average Supply Curves for a Commodity

The Commodity Supply Curve

The Firm's Supply Curve

Figure 1.1 shows the individual firm's short-run marginal (SMC) and average cost (SAC) curves. Underlying the shape and position of the curve are considerations such as the state of technical knowledge, the prices of commodities closely related to commodity X in production, and the supply curves of the factors of production employed in producing commodity X. Given the prices of the factors, there will be some optimum combination of factors for producing any given output, and some minimum marginal cost of producing that output. In the short run, for any given output at which marginal cost is less than the output price and above the shutdown point, the firm has an incentive to expand. (In the area below the minimum of the average cost curve, it will be minimizing losses, not maximizing profits.)

In the long run, the portion of the marginal cost curve that reflects the firm’s supply curve is the part above the minimum of the average cost curve. Only with an output price above the breakeven point is the firm able to pay the resources used in production enough to keep them committed to the production process.

The Industry's Supply Curve

The industry short-run supply curve might be thought of as the horizontal sum of such firm supply curves, S, shown in Fig. 1.2. However, in a competitive industry, all firms will try to expand along their SMC1 curves in response to a price increase from P1 to P2. The combined expansion of all firms may increase the prices of the variable factors of production. If so, each firm's average and marginal cost curves will shift upward to SMC2 and ATC2, and each firm will expand output to Q2, less than the amount Q3 suggested by the original marginal cost curve.

These smaller increases in each firm's output sum to a smaller amount of output at the industry level. Thus the actual supply curve of the industry, S*, is the horizontal summation of firms' SMC curves corrected for factor price changes as industry output expands or contracts. Factor price effects normally operate to reduce the magnitude of the supply response to changes in output prices, that is, they steepen the industry supply curve.

Figure 1.2: Multi-market for commodities

The Elasticity of Supply

Attention has already been directed to the role of factor markets in determining the position and shape of the commodity supply curve. These relationships are made explicit in farm and sector level optimization models where the decision about modeling factor markets such as land and labor is an important determinant of the model's response to prices. Market equilibrium methods, however, while acknowledging the underlying determinants of supply response, use an empirically derived estimate that implicitly incorporates these influences. In this type of analysis, the value that captures the total change in supply in response to a change in the output price is known as the total price elasticity of supply.

The total price elasticity of supply, denoted by the upper case Greek letter epsilon, is defined as:

where all factor and other relevant commodity prices are allowed to adjust to the output price change. In symbols,

where S = supply, DS = change in supply, P = price, and DP = change in price.

Price elasticities of supply are statistically estimated parameters which relate a proportional change in price to a proportional change in quantity. For example, suppose the elasticity of supply for rice in Indonesia is 0.2. This elasticity indicates than for every 10% change in the price of rice, the quantity produced will change by 2%. The changes in quantity and price are normally defined as infinitesimal changes although in practice they may be substantial. P and S are the price and quantity at the point at which the elasticity is measured. In calculations, these are often referred to as initial or base year P's and S's. (It is important to keep in mind that the definition refers to percentage changes in prices and quantities. By making the percentage changes, i.e., by introducing the initial or base year P and S into the definition, elasticities are independent of the units in which quantities and prices are quoted.)

A virtual industry has grown up around the estimation of supply response elasticities. The results of several decades of work in developing countries on supply response in agriculture is summarized in Askari and Cummings (1976).3 The results have been further summarized in Timmer, Falcon and Pearson (1983) and Isabelle Tsakok (1990).4

The definition of the elasticity given above applies to a point on the supply curve. A similar expression can be derived that makes it possible to compute an elasticity in the absence of continuous curves and statistically estimated mathematical functions. This is done by defining an arc elasticity as being the elasticity mid-way between two sets of price-quantity observations, P0, S0 and P1 and S1. In the absence of sufficient data for econometric estimation--such rough and ready methods may be required.

Producer Surplus

The notion of producer surplus follows from the analysis of supply presented earlier. Figure 1.1 showed how each point on the supply curve represents the marginal cost of producing that unit of output. Summing firm specific curves (Figure 1.2) gives the industry supply curve or the industry marginal cost curve. Under the assumption that the area under the curve is made up entirely of variable costs, this amount represents a payment to factors purchased in the market. Since all producers receive the same price in the market, firms other than the marginal firm (one whose revenue is exactly equal to its costs), will be receiving a rent over and above the returns needed to cover the payments to variable factors. The sum of the rent received by all inframarginal firms is called the producer surplus shown by the shaded area A in Figure 1.3. The producer surplus is the return to fixed factors such as land and/or management.

If the price rises to P2, production will increase from Q1 to Q2 and the rent earned by the inframarginal firms will increase by the shaded area B and C in Figure 1.3. Because the supply curve is based on payments to factors, producer surplus is a net concept that takes the additional costs of responding to the increase in the commodity price into account.

Figure 1.3: Producer Surplus

The concept of producer surplus is only one component of measuring the welfare implications of policy changes. Although producers benefit from the increase in the price of commodity X, consumers of the commodity suffer. Their consumer surplus declines. In general, policies that claim to improve overall welfare must benefit one group more than they hurt another.

Surplus concepts measure the change in welfare in moving from one allocation of resources to another. As explained above, the concept of producer surplus indicates the change in income (profits) accruing to owners of factors of production resulting from changes in policy or market conditions. As will be seen, the concept of consumer surplus indicates the changes in real income accruing to consumers also resulting from changes in policy or market conditions.

The Commodity Demand Curve

A demand curve for a particular commodity can be defined as a locus of points, each of which shows the maximum quantity of the commodity that will be purchased at a particular price. It is often useful to conceive of a demand curve as a boundary line separating two spaces, the space to the left of the demand curve representing the points that are attainable under the given conditions of demand, in the sense that the consumers would be willing to buy the indicated quantity at the indicated price, and the space to the right of the demand curve consists of points that are unattainable, i.e., consumers would not be willing to buy the indicated quantity at the indicated price.

Consumer Optimization

The derivation of an individual's demand curve begins with the set of indifference curves that describe the consumer's utility for two commodities. Figure 1.4 displays such an indifference map in which the curves I1 through I3 describe the points at which a consumer is indifferent between the quantities of X and Y at different levels of income. Figure 1.4 also indicates the line describing the consumer's budget constraint that limits the consumer's ability to purchase commodities, line BB. In a simple two-good world, these limitations on purchasing power may be expressed in the form of a budget constraint equation:

Figure 1.4: Consumer Indifference Map

When the consumer purchases all Y and no X, the maximum number of units of Y obtainable is R/Py. This is the vertical intercept in Figure 1.4. Similarly, if the consumer purchases all X and no Y, R/Px represents the maximum units of X obtainable, which is the intercept of the horizontal axis of BB in Figure 1.4. A consumer ordinarily will choose to buy some combination of goods rather than only one good; the alternative combinations available to the consumer may be visualized by connecting the two intercepts with a straight line, the slope of which is -Px/Py.

At point Q in Figure 1.4, the budget constraint is tangent to the indifference curve I2. Choosing the combination of X and Y described by the commodity bundle Q yields the highest utility the consumer can attain, given income and prices. Notice that the consumer is also able to purchase commodity bundles V and T, but these bundles represent lower levels of utility. Commodity bundle S is not available since it costs more than the available income.

The slopes of the indifference curves are defined as the marginal rate of substitution of Y for X. It is the rate at which consumers are willing to trade Y and X at a constant level of income. Maximum utility is reached at the point where the budget line is tangent to the highest possible indifference curve. At this point, the price line and the indifference curve have the same slope, so the condition of maximum utility can be written as follows:

The economic interpretation of this condition is that maximum utility is attained when the rate at which the consumer is just willing to trade Y in order to obtain a unit of X (MRSxy) is equal to the rate at which the consumer is able to trade Y for X (the price ratio).

Derivation of Consumer Demand

With a statement of the equilibrium conditions of consumer choice in hand, it is now possible to derive a consumer's reactions to changes in prices. This analysis leads, in turn, to the derivation of a consumer demand curve.

Figure 1.5a shows the impact of changes in the price of the commodity on consumer demand. Let the price of commodity X be the price that is changing. The budget line can then be written:

Figure 1.5: Derivation of Individual Demand Curves

As Px rises, the slope of the price line (-Px/Py) becomes a larger negative number--the price line becomes steeper. An array of price lines are drawn in Figure 1.5a. Again, the tangencies with indifference curves can be read off, and are connected by a curve called the price-consumption curve (PCC) or offer curve. The PCC curve records the different combinations of X and Y that the consumer will buy at different prices of X, holding income and the price of Y constant. The PCC curve has a negative slope indicating that the quantity of X purchased declines as its price rises (the basic "law of demand").

Using the above analysis, the demand curve, which records the maximum quantity of X that consumers will buy at different prices of X, holding the price of Y and income constant, can now be derived. When the price of X is equal to 2, point A is the consumer optimum and the consumer will purchase X3 units of X. This point is plotted in Figure 1.5b. When the price of X is equal to 3, point B is the consumer optimum and the consumer will purchase X2 units of X. Thus points A, B, C, and all others not shown are quantities of X demanded at different prices, where all other significant impacts on demand, such as income, the price of Y, and consumer preferences, are held constant. The collection of such points forms the income compensated demand curve, labeled D in Figure 1.5b.

Unfortunately, the demand curve just derived is not the one obtained by recording a consumer's observed purchases of a commodity as prices change. The problem is that while nominal income R can be held constant when the price of a commodity declines, the amount of income available for purchasing all commodities increases as a direct consequence of the price change. In other words, any relative price decrease causes a consumer's purchasing power or real income to increase. The demand curve derived in Figure 1.5b has ignored this last effect since the income effect of a price change cannot be easily separated from the price change that brought it about. The ordinary demand curve used in empirical analysis therefore includes both the relative price effects and the real income effects. However, unless the expenditures on the good, and the price variations in question are large relative to the consumer's income, the error in using a directly observed ordinary demand curve in empirical analysis will be small. For this reason, in policy analysis and in applied welfare analysis, the use of ordinary rather than income compensated demand curves is widely accepted.

The Market Demand Curve

Figure 1.6: The Market Demand Curve

The slope and position of the industry demand curve can, like the industry supply curve, be derived from an aggregation of individual consumer choices. Once the individual demand curves are derived from the indifference maps of each consumer, the market demand curve is obtained by horizontally summing over the individual demand curves.

In Figure 1.6 the demand curves d1 and d2 represent demand for the only two households in a particular market. Each point on the market demand curve D is the result of a horizontal sum of individual quantities demanded at a given price. Thus, added horizontally, A = a1 + a2 at price P1 and B = b1 + b2 at price P2. Plotting all points such as A and B defined the market demand curve, labeled D = Shd.

Demand Elasticities

Demand elasticities are similar to the supply elasticities discussed earlier in that they are a ratio of relative changes in price to the corresponding ratio of relative changes in quantity consumed. The price elasticity of demand depends primarily on consumption substitutes. Consequently, the more narrowly the commodity in question is defined, the more substitutes will be available and the greater will be the price elasticity of demand for the commodity. It is usually assumed that, in the course of changing a policy, the quantity of resources owned by different individuals is fixed and so a particular set of factor prices is taken as determining the income and wealth of the individual consumers.

Similarly, tastes and preferences are regarded as fixed. Thus, formulas for computing the elasticity of demand are the same as those shown in the previous section on supply elasticities. However, it must be remembered that there is a difference in the sign of the coefficient. When price increases, quantity demanded decreases. The price elasticity of demand is therefore negative. If the elasticity is -1, it is called a unitary elasticity. (Such a curve--a rectangular hyperbola--will produce a 10 percent decline in quantity for a 10 percent increase in price.) If the elasticity is numerically greater than a -1, for instance, -2, the demand is called elastic. This means that for a 10 percent change in price, there will be a greater than 10 percent change in quantity. If the elasticity is numerically less than -1, for instance, -0.5, the demand is inelastic and a 10 percent change in price will bring about a smaller percentage change in quantity.

Consumer Surplus

Figure 1. 7: Consumer Surplus

The notion of consumer surplus is straight forward. The demand function shown in Figure 1.7 represents the various quantities that consumers are willing to buy at different prices. A perfectly discriminating monopolist, by definition, could extract as revenue the whole area under the demand curve by selling to individual customers at sequentially lower prices. But in a competitive market producers must sell all units of the commodity at the same price. Therefore, the area under the demand curve and above the price line is "surplus" (unspent income) of consumers; consumers are able to obtain a unit of the commodity at a price which is less than their marginal willingness to pay for it. In Figure 1.7, at price P2, consumer surplus is the shaded area A. If the price falls to P1 and consumption increases from Q2 to Q1, consumers gain an additional surplus equal to area B + C. Consumers, therefore, gain from a price fall provided that the demand function slopes downward.

Limitations of Surplus Measures

While the use of surplus measures in policy analysis is quite common, their use requires acceptance of several restrictive assumptions. For example, implicit in all surplus measures is the assumption that a person's money or real income is a reasonable index of individual well-being. Surplus measures cannot account for the fact that an individual may derive satisfaction from such things as leisure as an alternative to maximizing income. Surplus measures should therefore be thought of as only approximate indices of a individual's well-being.

A more serious limitation of surplus measures is that they are technically only suitable in a perfectly functioning environment, i.e. one in which there are no further distortions in the economy preventing individuals from exploiting all opportunities for mutual gain. If this assumption does not hold, analyses of nth best worlds in which numerous distortions exist have shown that no unequivocal welfare conclusions can be drawn.

A final important limitation of surplus measures is that while economic theory demonstrates that the maximization of producer and consumer surplus will lead to the most efficient outcome in a perfectly competitive environment, such an outcome may not be the most equitable one in a normative sense.5 The problem is that the outcome actually achieved depends upon the initial pattern of ownership of society's primary factors of production among the households of the economy. If these factors of production are initially distributed unequally, the efficient outcome may be even more inequitable. If income distribution is a policy goal, the analyst may want to disaggregate the gains and losses due to a policy change by income group. There are potentially a large number of efficient allocations of resources in the economy, each associated with different patterns of factor ownership and different levels of well-being in the economy's various households. Maximizing surplus measures only finds the efficient outcome for a given pattern of ownership of factors of production. It does not indicate how society's resources should be allocated among households initially.

Despite these limitations, surplus measures are widely used in policy analysis because they are relatively easy to calculate and easy to interpret. Most importantly, they do provide a broad indication of which groups benefit and which groups are made worse off as a result of changes in world market conditions or changes in government policy.

Analyzing the Results of Market Models

The definition of supply and demand curves for a commodity opens the way for a discussion of market equilibrium. The graph in Figure 1.8 shows the traditional intersection of supply and demand curves for a commodity in which the equilibrium price is determined in a market without reference to trade.

Figure 1.8: Market Equilibrium

Suppose the supply and demand model is given by the following three equations:

Finding the point of intersection between these two lines can be done in several ways. In the single commodity model, simple graphing techniques can be used. For example, by using a spreadsheet or a calculator, values for S and D can be computed for a range of prices, and the equilibrium price that equates the marginal utility of consumers with the marginal costs of producers can be read from the graph. The solution can also be found algebraically by simple substitution or, as Chapter 4 demonstrates, a spreadsheet's matrix inversion capabilities can be used in the multi-market case.

Although endogenously determined agricultural commodity prices can be found in most economies, commodities whose prices are determined exogenously by government policy or by trade on international markets are likely to be even more important. Price exogeneity actually stimulates rather than dampens the need for multi-market analysis because it means that, in the presence of significant cross price elasticities, the impact of trade or policy related price changes in one market must be absorbed to a greater extent by quantity adjustments in that market. Such a result will be demonstrated in Chapter 3.

The initial exercises in Chapters 2-3 illustrate the welfare implications of price policy interventions when the adjusting variables are the quantities produced, consumed, and traded. An example of this type of approach is presented in Timmer, Falcon and Pearson (p.191-193) in which the authors analyze the impact of a subsidy on Indonesian rice.

Figure 1.9 illustrates the effect of a consumer subsidy on rice from the perspective of the government. In the example, the government is setting the domestic price of rice to both producers and consumers below the border price, causing domestic rice consumption to increase, and domestic production to decline. The deficit (Q3 - Q2) must be purchased by the government at world prices and then resold to consumers at the lower domestic price. In order to do so, it incurs a budgetary cost shown by the shaded area in the diagram. The area is equal to the subsidy on each unit (Pw - Pd) times the number of units imported (Q3 - Q2).

Figure 1.9: The Effect of a Consumer Subsidy

Figure 1.10 examines the policy from the producers' point of view. Obviously, due to the lower price received by producers, producer surplus has been reduced. Without the tax, producers would be earning total rents (profits) equal to the area ACJ. At the lower domestic price, however, producers only earn rents equal to the area FGJ. The difference - the shaded area ACGF - represents the loss in producer surplus due to the tax. From the economy's point of view, the reduction in production from Q1 to Q2 is inefficient. In the absence of the tax, producers could produce the (Q1-Q2) amount of rice at a cost equal to the area Q1Q2GC; yet with the policy the government is having to import this amount of rice at the world price at a total cost equal to Q1Q2BC. The difference, the triangular area BCG, is the additional cost to the economy of importing rice at a higher opportunity cost than domestic production. This triangle is commonly labeled the "production efficiency loss" of the rice subsidy.

Figure 1.11 shows the effects of a consumer subsidy on rice. Consumers are clearly better off; consumer surplus has increased by the area under the demand curve between Pw and Pd, i.e., the shaded area ACEF. However, to generate this increase, the government was required to expend an amount equal to the area CDQ3Q1--the cost of importing this rice at world prices. This amount is larger than the consumers marginal willingness to pay for the additional consumption equal to area

Figure 1.10: Production Efficiency Loss

CEQ3Q1. The difference--the triangle CDE--illustrates the excess the economy had to pay for the extra consumption over and above what consumers were willing to pay. This triangle is often labeled the "consumption efficiency loss" of the rice tax.

Figure 1.11 also makes it clear that only a portion of the subsidy to imported rice is coming from the government. The remainder, i.e., the area ACGF, is a transfer from producers to consumers. This aspect of maintaining low food prices, often supported by concessional sales from developed countries in their foreign aid programs, has had profound negative effects on agricultural output in many developing countries.

The above example illustrates the power of simple market level models in which, because prices are exogenous, adjustments to policy take place entirely through adjustments in commodity trade.

PAMS vs. Market Level Analysis

Another volume in this series provides an example of the PAM (Policy Analysis Matrix) approach developed in the text by Monke and Pearson.6 The following section provides a brief comparison between the PAM and market level approaches and discusses the strengths and weaknesses of each.

As demonstrated, the market level model in the previous section calculates the impact of output price policy on the quantities produced, consumed and traded of a single commodity, and the impact on the government budget. Moreover, the model addresses the distributional impact of price policy between consumers, producers and taxpayers, and the deadweight efficiency losses that arise from distorting price policies.

In contrast, the PAM approach to policy analysis examines the impact of price policies on the costs and returns of agricultural production and how per unit profits change as input and output prices are

Figure 1.11: Consumer Subsidy Efficiency Loss

altered. The strength of a PAM stems from its use of disaggregated crop budget data which allow the straightforward identification of the sources of policy distortions affecting profitability.

Yet by focusing on profits rather than supply response directly, PAMs provide little indication as to how quantities produced may adjust to price changes. Furthermore, because a PAM framework does not incorporate the demand side, it does not provide information on the impact of price polices on consumption, and therefore trade. Of course, without the demand side, the distributional impact between producers and consumers of price policy also cannot be addressed.

The market level approach is also subject to several limitations. One problem associated with this class of models is their heavy reliance on elasticities which, at best, are only guides as to how producers and consumers respond to prices. For example, because elasticities are often measured using historical data, they reflect past behavior and may therefore be inadequate for predicting behavior under new and different policies. Moreover, the information required to determine whether the elasticity is a partial or a total estimate may not be readily available. Finally, market level approaches depend upon point elasticities which provide no information on the true shape of the supply or demand curve. Hence, market level models are technically a legitimate guide only for small changes in policies (points near which the elasticity was measured).

A second important limitation of single commodity market models that employ partial elasticity estimates is their failure to account for multi-market effects. Multi-market effects are the indirect effects of policy and the feedback effects from other markets which arise because of the linkages of the commodity being analyzed with other commodities and with factor markets. For example, when two commodities are substitutes in production (i.e., they compete for the same resources), a single market analysis of either of the two commodities will overstate the impacts of any price change on the market being analyzed and will not provide any information on the impact of the policy on the other market.7 Chapters 3-5 focus specifically on incorporating multi-market effects.

There are strengths and weaknesses to both the PAM and market-level approaches to agricultural policy analysis. The decision as to which framework to use ultimately depends on data availability and the questions being addressed.

1

A good introductory micro text that deals with these issues is Paul Samuelson and William Nordhaus, Micro-Economics, 14th Edition, McGraw-Hill, Inc. It is available in paperback at the Bookstore. If it has been a long time since you last studied economic theory, spending some time with an introductory text is highly recommended.

2

The analysis of the large country case whose tradable commodity prices are also endogenous is not treated in this volume.

3

Hossein Askari and John T. Cummings, Agricultural Supply Response: A Survey of Econometric Evidence, New York, Praeger, 1976.

4

For a survey of the results by commodity, see p. 108 of Timmer, Falcon, and Pearson, Food Policy Systems, Johns Hopkins University Press, Baltimore, MD, 1983. (The entire chapter on “Understanding Farming Systems” is highly recommended.) An even more comprehensive review of empirical estimates can be found in Isabelle Tsakok, Agricultural Price Policy: A Guide to Partial Equilibrium Analysis, Cornell University Press, 1990.

5

This statement assumes that the feasibility of costless lump-sum payments to make the efficient outcome also more equitable, is limited.

6

Eric Monke and Scott Pearson, The Policy Analysis Matrix in Agricultural Development, Cornell University Press, 1989.

7

Note, however, that the impacts on the commodity market under investigation will not be overestimated if total elasticities are used in the analysis. This result is demonstrated in Chapter 4.


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