From Cambridge to Eternity: “Variation vs Change”

 

Imagine, as opposed to realizing, we are in the widget “market” of Mini-polis in the month of April 2036 wherein the unit of account is the thaler and the medium of exchange is thaler bills, solid (cash) or “thin-airy” (deposits). Ah, we are in the textbook not in the realty; demand schedules of households and supply schedules of firms exist ex ante, but lining either up in a “nicely” order for the purpose of accounting is ex post.    

            We further suppose the demand schedule of the community for the month instant to be: the demand “curve” p= -2∙q+ 47 (in thalers, meaning thaler bills).

            To begin, we never forget that half a widget is useless, not to mention the infinitesimal thereof. On the flipside, we understand that the intercept 47, which might conveniently be called “the constant,” equals the “marginal benefit” of the very first unit of widget as appreciated by the single most desperate household in town. Somehow, or by imagination more frankly, the collective marginal benefits diminish by two thalers unit by unit.    

         Still further, we imagine the aggregate supply schedule: the supply “curve” p= 1∙q+ 2 (in thalers)*. The intercept 2 (thalers), as “the constant,” represents the cost of production for the very first unit accruing to the single most productive supplier; it may include some overhead costs per unit or lump sum as well. “The constant” has nothing to do with the so-called “fixed cost” primarily because “strategic thinking,” popular may it be, is irrelevant in the run as short as the month, the Certified Public Accounting period of the commonwealth. [*Note: the popular notation p= q+ 2 is false out of mathematics. The price p and the quantity q have different metrics.]

            Needless to say, the supply curve cascades up by one thaler due to the law of diminishing returns. Incidentally, the law does not usually hold true even across the following period, not to mention in the standard short run of two years. Why would any firm stick to the steam engine, for instance?

            We are now ready to clap! The quantity traded was q=15 units, and the market-average price: p= 17 thalers. To our relief:        

1)     The market is cleared;

2)     There is no fractional widgets, sold or unsold at the household or at the firm;

3)     The inventory at the household or at the firm is not a matter in Economics of flows, but in Finance of stocks;

4)     The books of accounting are successfully closed “in equilibrium.”

The task of “market clearance” completed, let us go back home and take a sound sleep. While the time is lapsing over the time until tomorrow, we may dream of some changes in the month of May 2036 soon to arrive.

 

Lessons in the meantime. One, the intercept does not represent a penalty for a failure to demand the widget or for another to supply the widget. It is associated with the very first tangible and visible unit of widget. Two, mathematics are used for the sake of solving the simultaneous calculation only. Never attempt to differentiate or integrate the demand or supply curve. Nay, there in the first place is no such thing as a “curve” exogenous to a dream.