Comparative Statics
What is Comparative Statics?
Comparative statics is the method of solving a model for equilibrium, changing one exogenous parameter, solving again, and comparing the two equilibria.
You write the model so equilibrium price and quantity depend on exogenous parameters such as income, an input price or a tax rate. Change one parameter, resolve, and the difference between the old and new solutions is the prediction. Signs come almost for free, because the denominator of the standard result is positive whenever supply slopes up and demand slopes down, so the direction of the price change matches the direction of the shift. The method says nothing about the adjustment path or how long it takes, and it assumes the new equilibrium exists and is stable. Change two parameters at once and one of price or quantity usually becomes indeterminate, which is a genuine result rather than a gap in the analysis.
Comparative Statics: a worked example
Let Qd = 100 - 2P + 0.5Y and Qs = -20 + 3P, with income Y = 40. Demand becomes Qd = 120 - 2P, so 120 - 2P = -20 + 3P gives 5P = 140, P* = 28 and Q* = -20 + 3(28) = 64. Now raise income to Y = 60. Demand becomes Qd = 130 - 2P, so 5P = 150, P* = 30 and Q* = 70. The comparative-static derivative is dP*/dY = 0.5 / (3 - (-2)) = 0.1, and 0.1 x 20 = 2, exactly the rise from 28 to 30.
The mistake students make with comparative statics
The classic error is narrating the move as a process: sellers notice a shortage, bid the price up, and so on, as though the analysis tracked the journey. Comparative statics compares two resting points and is silent about everything in between, including whether adjustment takes a week or a decade. The second error is shifting both curves and then confidently reporting a direction for both price and quantity. When supply and demand move together, one variable has a definite direction and the other depends on which shift is larger, and the correct answer is to say it is indeterminate.
Comparative Statics questions
What is the difference between comparative statics and dynamics?
Comparative statics compares equilibrium outcomes before and after a parameter changes, while dynamics models the path between them. A comparative-static answer is a pair of endpoints, such as price rising from 28 to 30. A dynamic answer is a time path, such as price overshooting to 33 within a quarter and settling at 30 after a year. Introductory courses teach the first and assume the second works itself out.
Why does comparative statics assume the new equilibrium is stable?
If the new equilibrium is unstable, the market moves away from it after any small disturbance, so comparing it with the old one predicts nothing anyone would observe. Stability means the model's own forces push the variable back toward the solution, which is what makes that solution the outcome rather than just an algebraic root. The standard case is treated as safe for this reason: with supply sloping up and demand sloping down, excess demand falls as price rises, so price is pushed back toward the crossing.
Can comparative statics give the size of a change or only its direction?
It gives magnitudes as soon as you supply functional forms or elasticities, and directions alone when you know only the signs of the slopes. With linear supply and demand the change is exact arithmetic, as in the worked example above. With general functions you get an expression whose sign you can often pin down even when you cannot compute a number, which is why so many textbook results are stated as directions.
Formula / Example
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