Development & Labor Economics
Harris-Todaro Rural-Urban Migration & Unemployment Formula
Solve John Harris & Michael Todaro’s (1970) expected-wage migration equilibrium w_R = (L_M / L_U)*w_M, urban unemployment rate u* = 1 - w_R/w_M, and the Todaro job-creation paradox.
Explain why rural migration continues despite high urban unemployment — and quantify the Todaro Paradox!
John Harris and Michael Todaro (1970) solved a central puzzle of developing-economy urbanization: why do rural workers continue migrating to cities even when formal urban unemployment exceeds 30–40%? When formal urban wages are institutionally set at w_M > w_R (agricultural wage) across L_M formal urban jobs, risk-neutral migrants equate rural certainty wage w_R to EXPECTED urban wage (L_M / L_U) * w_M! Solving w_R = (L_M / L_U*) * w_M yields Equilibrium Total Urban Labor Pool L_U* = MIN(L_tot, L_M * (w_M / w_R)), Equilibrium Urban Unemployment Rate u* = 1 - (L_M / L_U*), and the famous Todaro Paradox: creating 1 new formal urban job attracts w_M / w_R migrants, INCREASING the number of unemployed urban workers by (w_M / w_R) - 1 > 0!
Check by hand with Rural_Wage_wR = 120 (B2), Formal_Urban_Wage_wM = 200 (B3), Formal_Urban_Jobs_LM = 300 (B4), and Total_Labor_Force_L = 1,000 (B5): equilibrium urban labor pool reaches L_U* = 300 * (200 / 120) = 500.00 workers (500 remaining in rural agriculture), leaving U_urb* = 500 - 300 = 200.00 workers in urban unemployment/informal waiting (u* = 200 / 500 = 0.4000 = 40.00%!) and generating (200 / 120) - 1 = 0.6667 EXTRA unemployed urban workers per formal urban job added!
| Harris-Todaro Metric (w_R=120, w_M=200, L_M=300, L=1,000) | Formula | Verified Output |
|---|---|---|
| Equilibrium Urban Labor Pool (L_U*) | MIN(L_tot, L_M * (w_M / w_R)) | 500.00 workers |
| Urban Unemployed / Informal Pool | L_U* - L_M | 200.00 workers |
| Equilibrium Urban Unemployment Rate (u*) | 1 - (L_M / L_U*) | 0.4000 (40.00%) |
| Todaro Paradox Extra Unemployed / Job | (w_M / w_R) - 1 | +0.6667 unemployed / job |
Equilibrium Urban Labor Pool L_U* & Unemployment Rate u* Formula
Cap L_U* cleanly at total national labor L_tot (rural depopulation corner) and require w_M >= w_R > 0 and 0 < L_M <= L_tot.
=LET(w_r, B2, w_m, B3, l_m, B4, l_tot, B5, IF(OR(w_r <= 0, w_m < w_r, l_m <= 0, l_tot < l_m), "Invalid Harris-Todaro Input", LET(lu_eq, MIN(l_tot, l_m * (w_m / w_r)), ROUND(1 - (l_m / lu_eq), 4))))Todaro Paradox Induced-Unemployment Multiplier (w_M / w_R - 1) Formula
Test raising Rural_Wage_wR to 200 (via rural irrigation/productivity investment): induced urban unemployment drops to 0.0000!
=LET(w_r, B2, w_m, B3, l_m, B4, l_tot, B5, IF(OR(w_r <= 0, w_m < w_r, l_m <= 0, l_tot < l_m), "Invalid Harris-Todaro Input", IF(l_m * (w_m / w_r) >= l_tot, 0, ROUND((w_m / w_r) - 1, 4))))Try the example
Use the original values or change them to test your understanding.