1. Lecture 7

2. Profit maximization

3. Profit maximization

4. Profit maximization

5. The Firm’s demand for factors in the long run
Section 15.1
The Firm’s demand for factors in the long run

6. Recap Production and Costs in the Long Run
Firm can adjust employment of capital and labor
Achieve the least cost method of producing a given quantity of output

7. Isoquants Geometry of LR production Least costly method
Requires labeling vertical axis with K, stands for capital
Requires labeling horizontal axis with L, which stands for labor
Requires fixed period of time
Least costly method
Avoid technologically inefficient points which are outside the boundary
General observations about isoquants
Slope downward
Fill the labor-capital plane
Never cross
Convex to origin

9. Marginal Rate of Technical Substitution
Absolute value of slope of isoquant
MPL divided by MPK
Amount of capital necessary to replace one unit of labor while maintaining a constant level of output
If much labor and little capital employed to produce a unit of output, MRTSLK is small
Provides geometric proof that isoquant is convex

11. Marginal Rate of Technical Substitution
The discussion above assumed a one-unit change in labor. More generally, if labor changed by some amount of ∆L, we will have:
and we would have:

12. Choosing a Production Process
Minimizing cost necessary for maximizing profit
Isocost curve
Tracks set of all baskets of inputs employed
Assume cost fixed
Slope: -PL/PK
Firm chooses point where isocost and isoquant curves tangent
Means MRTS = PL/PK
Tangencies lie along firm’s expansion path

14. Firm’s Demand in the LR All factors variable
Assume fixed technology (the production function), rental rate (PK), and market price (PX).
Note that making the assumption that PK is fixed incurs no loss of generosity, as only the relative price matters.

15. Construction of LR Labor Demand
Factor demand vs output demand:
The major difference is that a firm, unlike the case of output demand, has no budget constraint. Instead it has an infinite family of isocost lines, and it could choose to operate on any one of them.
So we call factor demand “derive” from output demand. In short, we have to consider the optimal decision on the output market.

16. Construction of LR Labor Demand
To be more precise, we need to determine how much to produce before we determine exactly how much factors to hire. Eg:
We, again, need to resort to the principle of MR=MC.

19. Construction LR Labor Demand
Substitution and scale effects associated with a factor price change
SubE: When the price of an input changes, that part of the effect on employment that results from the firm’s substitution toward other inputs.
ScaE: When the price of an input changes, that part of the effect on employment that results from changes in the firm’s output

20. Substitution and Scale Effects
Direction of substitution effect and scale effect
Always reduces firm’s employment of labor
An increase in the wage rate raises firm’s long-run total cost curve:
Could rise and become steeper, causing long-run marginal cost to rise.
Could rise and become shallower, causing long-run marginal cost to fall when labor is a regressive factor.

23. Substitution and Scale Effects
Combine effects
Labor demand curve always slopes downward
The proof is available at the appendix

25. SR and LR Relationship In LR
MRP shifts due to adjustments in capital employment
Infinite number of steps

27. The industry’s demand for factors of production
Section 15.3
The industry’s demand for factors of production

28. Industry’s Demand
Sum of individual firm’s demand curve for factor of production
Monopsony
Upward-sloping supply curve
Marginal labor cost (MLC)
Employment and wage rate

30. Industry’s Demand Existence of monopsony
Even a firm that is unique in its industry has no monopsony power, provided that firms in other industries compete with it for the use of the factors.
Monopsony is rare, especially in the long run.

31. The distribution of income
Section 15.4
The distribution of income

32. Distribution of Income
Payments to factors of production
In Figure 15.11, total revenue is A+B+C, of which B+C are paid to workers.
C refers to the opportunity costs for workers.
B is earned as rent.
A is payment to other factors, including the owner’s contribution.

34. Distribution of Income
Returns to scale
Decreasing return to scale (DRS) – AC curve is increasing – Price is higher than AC (why?) – positive profit.
IRS – negative profit.
CRS – zero profit.

35. Distribution of Income

36. Distribution of Income
Returns to scale
Decreasing return to scale (DRS) – AC curve is increasing – Price is higher than AC (why?) – positive profit.
IRS – negative profit.
CRS – zero profit.

37. Distribution of Income
Who benefits?
Recall the tax incidence.
Compare the cases of tax and subsidy.
Now we talk about rent in the case of factor supply.
Bottomline: factors that are supplied relatively inelastically earn more rents and gain more from a rise in demand.