Title: Describes the technology that the firm uses to produce goods and services
1Short-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 firms output
K E q
0 0 0
100 100 100
200 200 200
300 300 300
400 400 400
500 500 500
2Short-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 firms short-run output
K E q
400 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
3Law 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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
4Law 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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
5Law 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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
6Law 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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
7Law 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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
8The 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 firms labor demand.
9Profit Maximization
- Perfectly competitive firms cannot influence p,
w, or r. Suppose p 200, w 70 and r 30. 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
10Profit Maximization
- Perfectly competitive firms cannot influence p,
w, or r. Suppose p 200, w 70 and r 30. In
the short-run K is constant at say 100. - Revenue
- Short-run profit
11Profit Maximization
TE
Rev
Slope Rev Slope of TE
VMP w
p MPL w
FE
E
The profit max condition
Slope profit 0
E
profit
12Short-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
13Labor 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
204 625
2500 Employment
14Labor 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
250 100 319 70
250 400 1276 70
20
204
319
1276
Employment
15Profit 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
16Long-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
17Isoquant curves
- Example Isoquant curve with q0 500
1250
capital
E K
200 1250
400 625
1200 208
625
208
q0 500
200 400
1200
Employment
18Isoquant curves
- Example Isoquant curve with q1 600
capital
E K
200 1800
400 900
1200 300
900
300
q0 600
q0 500
200 400
1200
Employment
19Isocost 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
20Isocost 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
200 400 600
Employment
C0 45840
21Isocost lines
- Example What happens if costs rise to C1
50,400
1680
1528
1213
capital
1061
747
E K
200 1213
400 747
600 280
595
128
128
C1 50400
200 400 600
Employment
C0 45840
22Isocost lines
- 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 K
200 1061 1179
655 0 0
C0 45850
C0 45850
0
200
655
Employment
23Isocost lines
- Example What happens if r decreases to 27
1528
C0
70(0)
30(1528)
45,840
C0
55(0)
30(1528)
45,840
1179
1061
capital
E K K
200 1061 1179
655 0 327
C0 45840
C0 45840
327
200
655 Employment
24Long-run cost minimization
- Example Suppose w 70 per hour, r 30 per
hour, and q0 500
E 327
K 765
K
C2
30(1200)
70(204)
50280
C
C1
70(327)
30(765)
45840
C0
70(204)
30(834)
39300
E
25Long-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 91.68 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.
26Long 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)
27Long 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 3667.20
C 45840
C 45840
327
Employment
374
28Long Run Demand Curve for Labor
Dollars
When w 70, E 327
When w 60, E 374
70
60
DLR
374
327
Employment
29Substitution and Scale Effects
capital
q1
q0
sub
scale
Employment
30Elasticity 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)
31Imperfect 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
32Imperfect 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
firms 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
33Other 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.