[[For a 95m Video Lecture on this post, and related materials, see: Models and Reality ]]
In the context of the radical Macroeconomics Course I am teaching, I was very unhappy with the material available which tries to explain what Keynes is saying. In attempting to explain it better, I constructed an extremely simple model of a primitive agricultural economy. This model has a lot of pedagogical value in that it can demonstrate many complex phenomenon in very simple terms. In particular, Keynesian, Marxists, Classical and Neo-Classical concepts can be illustrated and compared within our model. We will show the failure of all neoclassical concepts of labor, Supply and Demand, equality of marginal product, value theory — the whole she-bang — in an intuitive and easy to understand plausible model of a simple economy.
An agricultural economy produces only one good, say corn, using a simple fixed proportions production function. One Laborer working on One Acre of Land can produce 10 units of corn. All the land is owned by Landlords, and they do not do any work themselves. Rather they hire laborers to work their land. The economy functions according to the following rules. At the start of the period, Landlords hire laborers and pay them the going market wage rates in money. Then goods are produced and the market for goods opens. The Landlords retain some of the goods for themselves – this is their profit, or equivalently, their rent. The rest of the goods are put up for sale in the market. The laborers are the only consumers and they purchase the goods with the money they have earned in wages. That ends the period.
First let us consider a static one period economy. To fix ideas and have some concrete numbers, let us assume that there are ten landlords, and each of them owns five acres of land. Suppose the going wage rate is RP 100. Suppose there are only 40 laborers, and that each landlord hires 4 laborers – each would like to hire 5 laborers, but there are not enough laborers to fulfill the total demand for 50 laborers. This model is for a land surplus economy. We will consider the case of labor surplus later.
The landlords will hire 4 laborers each, and pay them Rp 400 as total pay. They will each produce 40 units of corn. All 10 will produce a total of 400 units of corn. They keep some portion of the corn for self-consumption – this portion is the profit. They sell the rest on the open market. We will consider a variety of assumptions which can be used to determine the “self-consumption” (which equals profits and rent).
Assumption A: To start with, let us take a very simple assumption – there is a maximum limit to what one landlord can consume of corn. Set this limit to be 10 units of corn. This is a real economy which produces only food, and food can be consumed only upto a limit – later we will consider more complex situations.
Coming back to the agricultural economy, each landlord produces 40 units of corn, and consumes 10 units. He has 30 units of corn left for sale. All 10 landlords have a surplus of 300 units of corn for sale. The consumers are ONLY the laborers, who have earned a total of Rp 4000 = 40 x 100. In a one period static economy, they have no use for money, except to buy corn. So all of the wage income will be spent for corn. Thus the price of corn will be 4000/300 = 13.33 Rp per unit. Each laborer can buy 7.5 units of corn with his wages, and this will clear the market. All 300 units will be sold for a total of 4000 Rp, which will exactly re-coup the wage bill paid to the laborers by the Landlords. The profit to the landlords is the 10 units of corn which they did not put on the market, but which has a market value of 10×13.33=133.33 Rp.
Even though this is an extremely simple economy, we can use it to illustrate extremely complex phenomena, regarding which the latest microeconomic textbooks only create confusion.
Neutrality of Money: In this simple one period static economy, money is neutral. It disappears from the calculations. The amount of money paid by the landlords, is exactly recouped from the sales. The amount of money does not matter. If the wage is 1000 Rp, or 500 Rp, inflating the nominal wages and prices by the appropriate factor will lead to exactly the same result – provided that every landlord can afford to pay the initial wage bill. In primitive economy, the quantity theory of money holds perfectly in this economy. The amount of money only affects wages and prices, and exactly in proportion to the quantity. Money has no real effects on the economy. However, money will have real effects if some of the landlords are liquidity constrained and have to borrow in order to pay the initial wage bill of the laborers. This case will be considered later.
Say’s Law: Whether or not Say’s Law holds in this economy is not clear. One way to say that it holds is to consider the total Wage Bill of Rp 4000, and add to this the Profits of the Landlords, which are 1333.33. This amounts to a total earnings generated from production of Rp 5333.33, which is exactly sufficient to purchase the 400 units of corn produced at the market price of 13.33. So the earnings generated by the production process create the demand in exactly the right amount required to purchase the entire amount produced. This is exactly Say’s Law. However, there are many reasons why this point-of-view is wrong. We present one of these arguments below.
Utility of Food: It is reasonable to consider the utility function for food in ABSOLUTE terms, or as a cardinal utility function. Suppose that the marginal utility of corn is MU(C)=110-10C – the first unit of corn consumed yields 100 units and MU decreases linearly until the 10th unit yield 10 units while the 11th unit leads to 0 utility. This is why landlords upper limit for consumption of corn is 10 units. We now resurrect an ancient distinction between USE value and EXCHANGE value, which has been confined to the dustbin of history by modern economics. The USE value of corn has to with biological functions of food in relation to nutrition and health, and these are captured within the cardinal utility function. The EXCHANGE value (or market value) of food is determined by the market conditions to be Rp 13.33 in the above economy. While the USE value is fixed by biology, the market value can vary considerably depending on how we change specifications of how the market works. Use Value is determined by internal psychological and physiological conditions, while Market Value is determined by external market conditions related to production costs, supply, and demand. So, the two cannot be the same.
Complexity: This very simple economy clearly displays the phenomenon of complexity, which is ignored by standard treatments of economics. Suppose that one landlord decides to sell one of the units of corn he has kept for self-consumption – presumably, he can get Rp 13.33 for this unit, which is why the “value” of the 10 units of corn that has been kept for self-consumption has been evaluated to be 13.33 x 10 = 133.33 at market prices. HOWEVER, this market price is an illusion, in the sense that the amount retained by the landlords CANNOT be sold at the going market price. If some additional amount is put on the market, the price will decline by an exactly offsetting amount to keep the gross earnings from sales of the landlords equal to 4000, the gross wage bill.
The Aggregate Production Function: This economy illustrates clearly that the aggregate production is not just the sum of the separate production functions. Each Landlord has a Leontief-type Production function which is C= 10 min(L,5). However the aggregate production function is just constant – total production is fixed at 400 units of corn, because the total amount of labor available to the economy as a whole is 40 units. The marginal product of labor for one Landlord is 10 units of corn. However, any labor hired by one Landlord is one unit lost by someone else, so on an economy-wide basis, the concept of marginal product is not well-defined – that is, if an additional laborer comes into the economy from the outside, he would have a marginal product of 10 units of corn, but in a closed economy this is not possible. The properties of the Aggregate Production function at full employment level are radically different from the properties of the Production functions of individual Landlords. However, when there is unemployment, the properties of the sum of Landlord Productions are the same as that of the Aggregate Production function.
Wage is Less Than Marginal Product of Labor: The marginal product of labor is 10 units of corn, while the real wage is 7.5 units of corn, under the assumptions outlined. For each landlord, they are will to hire additional labor – they have surplus capacity, with one additional acre of land which could accommodate an additional laborer, and make profits. However, the total labor force within the economy is already occupied. In principle, this would lead to an increase in demand for labor, and an increase in the wage. However, increasing nominal wage will not solve the problem. It will only cause inflation in wages and prices. This is a Keynesian phenomenon mentioned in Chapter 2 of Keynes General Theory. The behavior of nominal wage does not govern the behavior of the real wage. The nominal wage is the object of negotiation between the landlord and the laborer. Given observed scarcity – every landlord wants to hire – nominal wage will go up. However, regardless of how the nominal wage is fixed, the real wage will always be exactly the same as the surplus production remaining after the self-consumption, which is 30 units per landlord, and 300 in the aggregate. Thus, excess demand for labor at going nominal wage cannot lead to increase real wages, which might induce entry of more labor, as per classical supply and demand mechanisms in the labor market. Also, the demand for labor at the firm level cannot be aggregated to derive the demand for labor at the industry level. “Complexity” refers to the fact that the whole is not the same as the sum of the parts. Even though the wage is less than the marginal product of labor, the industry as a whole cannot hire more labor, because the sum total of all labor available is already employed by the industry. What is true at the firm level is not true at the industry level.
The Paradox of Thrift: The one period static equilibrium described above can be repeated across periods. In every period, Landlords hire labor and pay them going wage. They consume 10 units of corn, while the laborers purchase the available surplus, ending up with 7.5 units each. The landlords recoup all of the wage bill from the sales of corn. Money washes out of the system, since payments to laborers exactly equal their spending, and the same is true of the landlords. So, there is no inherent tendency towards change in this fairly egalitarian society. However, suppose we introduce some uncertainty into the system. The minimum amount of food required for sustenance is one unit of corn. The laborers decide that there is some risk of not finding a job next period, so they should save some money, so as to be able to buy food next period even if they cannot find a job. In current equilibrium, they are spending their earning of Rp 100 by buying 7.5 units at 13.33 Rp per unit of corn. They decide to buy only 5 units, and save money on 2.5 units of corn, to allow them to survive without a job in the next period. Now the total demand for corn from the laborers is 5 x 40 = 200 units, while the total amount which has been produced is 300 units. Technically, with excess supply, the price of corn will decline. Under the assumptions that we have made, the price could even go to zero, since the surplus cannot be eliminated if laborers have decided to restrict consumption to 5 units, while the landlords have maximum consumption of 10. Let us assume that the price of corn goes down to Rp 10 only, while 100 units of corn remain unsold. The laborers had PLANNED to buy 5 units at 13.33 Rp and spend 66.66 Rp while saving 33.33 Rp. So Ex-Ante Savings were supposed to be 33.33 Rp. However, their collective decision to save leads to a decline in price of corn, enabling them to buy 5 units at 50 Rp, and creating and Ex-Post Saving of 50 Rp. However, next period, the landlords will reconsider their hiring and production decisions. They produced total of 40 units, consumed 10, and has a surplus of 30 units for sale. However, they were only able to sell 20 units. Instead of hiring 4 laborers to produce 40 units, they will now plan to hire only 3 laborers each, in order to produce on 30 units, which will give them a surplus of 20 units, which is what could be sold last period. They have also suffered a monetary loss. They paid 400 Rp to hire 4 laborers, but earned a revenue of 20 x 10 = 200 Rp only. The laborers have saved 200 Rp to use in the next period. Come next period, the demand for labor is only 30 units while 40 laborers are available. The precaution of the laborers has turned into a self-fulfilling prophecy – their anticipation of the possibility of future risk of joblessness has created joblessness! This is Keynesian uncertainty in operation. The desire to save by the laborers reduced the effective demand, and this led to unsold surplus food. This surplus signaled the producers to cut back on production, creating unemployment.
The Marxist Case, Subsistence Wages: We have put an artificial upper bound on the consumption of landlords – this creates surplus production, which must be sold to laborers. Now we remove this bound. Suppose that the landlords do not eat corn – they export corn abroad, and use the revenue to by luxury goods from abroad. Suppose that the subsistence wage is 1 unit of corn – laborers need this much to survive and will not work for less. We can isolate the domestic economy from the international economy by assuming the Rp are used for wages, and in the domestic market for corn, only. The laborers have zero demand for foreign products. We assume that the laborers have no outside options – they must work or starve to death. (Parenthetically, this is what occurred in England after the Enclosures deprived peasants of access to common lands. As Polanyi and others have noted, this is what created the market for labor.) Now the landlords will pay the laborers some nominal wage – just enough to enable them to buy one unit of food. They will also reserve one unit of food for the domestic market, to ensure that the laborers are fed. From the 40 units of production, they will have 36 units of surplus product. All of this surplus will be sold abroad at international prices, and the revenue will be used to create a luxury lifestyle for landlords based on foreign imports. The international price of corn need have no relationship to the domestic price of corn in this model. The domestic price of corn must be maintained at a relatively low level, sufficient to ensure that the nominal wages of laborers allow them to subsist, even if the international prices are high. If the landlords get greedy, and sell too much corn abroad to make excess profits, large scale discontent among laborers can lead to revolutions. Corn is the wage good, and the real wage is computed by taking nominal wage and dividing by price of corn. However, the profits of landlords come from selling surplus corn in international market and using revenues to buy imports. The profits and prices they face have no relationship with domestic price of corn.
Value Theory: So, what is the value of corn? We can distinguish three different values. One the use value to the laborers – it means the difference between life and death. So for them, they must work at whatever wages necessary, to earn enough to buy subsistence quantities. The domestic exchange value of corn is determined by the customary nominal wages, and the political requirements to ensure that domestic price is sufficient to enable the population to eat. The international value depends on the global economy, and the demand of the landlords for foreign goods. So our model differentiates between use value to laborers, domestic exchange value, and international exchange value, and allows all three to be different. Incidentally, we have assumed that Landlords don’t use corn, otherwise the use value to landlords could enter as a fourth factor into this equation.
Supply and Demand: Conventional supply and demand theory fails miserably at explaining the determination of prices and wages within this model. Note that this is a single good model, so that the issue of partial equilibrium versus general equilibrium does not arise. The problem arises from the timing sequence and the complexity issues. The nominal wages are settled at the beginning of the period in the wage bargain between laborers and landlords. It is on the basis of these nominal wages that production decisions are made, and the prices of the goods emerge. So the real wage is an endogenous variable, a product of decisions made about the real wage. This is exactly what Keynes writes in Chapter 2:
The traditional theory maintains, in short, that the wage bargains between the entrepreneurs and the workers determine the real wage … Now the assumption that the general level of real wages depends on the money-wage bargains between the employers and the workers is not obviously true.
This is exactly what our model demonstrates. In the first model, the nominal wages can be set to any level, but the real wage will always come out to be 7.5 units of corn. The bargain about nominal wages between the laborers and the landlords does not determine the real wage. So it follows immediately that the supply and demand for labor cannot be given in terms of “real” variables – neither for laborers, nor for the landlords. Keynes also mentions, without making it an issue, that the wage goods which determine the real wage for laborers are different from the goods consumed by landlords, so the two would have different price deflators. This is also the case in our model.
Supply and Demand theory fails in our model for a LARGE number of reasons. First, consider the supply of labor. In this primitive economy, labor has no outside options, and must work to survive. So they will accept any NOMINAL wage offer, and hope that the money they earn will enable them to buy enough food to survive. At the beginning of the period, when wages are paid, production decisions have not been made, and supply and demand conditions which will exist at the end of the period are not known – they are both determined by the decisions being made at this stage. So profit maximization assumed in textbooks is IMPOSSIBLE – it requires the Landlords to be able to forecast what will happen next period, which depends on a large number of random variables outside their control. If we ask a laborer how many hours of labor will you supply at a given NOMINAL wage, he cannot provide an answer to this question. This is because he does not know how many real goods he will be able to buy with this wage in the next period. Furthermore, the price of the wage goods in the next period cannot be known or predicted because it depends on this decision about the nominal wage which has to be made now. So the supply curve for labor cannot be defined in terms of the nominal wage. It may be possible to define it in terms of the real wage, which is what textbooks do. But this is not legitimate, as pointed out be Keynes, because nobody knows what the real wage is, and this real wage is NOT determined by the bargain between landlords and laborers.
[[For a 95m Video Lecture on this post, and related materials, see: Models and Reality ]]