Why wheat in China?

This thesis explores these models under the Price and Revenue Optimization techniques –PRO- and suggests some others and to test which one is better and if any outperforms the current ways all nations mistakenly are subsidizing its agricultural sectors.

Particularly is considered the productive sector of Wheat for China (regarded as the as part of an initiative to provide analyses of agricultural policies for four major agricultural economies outside the OECD area, with Brazil and South Africa).Moreover, wheat always has been considered a very price sensitive product in terms of offer and demand, especially in the difficulty to establish for it a constant tendency and price behavior. The thesis itself wants to present the revenue management (pricing optimization) as a tool to predict correct amount of subsidy in terms of demand and supply availability.

In following chapters, is intended to discuss the role of Basic Price Optimization, and discrete optimization applied for government domestic support and subsidies, finally

69  comparing it with the other traditional models. The forecasting model is the base of a successful revenue management model because this information will be latter used by leader/planners to implement an adequate pricing strategy. Therefore is also here important to remark the use of Agling-Cosimo FAO-OECD two partial equilibrium model, to establish the projection of the futures supply, demand and price for the following year till 2017. This is the third step of the revenue management process to adjust the optimal pricing to subsidize producers. Leaders/planners must decide how much subsidy they need to apply to fulfill is previous commitments with other nations in terms of supply, for full paying customers, and how many available offer need to leave to provide the out of season offer with low price (and sub-consequent subsidy).

This can be seen as a price optimization problem and later on defined as a problem with supply constrain if we include the Food security levels required by World Organizations.

Later on, as soon as other “real variables” are included, the model get not only more complicated also can present other ways to approach a realistic value to subsidies addressing the supply inventory problem.

70 

Chapter 5: RESEARCH METHODS & MODELING 

5.1. Basic Price Optimization

Under the revenue management theory, is well regarded that basic pricing revenue and organization problem can be formulated as an optimization problem, but always regarding the decision variables and constraints the affect the model output (subsidy). The objective is to maximize profit: total revenue minus total incremental cost from sales. This can be well applied to a producer of an agricultural good. As Landburg, 1989, cited (Phillip, R., 2005, 12 pp.), “a standard example used in economics text to exemplify the price response function is wheat: The best example to keep in mind is that of a wheat farmer, who provides a minuscule percentage of the wheat grown in the world. Regardless of whether he produces 10 bushels or 1,000, he remains too small to have any impact on the going market price… If he tries to charge even a fraction of a penny more, he will sell no wheat, because buyers can just as easily buy from someone else. If he charges even a fraction of a penny less, the public will demand more wheat from him than he can possibly produce.”^o

The key elements of the optimization problem are the price-response function in terms of willingness to pay and the incremental cost of sales. In the case of agricultural commodities, the second part is easy to cover, and in the case that can be dependent on the fluctuation of prices in agricultural supplies, usually don’t represent a big gap between the normal and well establish cost of producing a commodity. This thesis is intended to formulate and solve the pricing and revenue optimization problem for a single product (wheat) in a single market (China) without supply constraints. Although this doesn’t match the real world circumstances, is a good approach to define and present the revenue management techniques as a good alternative option at the moment of define an agricultural support policy.

A fundamental input to any price and revenue optimization (PRO) analysis is the price-response function (or curve) d(p). There is one price-response function associated with

o Phillip, R., 2005.

71  each combination of product, market-segment, and channel in the price response curve that in the case of a perfectly competitive market has the shape of a square (cube depending on the dimension evaluated). In this sense is very important to remark that the price-response function, d(p), specifies demand for the product of a single seller as a function of the price, d, offered by that seller. This contrast with the concept of a market demand curve which specifies how an entire market will respond to changing prices. In the case of agricultural commodities trade, different nations competing in the same market face different price-response functions because the price-response functions may differ due to various factors, such as the effectiveness of production, their international trade agreements, perceived customer differences in quality, product differences, volumes, location, etc.ⁱ

Commodity producers, such as the wheat farmer, have no pricing decision –the price is set by the operation of the larger market, and these operations are dependent on domestic and global policies. I.e., in a competitive market, each country only has to worry about how much output it wants to produce. Whatever it produces can only be sold at one price: the going market price.

Therefore, sellers of true commodities in a perfectly competitive market have no need for pricing and revenue optimization (PRO). But in reality is not the case, true commodities are surprisingly rare: The price-response curves which face most nations demonstrate some degree of smooth price response: As the price increases, the demand declines and demand reaches zero at some satiating price P. That what all the heart of revenue management relies, and quoting for second time the same source (Talluri, K., Van Ryzin, G., 2004, 4 pp.): “The forces of supply and demand and the resulting process of price formation –the “invisible hand”

of Adam Smith – lie at the heart of our current understanding of market economics. They are embodied in the concept of the “rational” (profit-maximizing) firm, and define the mechanism by which market equilibrium are reached.”^t

t Talluri, K., Van Ryzin, G., 2004.

72  Figure 10: Typical price response curve for basic commodity prediction

Important to remark in here is that the price-response functions used in PRO analysis are time-dependent. Is possible to set prices that will be in place for some finite period of time and at the end of each period we have the opportunity to change prices. The demand expected to see at a given price will depend on the length of the time period the price will be in place. 

In example there is no single price-response function without an associated time interval, and that’s why is so applicable to commodity trade and a good option to subsidize producers.

There are many different ways in which product demand might change in response to changing prices but all price-response functions are assumed:

9 Nonnegative price (p≥0).

9 Continuous (there is no gaps in market response to prices).

9 Differentiable (smooth and with well-defined slope at every point): Nevertheless this implies imprecision since the concept use derivatives rather than difference equations.

9 Is a downward sloping (raising prices decreases demand), the foundation for further analysis.

73  9 And finally, and most important, the market is completely competitive perfect or close to it. It is well known that in a perfectly competitive economy market, the market prices and shadow prices will coincide, if we ignore complications introduced by issues of income distribution. The revenue-cost analysis and all the calculations in order to maximize profitability will yield the same result in this case. Market distortions, however, will cause shadow prices and market prices to differ but in a very small amount to be considered for this thesis analysis.

The two most common measures of price sensitivity are the slope and the elasticity of the price-response function: The slope measures how demand changes in response to a price change and equals the change in demand divided by the difference in prices and the price elasticity is defined as the ratio of the percentage change in demand to the percentage change in price. Under these concepts, is important to set the formulas regarding these principles:

9 The slope equals the change in demand divided by the change in prices:

δ (P2, P1) = [d(P2) – d(P1)] / (P2 – P1) 9 Downward sloping: P1> P2 implies d(P1) ≤ d(P2), i.e. δ(P1,P2) ≤ 0

9 The slope at a single price, P1, can be computed as the limit of the above equation as P2 approaches P1:

δ (P1) = lim (h→0) [d(P1 + h) – d(P1)] / h Where d’(P1)is the derivative of the price-response function at P1.

9 For small price changes is possible to write: d(P2) – d(P1) ≈ δ (P1) = (P2 – P1). Just to exemplify, a large slope means that demand is more responsive to prices than a smaller slope.

On the other side, there is the price elasticity of price response functions, the most common way to measure the sensitivity on demand to price, defined as the radio of the percentage change in demand to the percentage change in price. The elasticity equals the percentage change in demand divided by the percentage change in prices:

74 

,  100 d P d P /d P

100 / 

Where ε(p1,p2)is the elasticity of a price change from p1to p2.

This equation can be reduced to:

,  d P d P P

Since downward sloping price-response curve, ε (P1, P2) ≥ 0.

Finally, The price elasticity at a single price, P1, (”point elasticity at P1”) can be computed as the limit of the above price elasticity equation as P2 approaches P1:

   ‐ d'     / d  

In example, the point of elasticity is equal to –1 times the slope of the demand curve times the price divided by the demand. The point elasticity is useful as a local estimate of the change in demand resulting from a small change in price. Is important to note that, unlike the slope, the price elasticity is independent of the units in which the price and demand is measured. In practice, some of these concepts don’t fit with reality, but they are a good approach to explain and implement measures and policies. In this sense, the term price elasticity is often used as a synonym for price sensitivity.

“High price elasticity” items have very price sensitive demand, while ”low price elasticity” items have much less price sensitive demand. Often, a good with price elasticity greater than 1 is described as elastic, while one with elasticity less than 1 is described as inelastic. Elasticity is dependent on whether we measure the total market response if all suppliers of a product change their prices or the price-response elasticity for an individual supplier within the market.

If all suppliers raise prices, the only alternative for customers is to purchase a substitute

75  product or to go without, that’s the importance to take international consented measure to guarantee the global production stable, regarding the food security and keeping the subsidies targeting the producers. If a single supplier raises prices, customers can go to its competitor.

Furthermore, as well as other aspects of price response, elasticity is dependent on the time period under consideration. There may be great difference in price elasticity in the short run and in the long run:

For most products, short-run elasticity is lower than long-run elasticity since buyers have more flexibility to adjust to higher prices in the long run. On the other hand, for many durable goods, such as cars and washing machines, the long-run price elasticity is lower than the short-run elasticity. The reason is that customers initially respond to a price rise by postponing the purchase of a new item.

However, they will still purchase at some time in the future, so the long-run effect of the price change is less than the short-run effect. In the case of agricultural commodities, particularly wheat has low price elasticity as a respond to market price changes (people will by wheat all the time even if prices go up) but for an individual seller, the price elasticity would be expected to be high due to competitiveness. In reality, the price-response function is not simply given.

Demand is the result of each potential customer observing the prices and deciding whether or not to buy a specific product, despite other intrinsic factors that affect the whole system and other extrinsic factors that distorts the commodities markets price.

The price-response function specifies how many more of those potential customers would buy if the price is lowered and how many current buyers would not buy if price is raised. In this sense, the price-response function is based on assumptions about customer behavior. The most important part of models of customer behavior is based on willingness to pay (w.t.p). The willingness-to-pay approach assumes that each potential customer has a maximum willingness to pay (also called “reservation price”) for a given product. Usually,

76  this so called reservation prices are stated in the free trade agreements or inner commercial contracts between nations.

A customer will purchase if and only if the price is less than his/her maximum w.t.p., that’s why is so important to mention here, that to take this concepts to practice, in terms of subsidies, is necessary to eliminate all trade barriers and promote the free trade between nations no matter what inner measure can take place inside the borderlines.

To explain in algebraic ways, the number of customers whose maximum willingness to pay (w.t.p.) is at least P is denoted d(P). Here, d(P) is the number of customers who are willing to pay the price P or more for the product (according to the thesis proposal, this can be the amount of money a producer has to receive in terms to promote production and maintain the supply tie with the food security, the amount of money that government needs to subsidize, is the difference between the real market price (defined by the “invisible hand” of Adam Smith) and the optimized prices obtained by the proper Pricing and Revenue Optimization analysis.

Defining the function w(x) as the w.t.p. distribution across the population, then for any values 0 ≤ p1< p2: _P^P  w x  dx is the fraction of the population that has w.t.p. between P1and P2. Is important to note that 0 ≤ w(x) ≤ 1 for all nonnegative values of x. So, the willingness to pay distribution let D = d(0), i.e. the number of customers willing to pay zero or more – i.e. willing to buy the product at all, be the maximum demand achievable. Then we can derive d(P) from the w.t.p distribution:  d P D  _P w x  dx .

Is important to remark that the price-response function is partitioned into two separate components: the total demand D and the w.t.p. distribution w(x).

5.1.1. The current RM systems dilemma 

Marginal revenue transformation: Lately, several researches present a marginal revenue transformation that transforms any price structure (with any set of constrains) into an

77  independent demand model. This allows all the traditional RM methods (that was invented assuming independent demand) to be used unchanged. The standard availability control methods can be used unchanged provided that the efficient frontier is nested (or approximately nested).

Figure 11: Marginal Revenue transformation inside the PRO process.

Under these conditions, marginal revenue transformation transforms a general discrete choice model to an equivalent independent demand model.  The marginal revenue transformation allows traditional RM systems (that assumed demand independence) to be used continuously. Some authors (Phillips, R., 2005) mentioned that the marginal transformation is valid for: static optimization, dynamic optimization and network optimization.^o

5.2. Discrete Optimization

Some authors stated that discrete optimization has a more realistic way to apply the revenue management concepts in terms of pricing and revenue optimizations than continuous

78  systems, because the most of the entities of interest (demand, supply, prices, agreements and so on), are discrete rather than continuous. Nevertheless, this represents a huge challenge in terms of knowledge to analyze and understand the concepts, discrete optimization is more computationally difficult and the interpretation of data requires a lot of expertise if the main target is the agricultural commodity markets.

Quoting Phillip, R. (2005, 326 pp.): “In continuous optimization we are navigating a smooth surface, looking for the highest point. If the continuous function is differentiable (as we have assumed), either we are at maximum or the local derivatives give us a clear direction to move. In contrast, discrete optimization is like hopping from island to island in an archipelago, looking for the island with the highest peak. When we are on a particular island there may be no indicator to tell us which island to jump to next.”^o In this sense, the above state can explains the nature of global commerce, particularly in the whole mosaic of agricultural goods and related commodities.

The continuous approach is not exact, but is enough. In other words, most of the pricing and revenue optimization problems, and using the RM principles as a guide to correct policy decision, specifically in terms of agricultural subsidies can be a simple (but not ordinary) nearest feasible integer solution that usually can provide a good output to the strategy and actions to take. In the case of discrete approach, can be more accurate but requires complicated formulas and a lot of expertise, that usually and ironically can distorted the researcher mind to take crucial decisions clearly. In summary, depending on the expertise, time and available resources can represent a titanic task.

79 

Chapter 6: RESULTS 

6.1. Period of analysis (1993-2007)

The data available for the analysis and later on forecasting come from the FAOSTAT database (Agriculture Statistics) of Food and Agriculture Organization of the United Nations –FAO- and OECD Review of Agricultural policies for the Chapter of China. Yet though the importance of agriculture in China’s economy has declined, it is still an important sector, accounting for almost 15% of GDP and above 40% of employment^d. Is important here to remark that inside the cereal sector there was also an significant reorganization as land sown to rice and wheat tended to decline, while land sown to maize increased, maybe regarding the bio-fuels increasing offer.

Nevertheless, wheat is a primary agricultural commodity inside China & generally world’s economy. Is well known, that increased food production was accomplished by increasing agricultural land, but the area of cultivated land has been declining and output rising due to higher productivity regarding the greater use of fertilizer, pesticide and mechanical inputs and investment. The safeguard of the environment and the aptitude to develop agricultural productivity are integrally linked, and where markets are not able to take environmental externalities into account, there is a need for effective policies, from the economic perspective, at macro and micro level, a lot of this related issues can be mend through the implementation of well targeted subsidies.

The main agricultural policy measures employed by the government cover producer support measures, general services and consumer support measures. In turn, producer support measures cover both domestic and trade policy measures; these can be through input subsidies (water, fertilizer, seeds in a very low cost) or on the other hand, can be as the form of direct payments in terms of money related with quantities produced or total value of production. In line with its WTO accession commitments, China is not allowed to apply export subsidies. The

80  distortions on grain markets are still relatively high, mostly due to state trading, which

80  distortions on grain markets are still relatively high, mostly due to state trading, which