Economics Tuesday: A perfectly competitive Market

So, I was think about economics, and I was drawn to the idea of competitive markets. For an economist, a market is considered to be its most efficient when it is perfectly competitive. A market is perfectly competitive when the marginal revenue(MR) of a product is equal to its marginal cost(MC).

To explain this further, I need to define what MC and MR are. MC is the change in cost associated with making one more, or one less, widget. Cost is equal to the variable cost plus the fixed cost. Fixed Costs are the costs that do not change (up or down) based on the amount of products produced, examples are: rent, electricity, the company car for the president, the production equipment. Variable Costs are costs that go up or down in proportion to the quantity produced, examples are: production labor, raw material, shipping material, shipping fees, equipment maintenance, etc. Marginal Cost being the change in cost associated with the smallest change in quantity possible ends up being the first derivative of the cost equation: C = VC + FC: d(C) /d(q) = d(VC)/d(q) + d(FC)/d(q). Since fixed cost is a constant, it becomes MC = d(VC)/d(q).

The second definition, MR, is a close cousin of MC: it is the change in revenue (up or down) due to the smallest possible change in quantity of production. Revenue equals Price times Quantity. Again, the first derivative of the Revenue equation is the Marginal Revenue; thus MR = d(r)/d(q) = d(Pq)/d(q). Since P is a constant, the equation can be simplified to MR = P * d(q)/d(q); or, MR=P. This is somewhat intuitive in that if you sell one more widget, you should get the price of the widget as your increase.

So, now that I have defined MC and MR, why is it that a market is perfectly competitive when MC=MR? Here’s why, when MCMR, the firms are losing money, it costs more to produce an extra widget than what is made off of it. As the firms start to lose money, some firms will leave the market, as they do so, the surviving firms will raise their prices (less competition to keep the prices down) until MR is equal to MC.

The natural question is this: if MC=MR and profit, pi, is equal to revenue minus cost, are you saying that firms make no profit when the market is perfectly competitive? Yes, and no. Firms do make a profit, but not economic profit. This is different in that the firms allocate a cost of capital in to their cost. Cost of capital is what the investors in the firm must earn to make the investment a success: think of it as interest on a bank account. Economic profit is the profit that exceeds the return on cost of capital. If an investor must make four percent a year on his/her money, and the profit margin on his/her widgets is five percent, economic profit is being made. A perfectly competitive market says that the investor can only make his/her four percent, not anymore. Thus the cost of capital can be recovers, but economic profit does not occur.


Later,

B