Economics & Market Microstructure
Baumol’s Cost Disease Formula: Relative Unit Labor Cost & Stagnant Sector GDP Share
Model William Baumol’s (1967) Unbalanced Growth Law: explain why healthcare, education, and live-service unit costs compound at ((1 + g_p) / (1 + g_s))^t when economy-wide wages track progressive-sector productivity.
Why string quartets, universities, and bedside nursing grow relentlessly more expensive even with zero waste!
Formulated by William J. Baumol and William G. Bowen (1966/1967, American Economic Review), Baumol’s Cost Disease explains why labor-intensive personal services (bedside healthcare, classroom teaching, live performing arts) experience relentless above-CPI inflation! Suppose a "progressive" manufacturing/tech sector raises output per hour at annual rate g_p = 3.5%, driving economy-wide nominal/real wages up by 3.5%/yr to retain workers in competitive labor markets, while a "stagnant" personal-service sector can only raise productivity at g_s = 0.5%/yr without degrading quality.
Because unit labor cost equals Wage / Productivity, the progressive sector’s real unit cost stays flat while the stagnant sector’s relative unit cost compounds over t years by the exact factor R(t) = ((1 + g_p) / (1 + g_s))^t! Over t = 25 years at g_p = 3.5% and g_s = 0.5%, relative service unit costs surge by (1.035 / 1.005)^25 = 2.0864x (+108.64%)—and if households keep real output ratio constant (price-inelastic demand), the stagnant sector’s nominal expenditure share s(t) = 1 / (1 + ((1 - s_0) / s_0) / R(t)) expands from s_0 = 15% of GDP to 26.90% of GDP even as every citizen consumes MORE of BOTH goods!
| Horizon t (g_p = 3.5%/yr, g_s = 0.5%/yr, Initial Share s_0 = 15%) | Relative Unit Cost Multiple R(t) | Constant-Real-Ratio GDP Share s(t) |
|---|---|---|
| t = 0 Years (Base Year) | 1.0000x | 15.00% of Total Expenditure |
| t = 25 Years | 2.0864x (+108.64% Real Price Surge) | 26.90% of Total Expenditure |
| t = 50 Years | 4.3531x (+335.31% Real Price Surge) | 43.44% of Total Expenditure |
Baumol Relative Unit Labor Cost Multiplier R(t) = ((1 + g_p) / (1 + g_s))^t
Computes the cumulative relative unit-cost multiple of the stagnant sector (g_s in B3) vs. the progressive sector (g_p in B2) over t years (B4).
=IF(OR(B2 <= -1, B3 <= -1, B4 < 0, B5 <= 0, B5 >= 1), "Invalid Baumol Growth Parameters", ROUND(((1 + B2) / (1 + B3)) ^ B4, 4))Constant-Real-Output Stagnant Sector Nominal Expenditure Share (%) After t Years
Projects the stagnant sector’s nominal budget/GDP share when real quantity ratio stays fixed from initial share s_0 (B5).
=IF(OR(B2 <= -1, B3 <= -1, B4 < 0, B5 <= 0, B5 >= 1), "Invalid Baumol Growth Parameters", ROUND(100 / (1 + ((1 - B5) / B5) / (((1 + B2) / (1 + B3)) ^ B4)), 2))Try the example
Use the original values or change them to test your understanding.