Where the goods market and the money market agree at once. Hicks read Keynes as two curves in one plane: the IS curve — output falls as the interest rate rises (investment gets dearer) — and the LM curve — the rate rises as output grows (money gets tighter). They cross at a single point (Y*, r*), and that crossing is the Keynesian cross of macro policy. Feed the parameters in, solve the 2×2 live, read the equilibrium out. These are models, not investment advice.
source J. R. Hicks, Mr. Keynes and the "Classics": A Suggested Interpretation, Econometrica 5(2), 147–159 (1937) — jstor.org/stable/1907242 (paywalled, cited by DOI 10.2307/1907242). Rendered, not quoted.
IS (goods clear): consumption C = c₀ + c₁(Y−T), investment I = I₀ − b·r, and Y = C + I + G. Collecting terms gives (1−c₁)Y + b·r = A, autonomous spend A = c₀ − c₁T + I₀ + G. Downward: r↑ ⇒ Y↓.
LM (money clears): demand L = k·Y − h·r meets real supply M/P, so k·Y − h·r = M/P. Upward: Y↑ ⇒ r↑.
Solve the 2×2 for the current sliders — the unique intersection:
| quantity | value |
|---|
Hicks 1937 built the intersection that sets output and the interest rate together — the frame in which fiscal and monetary shifts can be compared, crowding-out and all.
The LM curve stands on the-quantity-theory: money demand L = kY − hr is what MV = PQ becomes once you let the rate move the velocity term. That sphere is this one's premise; here the money market meets the goods market and neither clears alone.
The blue team re-solves the canonical case each frame and confirms the four claims: unique crossing, LM upward, fiscal raises the rate, monetary lowers it (opposite signs). If red tampers, this badge is where it shows.
Two markets, five behavioural pieces. The middle term is the interest rate r — the price that clears both at once.
| piece | rule | meaning |
|---|---|---|
| C | c₀ + c₁(Y−T) | consumption, c₁ = MPC |
| I | I₀ − b·r | investment falls with r |
| L | k·Y − h·r | money demand |
| G, T | fiscal levers | spending, taxes |
| M/P | real money | the monetary lever |
Slide G (fiscal) or M/P (monetary) in the panel below — the intersection re-solves on the spot, never looked up.
At the base case, solve for the crossing. Push a lever and watch which way each curve slides.
Blue = IS, amber = LM, dot = (Y*, r*). Faint = the base case, so a policy shift is visible as a slide.
What the machine proves, exactly: (Y*, r*) is the unique solution of the 2×2; expansionary fiscal shifts IS right and raises both Y and r — but Y by less than the simple multiplier 1/(1−c₁), the gap being crowding-out; expansionary monetary shifts LM right, raising Y while lowering r. Forecasts from such a model are AMBER — a teaching frame, not advice.
The behavioural equations assume rational, stable agents and ceteris paribus AMBER — idealizations, not laws of nature. Economics is not physics: the curves are a story that clears two markets, useful precisely where its assumptions nearly hold.
"IS-LM is Keynes's own model." Cut. It is Hicks's 1937 reading of Keynes; Keynes never drew these curves. Rendered as Hicks's, credited as such.
"Monetary easing always lowers interest rates." Cut. Only the LM-shift (impact) effect does; once prices, expectations, and the horizon move, the sign can flip. The engine shows the short-run comparative static, labelled.
"The model forecasts the economy." Kept, corrected. It is comparative statics — directions of change, not a prediction. Marked AMBER, never sold as advice.
The red team's move: give the LM curve a downward slope (make the rate fall as output rises). Then IS and LM need not cross uniquely and the fiscal/monetary signs invert. The witness (window 7) is watching.
Flip LM and the money market slopes the wrong way — fiscal now lowers the rate, monetary raises it, and the witness recomputes, disagrees, and turns red. Nothing is faked; the attack is real and it is caught.