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Describes the technology that the firm uses to produce goods and services

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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 – PowerPoint PPT presentation

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Title: Describes the technology that the firm uses to produce goods and services


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 firms output

K E q
0 0 0
100 100 100
200 200 200
300 300 300
400 400 400
500 500 500
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 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
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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
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 0 0
400 100 200
400 200 283
400 300 346
400 400 400
400 500 447
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 firms labor demand.
9
Profit 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

10
Profit 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

11
Profit Maximization
TE
Rev
Slope Rev Slope of TE
VMP w
p MPL w
FE
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
204 625
2500 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
250 100 319 70
250 400 1276 70
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

1250
capital
E K
200 1250
400 625
1200 208
625
208
q0 500
200 400
1200
Employment
18
Isoquant 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
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
200 400 600
Employment
C0 45840
21
Isocost 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
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 K
200 1061 1179
655 0 0
C0 45850
C0 45850
0
200
655
Employment
23
Isocost lines
  • Example When w 70
  • 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
24
Long-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
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 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.

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 3667.20
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
374
327
Employment
29
Substitution and Scale Effects
capital
q1
q0
sub
scale

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
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
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.
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