What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

What is a production function?

A relationship between inputs used and the maximum output a firm can produce, given technology, written \(q=f(L,K)\).

Distinguish between the short run and the long run.

In the short run at least one factor is fixed and only others can be varied; in the long run all factors of production are variable.

State the law of variable proportions.

As more units of a variable factor are combined with fixed factors, the marginal product first rises, reaches a maximum, and then falls.

Explain the relationship between MP and AP.

When MP is greater than AP, AP rises; when MP is less than AP, AP falls; MP cuts AP from above at the maximum point of AP.

What are the three types of returns to scale?

Increasing returns (output rises more than proportionately), constant returns (in the same proportion), and decreasing returns (less than proportionately).

Why is the average fixed cost curve downward sloping?

Because total fixed cost is constant, dividing it by a rising output makes AFC fall continuously, forming a rectangular hyperbola.

Why are the AVC, SAC and SMC curves U-shaped?

Because of the law of variable proportions — costs first fall as productivity rises and then rise as productivity falls.

At what point does SMC cut the AVC and SAC curves?

SMC cuts each of them from below at their respective minimum points.

Why are there no fixed costs in the long run?

Because in the long run all factors of production can be varied, so no factor — and hence no cost — remains fixed.

How are total cost, total fixed cost and total variable cost related?

Total cost equals total fixed cost plus total variable cost; TFC is constant while TVC rises with output.

Production and Costs

Class 12 Economics · Introductory Microeconomics · Chapter 3

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Summary

A firm transforms inputs into output, and the production function gives the maximum output obtainable from given quantities of inputs such as labour (L) and capital (K), written \(q=f(L,K)\). In the short run at least one factor is fixed; in the long run all factors can be varied. Three product concepts measure the contribution of a variable input: total product (TP), average product \(AP_L=\dfrac{TP_L}{L}\), and marginal product \(MP_L=\dfrac{\Delta TP_L}{\Delta L}\). The law of variable proportions states that as a variable factor is added to fixed factors, marginal product first rises and then falls; both AP and MP curves are inverse-U shaped, and MP cuts AP from above at AP’s maximum. When all inputs change together we examine returns to scale — increasing, constant or decreasing. On the cost side, total cost is the sum of total fixed cost and total variable cost, \(TC=TFC+TVC\). Per-unit costs are average fixed cost, average variable cost and short-run average cost \(SAC=AVC+AFC\), while marginal cost \(SMC=\dfrac{\Delta TC}{\Delta q}\). AFC falls continuously, SMC, AVC and SAC are U-shaped, and SMC cuts both AVC and SAC from below at their minimum points. In the long run there are no fixed costs and the LRAC and LRMC curves are also U-shaped.

Key terms

Production function

The relation giving maximum output for each combination of inputs, \(q=f(L,K)\).

Marginal product

The change in output from employing one more unit of a variable input, \(MP_L=\dfrac{\Delta TP_L}{\Delta L}\).

Law of variable proportions

Marginal product of a variable factor first rises, then falls, as more of it is used with fixed factors.

Returns to scale

How output responds when all inputs are increased in the same proportion.

Total cost

The sum of total fixed cost and total variable cost, \(TC=TFC+TVC\).

Marginal cost

The addition to total cost from producing one more unit, \(SMC=\dfrac{\Delta TC}{\Delta q}\).

Extra questions & answers

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A production function gives:

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