Chapter 3 — Production and Costs

A production function is the relationship between inputs used and output produced by a firm. For various quantities of inputs, it gives the maximum quantity of output that can be produced. With labour (L) and capital (K) it is written as q = f(L,K).

In the short run, at least one factor — labour or capital — cannot be varied and remains fixed; the firm varies output by changing only the variable factor. In the long run all factors can be varied. The distinction is based on input flexibility, not calendar time.

Total product is the relationship between a single variable input and output when all other inputs are held constant. It is also called total return to or total physical product of the variable input.

Average product is output per unit of the variable input: APL = TP ÷ L. It represents the average contribution of each unit of labour to total output.

Marginal product is the change in output per unit of change in the variable input when all other inputs are held constant: MPL = ΔTP ÷ ΔL. For example, when labour rises from 1 to 2 units and TP rises from 10 to 24, the marginal product of the 2nd unit of labour is 14.

The law states that as employment of a variable input increases (with other inputs fixed), its marginal product initially rises but after a certain level of employment starts falling. This happens because factor proportions first become more suitable for production, then the process becomes overcrowded with the variable input.

The TP curve is positively sloped (output rises as input rises). Both the MP and AP curves are inverse U-shaped. The MP curve cuts the AP curve from above at the maximum point of the AP curve.

When all inputs increase by a given proportion and output increases by the same proportion, the production function shows constant returns to scale (CRS). If output increases by a larger proportion, it shows increasing returns to scale (IRS). If output increases by a smaller proportion, it shows decreasing returns to scale (DRS).

The Cobb-Douglas production function is q = x1^α × x2^β. When α + β = 1, it exhibits CRS; when α + β > 1, it exhibits IRS; when α + β < 1, it exhibits DRS.

Total fixed cost (TFC) is the cost of fixed inputs and does not change with output. Total variable cost (TVC) is the cost of variable inputs and increases as output increases. Total cost (TC) = TFC + TVC. At zero output, TC equals TFC alone.

Average fixed cost (AFC) = TFC ÷ q; average variable cost (AVC) = TVC ÷ q; short-run average cost (SAC) = TC ÷ q. They satisfy SAC = AVC + AFC. AFC falls continuously as output rises and is a rectangular hyperbola; both AVC and SAC are U-shaped.

AFC = TFC ÷ q. Since TFC is a constant, multiplying any output level q by its corresponding AFC always gives the same value (TFC). This constant-product relationship defines a rectangular hyperbola.

Because of the law of variable proportions, marginal product initially rises then falls. When MP rises, the extra input needed per unit of output falls, so SMC falls. When MP falls, more input is needed, so SMC rises. AVC, being the average of marginal costs, follows the same pattern but is flatter, giving both a U-shape.

The SMC curve cuts the AVC curve from below at the minimum point of the AVC curve. Similarly, the SMC curve cuts the SAC curve from below at the minimum point of the SAC curve. The minimum of SAC lies to the right of the minimum of AVC.

No. In the long run all factors of production can be varied, so there are no fixed inputs and therefore no fixed costs. Total cost and total variable cost coincide in the long run.

Both the long-run average cost (LRAC) and long-run marginal cost (LRMC) curves are U-shaped. IRS causes the downward-sloping portion of LRAC; CRS is observed at the minimum point; DRS causes the upward-sloping portion. The LRMC curve cuts the LRAC curve from below at LRAC's minimum.

Yes — cbseprepmaster.com provides the NCERT PDF for this chapter completely free. No account, login, or sign-up is required.