1. Labor demand in the long run
Lecture notes

2. Yesterday
We wrote down the profit maximization problem for the firm in the short-run.
And derived the short-run labor demand curve.
Negatively sloped.
Next, we wrote down the problem in the long-run, when the firm can adjust both K and E.
We wanted to derive the long-run labor demand curve.

3. The two-stage problem
For ease of interpretationm, we can split the problem for the firm into two stages:
Choose the optimal combination of K, E, for a given q.
Choose the optimal level of q.
Then, we can think about what happens when Dw:
A “scale effect” (on q).
A “substitution effect” (on the combination of K,E).

4. The graphical analysis
We depicted the two effects graphically.
Concluding that a Dw will:
Decrease employment (both scale and substitution effects).
Have an ambiguous effect on K (conflicting scale and substitution effects).

5. A more formal analysis Stage 1: Cost minimization
The minimization problem.
Solution: The “conditional demands” for E and K.
They depend only on q, and w/r.
The “cost function” of the firm.

6. Porperties of the cost function
C is increasing in each of its arguments (w, r and q).
C is concave in w and r.
C satisfies Shephard’s lemma.

7. Properties of the conditional factor demands
How do E and K vary with w, r?
Conditional labor demand.
Conditional demand for capital.
Symmetry of cross-price effects.

8. Variation in the level of output
Effect of an exogenous change in q on the total cost.
We can differentiate with respect to q ad take into account the optimality condition.
Total cost rises with the level of output.
At least one factor increases, but the other one doesn’t have to.
Common to assume “normal inputs”.

9. Stage 2: Choosing the level of production
The firm chooses the level of output (the isoquant) that maximizes profits.
The maximization problem.
The first order condition.
Price equals marginal cost.

10. Imperfect competition
Price equals marginal cost, times a “mark-up”.
See Cahuc & Zylberberg.

11. The long-run unconditional demands

12. The “laws” of demand
The unconditional demand for a factor decreases with its cost.