Graphing Exercise: Production and Costs

In making payments for its resources, the firm incurs costs of production.  In the short run, a time frame over which the quantity of capital is fixed, the total cost of any given level of output can be broken into fixed cost and variable cost.  On a per unit basis, these can be expressed as average fixed cost and average variable cost, which together sum to average total cost.  Marginal cost refers to the extra cost of producing one additional unit.  Obviously, these short-run costs reflect both the costs and the productivity of the inputs.

Exploration: What is the relationship between input prices, productivity, and costs?

The applet contains productivity data – the physical relationship between inputs and output – for a hypothetical firm.  Total product, the relationship between labor input and output, is graphed on the upper panel, while marginal and average product are graphed below.  Clicking and dragging the Productivity Index slider to the right allows you to increase the productivity of labor by any amount up to 25 percent.

By clicking on the Production/Costs button, the applet toggles to the graphical portrayal of the firm’s cost curves:  Variable Cost, Fixed Cost, and Total Cost are in the upper graph, while the lower panel contains the corresponding Marginal and Average-Total-Cost curves.  You can change the wage rate and fixed cost by clicking on the corresponding bold values below the tabular productivity data.  In either the production or the cost mode, clicking Reset restores all values to their initial levels.

1. How are the positions of the production graphs affected by an increase in labor productivity?
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2. Over what range of labor input are there increasing marginal returns to labor?  Over what range are there decreasing marginal returns to labor?
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3. Reset productivity to its original level.  Over what range of output does marginal cost decrease?  Over what range does it increase?  How do these ranges correspond to labor productivity?
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4. When the wage is $20 and fixed cost is $100, what is the marginal cost of the 420th unit of output?  How is this affected by a decrease in fixed cost?  How is it affected by an increase in the wage?  How is it affected by an increase in labor productivity?
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5. Experiment on your own.  Considering the three factors investigated in the applet – fixed cost, wage rate, and productivity – which factor(s) will increase marginal cost?  How will these same factors affect average total cost?  Can average total cost increase without an increase in marginal cost?
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