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Production and Costs

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**Average and Marginal Product**

Marginal Product of Labor=Increase of Product when Employing an Additional Worker (≠ marginal benefit) Average Product of Labor or Product per Worker=Total Product/Number of Workers Note the difference between marginal product and marginal benefit, product is measured in units of the good and marginal benefit is measured in $. Marginal product of labor is the increase in PRODUCT (measured in units, for example one dress) when employing one additional unit of LABOR (say an additional worker). Marginal benefit is the increase in BENEFIT (measured in money) when increasing PRODUCTION in one unit (say one dress).

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**Total, Marginal and Average Products**

Labor Total Product Marginal Product Average Product 1 (worker) 5 (dresses) 5 (d. added by additional worker) 5 (d.p.w.) 2 12 7 6 3 21 9 4 28 5 33 6.6 36 37 1 5.3

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**Total, Marginal and Average Products**

Output TP Output per Worker MPL Q Diminishing Marginal Returns Gains of Specialization APL L Number of Workers L0 L1 Number of Workers

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**Average and Marginal Product**

Suppose that 5 bakers bake 500 cupcakes. The average product of labor is 100 (500/5). A new baker is employed and total output goes up to 630 cupcakes. The marginal product of adding an additional worker is 130. The new average product of labor is 630/6=105. If the marginal product of labor is larger than 100, the average product of labor rises. If the marginal product of adding an additional worker is less than 100, the average product of labor falls. Then, the marginal product curve cross the average product curve when the average cost of labor is at the maximum.

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**Costs (5 machines $10 per machine, wage is $15 per worker)**

Labor Total Product 1 5 2 12 3 21 4 28 33 6 36 7 37 Variable Cost 15 Total Costs 65 80 95 110 125 140 155 30 45 60 75 90 105 Costs depend on how much you produce and how you produce. In the short run a firm can only change some factors of production but not others. For example, it is not possible to build a new factory overnight. We assume that the only factor that companies may change in the short run is labor.

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**Average Costs (per unit cost)**

AVC=VC/Q AC=TC/Q If labor is the only Variable Input: Variable Cost AVC=VC/Q=(PL*L)/Q=PL/(Q/L)=PL/APL Marginal Costs The increase in total cost when increasing production by 1 unit (not when increasing labor by 1 unit!). MC=PL*(1/MPL) One additional worker adds MPL to product. It is needed 1/MPL units of workers to produce one unit of the product.

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**Cost Curves Labor Product MPL APL VC TC AVC AC MC 1 5 15 65 3 13**

3 (1/5)*15 2 12 7 6 30 80 2.5 6.6 2.14 3 21 9 45 95 4.5 1.67 4 28 7 60 110 2.14 3.9 5 33 6.6 75 125 2.27 3.7 3 6 36 90 140 2.5 3.8 37 1 5.3 105 155 2.84 4.1 15

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**Total and Variable Costs**

$ TC VC The shape of the costs functions are related to the shape of the production function. Output

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**Relationship Between Marginal and Average Products and Costs**

MC=PL*(1/MPL) Output per Worker $ per unit of output MC MPL AC AVC APL AC=TC/Q=F/Q+(PL/APL). F/Q decays with Q but PL/APL start to increase after Q1. Thus, AC reaches a minimum to the right of Q1. AVC=PL/APL Q0(L0) Q1(L1) Output L0 L1 Number of Workers

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**Average and Marginal Cost**

Suppose the total cost of producing 5 units is $100. The average cost is $20. A new unit is produced and the total cost goes to $130. The marginal cost of producing an additional unit is $30. The new average cost is 130/6=25. If the marginal cost is larger than 20, the average cost rises. If the marginal cost of producing an additional unit is less than 20, the average cost falls. Then, the marginal cost cross the average cost curve when the average cost of labor is at the minimum.

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**Fixed Costs $ Cost per unit of output ATC FC AVC AFC Output Output**

Dilution of fixed costs imply that the minimum of ATC is to the right of the minimum of AVC. AFC Output Output

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**Short Run and Long Run Cost per Unit AC long run ACSR Q* Output**

In the long run the firm can change the amount of capital. Each short run cost curve is defined for a given amount of capital. If there are only four possible amounts of capital there are 4 short run cost curves. If the firm wants to produce Q*, it will choose a lung run amount of capital such that the costs are as low as possible. If a continuous range of capital sizes is available, the long run cost curve is the envelope of the short run cost curves. Q* Output

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