Check Your Understanding: The Profit Motive-The Marshallian Diagram

Transcription

1 Check Your Understanding: The Profit Motive-The Marshallian Diagram EC 11, 140, 237 October 16, 2017 Why people not profits" makes no sense in a market economy. Introduction Many people, especially politicians, say that firm should not maximize profits for shareholders, but look out for interest of all the stakeholders, including consumers, workers, those concerned with the environment and other issues of social justice. Economic theory holds that this is fundamentally incorrect and that the only mission that a firm should undertake is to maximize profits for shareholders, not stakeholders. In fact, there is no definition of stakeholders in economic theory. Introducing the idea is just a way to give some consumers more power and influence than they would have in a competitive market. It is a way of defining a social welfare function that seems to get around the Arrow Impossibility Theorem, which after all, remains a real impossibility. The main reason that firms should not do anything but maximize shareholder value is that firms are owned by households. If firms earn the maximum amount possible that will lead to the largest incomes for the households. The more efficient a firm is in maximizing profits, the better off are households. They then can use this extra income to pursue their own goals, whether they are helping the working poor, improving the environment or fighting for social justice. When consumers who wish to do this argue that firms should join forces in these efforts, they are attempting to multiply the impact of their own preferences through non-economic means. In economic theory, this amounts to double counting preferences. The reason is that the same individuals are in the firms as in households. If the preferences of firms are taken into account then some individuals are counted twice. The Marshallian diagram shows how the profit motive is part of the signaling system consumers use to direct firms to produce the goods and services the households want. This what is meant by an efficient allocation of scarce resources. As consumers change their preferences, firms must respond to the change and reorganize production to deliver different goods and services.

2 check your understanding: the profit motive-the marshallian diagram 2 The Marshallian Diagram The diagram is a combination of a market supply and demand (SD), in figure 1, diagram and the cost curve of the representative firm in figure 2. The SD diagram determines the price and total quantity sold in the market. There are usually many firms in a market and in a competitive market, there must be more than one (monopoly) and even more than a few (oligopoly). The average and marginal cost curve for the representative firm is given in figure 2. Assume that there are n firms in the market and n c consumers. The output level is determined by where the price from the SD diagram is equal to the marginal cost for the representative firm. The output is shown as Q from the SD diagram divided by n. The profit is shown in the shaded area and is determined by the difference between the price and average cost at the level of output Q /n. Since average cost includes the capital cost, this profit indicates that the cost of producing the output is higher the costs of the inputs, This is where the efficiency loss occurs. Price is equal to marginal cost but marginal cost is higher than the minimum average cost. Competition in the market will bring down the level of output in the representative firm until the price is equal to both the average and the marginal cost. The profit above the costs of capital attracts additional firms into the market. Assume for the moment that n n + 1, that is,one additional firm comes into the market. This causes the supply curve to shift to the right by S as shown in figure 3. The change in output divided by n + 1 may be greater than, equal to or less than the original value of Q/n. In any event, the total supply increases to Q + Q and the price falls to p. Figure 4 shows that the process leads to lower profits, mainly driven by the fall in the price. Marginal cost, however, is not yet equal to the minimum average cost. If the price does not fall the quantity demanded will not change. Thus the same quantity of demand will have to be shared by a larger number of firms. In this case, P P Q Figure 1: Price and quantity determined Cost P Profit Q /n MC Figure 2: Short-run marginal and average cost S D AC Q (Q + Q)/(n + 1) = Q/(n + 1) which is smaller than Q/n. Only if the price falls will Q > 0. If the profit in the marginal firm is π = pq C(Q) where C(Q) is the cost function of the representative firm, profits will fall so long as π = p Q + Q p C(Q)

3 check your understanding: the profit motive-the marshallian diagram 3 This gives π/ Q = p + Q p/ Q C(Q)/ Q where the term on the right, C(Q)/ Q, is the marginal cost. Since price is equal to marginal cost, in both figures 2 and 4, this last condition can be written as or π/ Q = Q p/ Q π = Q p so that profits fall so long as p < 0. P P P S S Competition in the long run In the long run, more firms enter the industry. This reduces the level of output, Q, for each firm. As Q falls, figures 2 and 4 show that marginal costs falls toward average cost. At the minimum of average cost, marginal and average cost are the same and profit is zero. 1 The process of competition comes to a halt. The result is shown in figure 5. 0 Q Q + Q Figure 3: Profits attract entry of new firm Cost P Profit MC D AC Q (Q + Q)/(n + 1) Figure 4: Profits fall for every firm 1 This does not mean that capital earns no rate of return. Capital is a cost and is paid according to its marginal product. When profits are zero, the firm earns no profits over and above the cost of capital. Cost MC P Profit = 0 AC Q /n Figure 5: Profits fall to zero for every firm

4 check your understanding: the profit motive-the marshallian diagram 4 Numerical examples 1. Demand is: X = αb/p (1) where: α = 0.2 and the budget B = Assume that there are 12,000 customers in the market. The supply is given by the production function Q = K β L (1 β) while labor demand is normally the marginal product. With fixed capital however it is given by L = (Q/K β ) [1/(1 β)] where β = 0.6. The prices of the factors of production are r = 0.25 and w = 1. Let capital be fixed in the short run at K = 2.12 and the number of firms is n = 50. The fixed cost is the cost of capital, r = 0.25 times the quantity of capital and variable costs are wl, while total cost is the sum of variable and fixed. Marginal cost is the change in total cost divided by the change in output, while average is the total cost divided by quantity. Aggregate supply is nq. The supply price is the marginal cost. This is a basic principle of economic logic; firms are only able to supply more output if the price covers its marginal cost. The demand price is derived from equation 1, solved for p. Equilibrium is when the supply price is equal to the demand price. The solution for this problem is given in tables 1 and 2 and shown in figure 6 It is important to see that if this process did not work this way, there would be little justification for profit in a market economy. In the Marshallian diagram, however, the role of profit is clear. It acts as a signaling mechanism for firms to respond to consumer demand. As long as profit is positive more firms will enter the industry and compete with existing firms. This is competition. 2. Now raise the number of firms until the profit goes to zero. Compute the equilibrium price and quantity. Solution: The number of firms is approximately 78. The price falls to Aggregate supply is 88.1 and each firms produces units. Conclusions Without the profit mechanism, firms would have no idea of what the households wanted them to produce. One often hears that firms

5 check your understanding: the profit motive-the marshallian diagram 5 Table 1: The solution Labor Fixed Variable Total Marginal Quantity Demand Cost Cost Cost Cost Source: Made up numbers

6 check your understanding: the profit motive-the marshallian diagram 6 Table 2: The solution (con t) Aggregate Supply Demand Equilibrium Supply Price Price Profit Price average Aggregate Supply Demand cost Supply Price Price Profit Source: Made up numbers

7 check your understanding: the profit motive-the marshallian diagram 7 Figure 6: The Marshallian Diagram should not be greedy profit maximizers" but should be concerned with issues of social justice, racial and sexual equality and the environment: people not profits." The Marshallian diagram shows why it is important for firms to stay focused on profits to the exclusion of issues of social justice or other priorities that firms might wish to pursue. If the economy is to function properly it is best to look to firms for production, efficiency and growth and to government for fairness and social justice, and not the other way around.