1. Long-Run Demand for Labor
Production Function: Q = F(K, N)
Assume diminishing marginal product of labor and capital
Both K and N are variable in the long run
Isoquant: All combinations of K and N that yield the same level of output
Slope = - MPN
MPK

2. Long-Run Demand for Labor
w = wage (rental rate on labor)
r = rental rate on capital
C = cost
Isocost (Isoexpenditure) line: All combinations of K and N that yield the same level of cost
C = rK + wN
rK = C – wN
K = C/r – (w/r)N
Slope = -(w/r)

3. Long-Run Demand for Labor
Cost minimizing combination of K, N
MPN P*MPN w
MPK P*MPK r = =

4. Long-Run Demand for Labor
Cost minimizing combination of K, N
MPN P*MPN w
MPK P*MPK r = =
Short-run Maximization

5. Peter F. Orazem (1998) “Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy” Review of Agricultural Economics 20:

6. Q=1
Peter F. Orazem (1998) “Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy” Review of Agricultural Economics 20:

7. Q=1
Peter F. Orazem (1998) “Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy” Review of Agricultural Economics 20:

8. K/N W
Peter F. Orazem (1998) “Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy” Review of Agricultural Economics 20:

9. K/N
As w increases relative to r, move to more capital intensive production methods W
Peter F. Orazem (1998) “Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy” Review of Agricultural Economics 20: