Microeconomics for calculus experts

I took a microeconomics course with a mediocre professor. My understanding came, in large part, from looking at graphs, inputs, and outputs, deriving the (highly compressible) maths myself. The course assumed little maths background, but an intense maths background (calculus and beyond) made that style of thinking easy.

I waited to write this until I got a score for my economics exam. It was a good score. Apparently my method worked. Here's what I learned. Hopefully you learn something; it would be most helpful for calculus experts taking classes that go light on the maths and leave concepts disparate.

"Marginal" (abbreviated as M) is a prefix meaning "derivative wrt quantity of".

"Utility", for each good, roughly means "satisfaction", and is a function of quantity consumed, U_k(Q_k) for good k. To be as satisfied as possible, maximise the sum over all goods of U_k, at a given sum of P_k·Q_k, where P_k is the unit price of good k. By the method of Lagrange multipliers (∇f = λ∇g), that happens when MU/P is the same for all goods.

"Demand" (resp., "supply") can be seen as a function from price to quantity demanded (resp., supplied), indicating how many of a good would be bought by consumers (resp., sold by producers) in a market. D(P) = Qd, and S(P) = Qs.

Less intuitive, but more mathematically convenient, is to view it as a function of quantity, outputting a price. By that view, demand (resp., supply) is the price paid by the least desparate consumer (resp., charged by the most reluctant producer) when producers in the market have sold to consumers a given total quantity. D(Q) = P, and S(Q) = P. The Ps may differ, but Q is the same.

Demand decreases (resp., supply increases) wrt quantity, sith quantity increases as less desperate consumers, paying less (resp., more reluctant producers, charging more) come to buy (resp., sell) more of the good. If D > S, then the next potential consumer would pay more than the next potential producer would charge, so those consumers would buy more. If S > D, then the most reluctant producer would expect more than the next potential consumers would pay, so those producers would sell less. Except when acted upon by an outside force (government), the stable condition (equilibrium) has S = D.

Vegetarianism-by-ethics decreases meat production by making one stop contributing, as a consumer, to demand. The decrease in demand implies a decrease in equilibrium quantity.

The "X elasticity of Y" is E = dy/dx·x/y. Most often, this is the price elasticity of demand, which is really of quantity demanded. A good is, resp., inelastic, unit elastic, or elastic, when, resp., |E| < 1, |E| = 1, or |E| > 1. Goods tend to have more elastic demand when more substitutes are available. Essential goods have few substitutes — e.g. other drinks are mediocre substitute for potable water, and clean water is the only option for some other purposes — so essential goods tend to be inelastic. Frivolous luxuries have plenty of substitutes — low-end versions of the products, or less fancy things to enjoy — and so tend to be elastic.

Cross-price elasticity has an annoying definition, and is positive for substitutes, but negative for complements (goods best used in combination).

Consumer (resp., producer) surplus is defined in terms of actual quantity and price as ∫₀^Q dx (D(x) - P), or, resp., ∫₀^Q dx (P - S(x)).

Taxes decrease effective demand or supply (as quantities), or increase them (as prices). By "effective", I mean that taxes affect equilibrium price, but consumer and producer surpluses are defined in terms of raw demand and supply. Taxes decrease surpluses by an amount called "deadweight loss". Subsidies act in the opposite direction, but likewise create deadweight loss.

"Average" (abbreviated as A) is a prefix meaning "divided by quantity".

A firm — a single producer or cluster thereof — produces a quantity of a good at a total cost TC(Q). We call FC = TC(0) and V(Q) = TC(Q) - FC.

We distinguish markets for goods by the fungibility of the goods between firms (variety of substitutes), sith they have qualitative differences. "Monopoly" has zero fungibility, which arises from one firm dominating the market. Monopolies are only legal as "natural monopolies" or when they are inevitable for new inventions (emerging industries). "Oligopoly" has low fungibility, which arises from a few firms dominating the market. "Monopolistic competition" has higher fungibility, which arises from many firms competing with meaningfully distinct products. "Perfect competition" has maximal fungibility.

The more fungible the good, the more elastic the demand for any one firm, and so the more the firm is forced to match its price to that of the market around it.

"Profit" is revenue (R) minus cost, i.e. P·Q - TC(Q). P here is the price the firm charges. Firms in any market usually operate by maximising profit. New firms enter markets when they could profit; existing firms leave markets when they are forced into a loss (negative profit).

"Efficient" can mean "productively efficient" (producing quantity to minimise ATC) or "allocatively efficient" (selling at P = MC). A firm efficient both ways necessarily has zero profit. Perfect competition achieves both, in the long run. Monopolies can achieve one or the other only if appropriately taxed or subsidised.

The revenue calculation R = P·Q assumes the firm charges the same price to all consumers. Monopolies can price-discriminate, increasing producer surplus.

Externalities are differences between the moral/social effects of a purchase and the consumer's desire for the purchase. We may seek a social optimum defined as the equilibrium between social benefit and social cost, in place of demand and supply. When there are externalities, the demand/supply equilibrium differs from the social equilibrium. Government action (hopefully) fixes the difference.