Saving "the Market” out of Cambridge: “Supply Curve”

 

Suppose there in town are five manufacturers of widget: J. Watt & Co. with a machine of steam engine, N. Otto & Co. of internal combustion engine, N. Tesla of electric motor, S. Jobs of CAM, and S. Altman of AI.

             Over the quarter as the communal accounting period, all the firms are fixated each with a single unit of machine or “physical capital” as called in economics. The only way to aggrandize the quantity of production is hiring more “labor” as in economics.

             The capital cost is “sunk” and does not count as far as the particular quarter is concerned. In other words, there is no such thing as a “fixed cost.” With the machine “invariable,” does the labor cost of production remain constant as the unit of widget multiples from one, two, three and on? Unfortunately No, no, no! Each step forward, the “marginal production cost” increases due to the iron law of diminishing returns or the law of increasing marginal cost of production. One great caveat: However steely the law may be, it does not apply to “service industries” which take the vast majority share of modern economy.

            Here, with the term “marginal,” we mean a unit of widget in its entirety. All in all, the “supply schedule” of each firm is cascading up in the diagram with the MPC on the ordinate and the number of units aka the “quantity supplied” on the abscissa. No to mention, the cost is stated in the US dollar, the legal unit of account. Notably, the schedule exists regardless of the price or even the market.

             Good news: We are ready to draw the communal supply curve for the quarter. We just horizontally sum the five schedules up wherever each may be located. We find the supply curve climbing up. Bad news: The curve by providence is beyond mathematical differentiation. More clearly than apparently, the marginal unit is in full (Δq), not anything like infinitesimal of widget (dq).     

             As opposed to Alicia at dinner, we are in the market. Nevertheless, we might or might not be ready to clap. When the demand and the supply curve have a meeting point, there is a unique clapping number of widgets traded, usually called “equilibrium quantity.” Otherwise, no equilibrium, no clapping, no nothing: The market is unsustainable in that particular accounting period.

             A few inquiries: Which of the five would first be able to supply? By engineering, S. Altman would be. We know the last one already. Does the law of diminishing returns apply to the market as a whole? Not necessarily, because at a certain price all the five firms might supply in larger or smaller quantities. Where is the place for the law of diminishing?

             Would the demand curve stay constant over time (T^-1)? Never in this world! Would J. Watt and Co. stick to stem engine? Not in the right mind! Would the number of firms be stable? Not in our lifetime! Would Alicia’s Mom be loyal to a particular supplier? Well yes and no! Would Alicia’s taste for widget remain the same “in the short run”? No, her whim wouldn’t allow it. Would there be a guarantee that any of the quantity, the price, the demanders, the suppliers, the taste and the technology remains the same in the following quarter? No, not at all!

             In fine, where is the beef of the Solow growth model? The beef is everywhere except for in Cambridge’s burgers, whether ham, cheese or ham and cheese.