Capital and Labour Allocation in a Two-Sector Macroeconomy

Follow tractors (capital) and workers (labour) from Industry to Agriculture, and observe sectoral output, costs and profits.

Short-run baseline
SHORT RUNLONG RUN
Agriculture is capital-scarce relative to its labour.

The Economy

BASELINE ALLOCATION

Agriculture

Produces crops using tractors and farm workers.
Output: Yag = 0
Cobb–Douglas production function

Capital Kag

Kag = 2
tractor units

Labour Lag

Lag = 6
worker units

Industry

Produces manufactured goods using machinery and workers.
Output: Yind = 0
Cobb–Douglas production function

Capital Kind

Kind = 8
tractor / machine units

Labour Lind

Lind = 6
worker units
Baseline: capital is concentrated in Industry while Agriculture has a relatively high labour-to-capital ratio. The animated reallocation transfers one capital unit and one labour unit from Industry to Agriculture.

Firm-level production, costs and profits

Illustrative Cobb–Douglas technology: Yi = AiKi0.4Li0.6; profit = revenue − wage bill − capital cost.
Sector / phaseKLYRevenueCostsProfit
Agriculture · short run26————
Agriculture · current26————
Industry · short run86————
Industry · current86————
Illustrative values only. Industry profit starts at 300 and rises to 500 at the long-run allocation; agricultural profit also reaches its modelled long-run maximum. A simple misallocation adjustment is used to teach the transition, so reported profit is not just revenue minus the displayed factor costs.

Aggregate output over time

One cycle: output moves above trend, dips below it, then returns to the rising long-run trend.
YTimePotential output (trend)Actual output
Aggregate outputPotential-output trend
Illustrative cycle: boom above trend, downturn below trend, then recovery to trend. The green potential-output path rises with productivity over time.