A firm hires labor up to the point where MPL = real wage. Move the wage slider and watch the firm's optimal labor demand respond.
P · MPL = W ⇒ MPL = W / P
How to read it
The downward-sloping curve is MPL — diminishing because of fixed K. The horizontal line is the real wage. The firm hires up to where the two cross. A higher wage → fewer workers hired. Profit before capital costs = total output minus labor bill = Y − W·L.
Euler's theorem: under CRS, paying every factor its marginal product EXACTLY exhausts output. Verify this with the live calculation below.
Y = MPK · K + MPL · L
Total Output Y 203.16
Capital income MPK·K 61.0
Labor income MPL·L 142.2
Sum (must equal Y) 203.16
Why exact?
For any CRS function, F(K, L) = MPK·K + MPL·L exactly (Euler's theorem). For Cobb-Douglas: capital income = α·Y, labor income = (1−α)·Y. There is NO room for economic profit when CRS firms compete freely. Profits in real life come from market power, intangibles, or risk premia.
Click a scenario to apply a shock and see how factor prices, output, and shares respond. Each scenario shows the new equilibrium relative to baseline.
What you should notice
A productivity boom (A↑) raises BOTH the real wage and the real rental — both factors gain proportionally. A capital infusion (K↑) raises wages but lowers the rental (capital is now less scarce). Labor share is constant under Cobb-Douglas (always 1−α) — challenging the empirical finding that the labor share has fallen since 1980.