1. Short-run Production Function
Describes the technology that the firm uses to produce goods and services
E.g.,
The more E and K the higher the firm’s output K E q
100
200
300
400
500

2. Short-run Production Function
Over the long-run K varies, but in the short-run K is fixed
E.g., K = 400 and
The more E the higher the firm’s short-run output K E q
400
100
200
283
300
346
500
447

3. Law of diminishing marginal productivity
The marginal product of labor is (MPL) the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs K E q
400
100
200
283
300
346
500
447

4. Law of diminishing marginal productivity
The marginal product of labor is (MPL) the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs K E q
400
100
200
283
300
346
500
447

5. Law of diminishing marginal productivity
The marginal product of labor is (MPL) the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs K E q
400
100
200
283
300
346
500
447

6. Law of diminishing marginal productivity
The marginal product of labor is (MPL) the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs K E q
400
100
200
283
300
346
500
447

7. Law of diminishing marginal productivity
The marginal product of labor is (MPL) the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs K E q
400
100
200
283
300
346
500
447

8. The Total Product and Marginal Product curves
Value
If p = $1 per unit … w LD
The total product curve gives the relationship between output and the number of workers hired by the firm (holding capital fixed).
The marginal product curve gives the output produced by each additional worker, and the average product curve gives the output per worker.
If we multiply each MPL value by p we get the VPL, the resulting graph is the firm’s labor demand.

9. Profit Maximization
Perfectly competitive firms cannot influence p, w, or r. Suppose p = 200, w = 70 and r = In the short-run K is constant at say 100.
The short-run production function is
Fixed capital expenses:
Variable labor expenses
Total production expenses

10. Profit Maximization
Perfectly competitive firms cannot influence p, w, or r. Suppose p = 200, w = 70 and r = In the short-run K is constant at say 100.
Revenue
Short-run profit

11. Profit Maximization Slope Rev = Slope of TE VMP = w p ∙ MPL = wFE E
The profit max condition:
Slope profit = 0 E
profit

12. Short-run Profit Maximization
Maximum profits occur when the profit curve reaches its peak (slope = 0)
Profit maximizing employment
Labor demand equation
Slope of profit
VMP = (0.5)(200)(10)E –0.5 = w

13. Labor Demand Curve
The demand curve for labor indicates how the firm reacts to wage changes, holding K = 100, r = 30, and p = 200 constant
wage E w
2500 20
625 40
204 70 70 40 20
Employment

14. Labor Demand Curve Recall VMP = (0.5)(200)(100 0.5)E –0.5 = 1000E –0.5
Since p = 200 and K = 100, the most general form of the labor demand curve is
wage 70 40 p K E w
200
100
204 70
250
319
400
1276 20
204
319
1276
Employment

15. Profit Maximization Rules
The profit maximizing firm should produce up to the point where the cost of producing an additional unit of output (marginal cost) is equal to the revenue obtained from selling that output (marginal revenue)
Choose q* so that
MR = MC
Marginal Productivity Condition: this is the hiring rule, hire labor up to the point when the added value of marginal product equals the added cost of hiring the worker (i.e., the wage)
Choose E* so that
VMP = w

16. Long-run Production
In the long run, the firm maximizes profits by choosing how many workers to hire AND how much plant and equipment to invest in
Isoquant: describes the possible combinations of labor and capital that produce the same level of output, say at q0 = 500 units.
Isoquants…
Must be downward sloping
Cannot intercept
That are higher indicate more output
Are convex to the origin
slope is the negative ratio of MPK and MPL

17. Isoquant curves Example: Isoquant curve with q0 = 500 E K 200 1250 400
capital E K
200
1250
400
625
1200
208
625
208
q0 = 500
Employment

18. Isoquant curves Example: Isoquant curve with q1 = 600 E K 200 1800 400
capital E K
200
1800
400
900
1200
300
900
300
q0 = 600
q0 = 500
Employment

19. Isocost lines
The Isocost line indicates the possible combinations of labor and capital the firm can hire given a specified budget
C0 = rK + wE
C0 – wE = rK
Isocost indicates equally costly combinations of inputs
Higher isocost lines indicate higher costs

20. Isocost lines
Example: Suppose w = $70 per hour, r = $30 per hour, and C0 = $45,840.
1528
capital
1061 E K
200
1061
400
595
600
128
595
128
Employment
C0 = 45840

21. Isocost lines Example: What happens if costs rise to C1 = $50,400 E K
1680
1528
1213
capital
1061
747 E K
200
1213
400
747
600
280
595
128
128
C1 = 50400
Employment
C0 = 45840

22. Isocost lines Example: When r = $30
Example: What happens if r decreases to $27 C0
= 70(655)
+ 30(0)
= $45,850 C0
= 70(655)
+ 27(0)
= $45,850
1698
1528
capital
1179
1061 E K
200
1061
1179
655
C0 = 45850
C0 = 45850
Employment

23. Isocost lines Example: What happens if r decreases to $27
Example: When w = $70
1528 C0
= 70(0)
+ 30(1528)
= $45,840 C0
= 55(0)
+ 30(1528)
= $45,840
1179
1061 E K
200
1061
1179
655
327
capital
C0 = 45840
C0 = 45840
327
Employment

24. Long-run cost minimization
Example: Suppose w = $70 per hour, r = $30 per hour, and q0 = 500
E* = 327
K* = 765 K C2
= 70(204)
+ 30(1200)
= 50280 C* C1
= 70(327)
+ 30(765)
= 45840 C0
= 70(204)
+ 30(834)
= 39300 E

25. Long-run cost minimization
This least cost choice is where the isocost line is tangent to the isoquant
i.e., Marginal rate of substitution = w/r
Profit maximization implies cost minimization
The firm produces q0 = 500 units no matter what the K and E are.
The competitive firm is a price taker not a price maker (p = was given)
Hence firm revenue = $45,840 no matter what the K and E are.
On the highest isocost line the firm would lose $4440 because C2 = 50280
On the lowest isocost line the firm is unable to make 500 units
On the “just right” isocost line the breaks even because C* = $45,840.

26. Long Run Demand for Labor
If the wage rate drops, two effects take place
Firm takes advantage of the lower price of labor by expanding production (scale effect)
q can be increased at the same cost!
Firm takes advantage of the wage change by rearranging its mix of inputs (while holding output constant; substitution effect)

27. Long Run Demand for Labor
Example: Suppose w falls to 60 per hour
1528 C*
= 60(374)
+ 30(780)
= $45,840
E* = 327
K* = 765
780
765
capital
p = 91.68
Profit = $
C* = 45840
C* = 45840
327
Employment
374

28. Long Run Demand Curve for Labor
Dollars
When w = 70, E* = 327
When w = 60, E* = 374 70 60
DLR
327
374
Employment

29. Substitution and Scale Effects
capital q1 q0
scale
sub
Employment

30. Elasticity of Substitution
The curvature of the isoquant measures elasticity of substitution
Intuitively, elasticity of substitution is the percentage change in capital to labor (a ratio) given a percentage change in the price ratio (wages to real interest)
This is the percentage change in the capital/labor ratio given a 1% change in the relative price of the inputs (w/r)

31. Imperfect substitutes in labor
Black Labor
An affirmative action program
can encourage the discriminatory firm to minimize cost
A discriminatory firm hires fewer blacks than what is optimal
and hires more whites
(it might have to import them!)
Discriminatory firms production costs are higher than they would have been had they been color-blind q*
White Labor

32. Imperfect substitutes in labor
Black Labor
An affirmative action program forces the color-blind firm to hire more blacks
An affirmative action raises the color-blind firm’s production cost
Which means the color-blind firm must hire fewer whites
A color-blind firm hires relatively more whites because of the shape of the isoquants. q*
White Labor

33. Other types of isoquants
Capital and labor are perfect substitutes if the isoquant is linear.
Hence, the firm can substitute two workers with one machine and not see its output change.
The two inputs are perfect complements if the isoquant is right-angled.
The firm then gets the same output when it hires 5 machines and 20 workers as when it hires 5 machines and 25 workers.