Production Costs PDF

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Production Costs Summary...

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A Production table Number of workers

Total Output Marginal (total units product produced) (change in total output)

Average product (total output per number of workers)

0 Increasing marginal productivity

Diminishing marginal productivity

Diminishing absolute productivity

1

4

4

4

2

10

6

5

3

17

7

5.7

4

23

6

5.8

5

28

5

5.6

6

31

3

5.2

7

32

1

4.6

8

32

0

4.0

9

30

-2

3.3

10

25

-5

2.5

Definition: The marginal product is the additional output the will be put out by an additional worker, while other inputs (capital) remain fixed. Definition: The average product is calculated by dividing total output by the number of workers that produced that output: AP = TP/L

A Production Function A production function describes the firm’s technology and the relationship between output and factors of production. It tells us the maximum amount of output that can be derived from a given number of inputs. For a fixed amount of capital, the production of output as we increase labor will look like:

1

Output

TP

A

B

C

Number of workers

Output per worker

A

B

C

AP

Number of workers MP Area A: average and marginal productivities are rising Area B: marginal productivity is falling, average productivity still rising but eventually falling; Area C: Both marginal and average productivities falling. When firms make production decisions, the most relevant of the production function is the part exhibiting diminishing marginal productivity (area B). The law of diminishing marginal productivity states that if the amount of one input (capital) is fixed, using more and more units of a variable input (labor) will result in the marginal product of the variable input to start falling after some point. The law of diminishing marginal productivity assumes that at least one input is held fixed and cannot be increased. 2

Total Costs, Fixed costs, and Variable Costs Total costs (TC) are the sum of Total Fixed Costs (TFC) plus Total Variable Costs (TVC): TC = TFC + TVC Total fixed costs: the total costs incurred by the firm for variable inputs that are held fixed in the short-run. If the period under consideration is the long-run, then there are no fixed costs because all inputs in the long run are variable and therefore, the cost associated with those inputs are also variable. Total variable costs are the total costs incurred for variable inputs.

Average Total Costs, Average Fixed Costs, and Average Variable Costs. Average total cost (ATC) of the firm is the total cost divided by quantity. ATC = TC / Q Average fixed cost (AFC) of the firm is the total fixed cost divided by quantity. AFC = TFC / Q Average variable cost (AFC) of the firm is the total variable cost divided by quantity. AVC = TVC / Q Average total costs can also be expressed as the sum of AFC and AVC ATC = AFC + AVC In deciding how many units to produce the most important variable is the marginal cost – the increase (decrease) in total costs from increasing (decreasing) output.

3

Graphing cost curves To gain greater understanding of cost concepts, it is a good idea to draw a graph, with quantity on the horizontal axis and a dollar measure of various costs on the vertical axis. 1. Total cost curves 2.

Costs

TC

VC

Output Note: The difference between total costs and total variable costs is the total fixed costs. The total variable cost curve has the same shape as the total cost curve – increasing output increases variable costs and therefore total costs. The rate at which variable costs increase will determine the shapes of both the variable and total cost curve.

4

Cost

Average and Marginal Cost Curves

18 16 14 12 10 8 6 4 2 0

IV III E

II F

I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Quantity

I = AFC; II = AVC; III = ATC; IV = MC Notes about the shape and position of the unit cost curves: (i) MC curve passes through the minimum points of the ATC and the AVC. (ii) AFC slopes downward continuously – this tells us that as output increases the same fixed costs can be spread over a larger range of output. (iii) MC, ATC, and AVC are U-shaped – reflecting the fact that initially costs on the margin and on the average are falling but after some point they start rising. The relationship between marginal and average cost curves is as follows: If MC < ATC (AVC), then ATC (AVC) is falling If MC = ATC (AVC), then ATC (AVC) is at its minimum If MC > ATC (AVC), then ATC (AVC) is rising The reason for the U-shape of these curves is that in the short-run, output can only be increased by increasing the variable input. As diminishing marginal productivity sets in the cost begin to rise since producers pay the same for each additional unit of the variable input while what they get (the marginal product) is less and less.

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