I'm currently reading The Great Equations*; a book about the fundamental mathematical equations that have changed science. Equations included are the Pythagorean Theorem, E=mc^{2 } and Euler's equation among others. This got me thinking, what are the great equations in economics? In no particular order, here's an incomplete, premature and highly biased list of 5 great equations in economics**--with apologies for the mathematical notation that is difficult to replicate in Typepad. These aren't all 'equations' in the mathematical sense, but rather mathematical-looking expression that represent familiar economic concepts.

Feel free to disagree or suggest your own favorite in the comments.

- The Fundamental Condition for Efficiency. As I tell my students: If you don't know the answer, you'll always get at least partial credit for giving me some variation of marginal benefits equals marginal costs:

MB=MC

- The Slutsky Equation for Duality: The breakdown of a price change on quantity demanded (Marshallian demand) into its two basic components--a substitution effect (the movement along Hicksian demand ) and an income effect (the shift in the Marshallian demand due to the resulting change in purchasing power).

dx_{j}/dp_{i}=(dh_{j}/dp_{i})-(dx_{j}/dy)x_{i}

- The OLS estimator: Technically a statistical result, but this one is so ingrained in every first year econ PhD's head (at least those who take a basic econometrics course) they can repeat it in their sleep. Say it together now: Beta equals X prime X inverse X prime Y.

B=(X'X)^{-1}(X'Y)

- Roy's identity and Hotelling's Lemma: I can never keep these straight so I list them both together. One gives the relationship between a demand curve and an indirect utility function (Roy's) and the other gives the relationship between a firm's profit function and it's supply curve and input demands (Hotelling's):

x=-(dv/dp)/(dv/dy)

y=d(pi)/dp

x=-d(pi)/dw

- Conditions for equilibrium in the presence of an externality: The recognition that in the presence of an externalitiy, the private producer considers only his own costs (marginal private costs--MPC) while society desires the producer to consider both the marginal private costs and the marginal external costs (MEC). The condition for social efficiency is the foundation for any optimal externality pricing policy (tax or cap'n trade or coasian bargaining).

MB=MPC+MEC

Honorable mentions:

- Rho=1
- P=MR
- MRS=-p
_{1}/p_{2}

*Yes, I'm reading it for fun. My reading tastes are best described as random. Immediately preceding The Great Equations I read Grisham's latest (The Associate).

**You'll note the absence of macro-equations. I've been told in the past that I don't know s*** about Macro, so I'll leave the Macro equations to the more intelligent.

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