Theory of Production, Cost & Price Determination in Markets

Weightage: Chapters 3 and 4 of ICAI's Paper 4 syllabus, roughly 22 marks. The relationship between average and marginal cost, and the comparison across the four market forms, are the two most reliably examined items.

Production

The factors of production are land, labour, capital and enterprise. A production function states the maximum output obtainable from given quantities of inputs with a given technology.

The distinction between the two time periods governs the whole chapter:

• In the short run, at least one factor is fixed and output can be varied only by changing the variable factors.
• In the long run, all factors are variable and the firm can alter its entire scale of operations.

The law of variable proportions

This is the short-run law. As successive units of a variable factor are combined with a fixed factor, the marginal product of the variable factor eventually falls.

Three stages arise:

Stage I — increasing returns. Total product rises at an increasing rate; marginal product rises and reaches its maximum. The fixed factor is under-utilised relative to the variable factor, so each additional unit of the variable factor allows better use of it — more specialisation and division of labour.

Stage II — diminishing returns. Total product rises at a decreasing rate; marginal product falls but remains positive. Total product reaches its maximum where marginal product is zero. This is the rational stage of production, and a firm will always operate here. In Stage I it could gain by adding more of the variable factor; in Stage III it would gain by using less.

Stage III — negative returns. Total product falls; marginal product is negative. Too much of the variable factor is crowded onto the fixed factor and additional units get in the way.

The relationship between average and marginal product mirrors the cost relationship discussed below: marginal product cuts average product at the maximum of average product.

Returns to scale

This is the long-run concept, and confusing it with the law of variable proportions is a standard error. Here all factors are increased together, in the same proportion.

• Increasing returns to scale — output rises more than proportionately. Caused by economies of scale.
• Constant returns to scale — output rises in the same proportion.
• Decreasing returns to scale — output rises less than proportionately, generally caused by managerial difficulties as the organisation grows beyond effective control.

An isoquant shows the combinations of two inputs giving the same output. It is downward sloping and convex to the origin, for reasons exactly parallel to the indifference curve. Producer's equilibrium is the tangency of an isoquant with an isocost line, at which the marginal rate of technical substitution equals the ratio of input prices.

Cost

Cost concepts

Explicit costs are actual money payments to outsiders. Implicit costs are the opportunity costs of resources the firm owns — the salary the proprietor could have earned elsewhere, the rent the firm's own building could have fetched.

Accounting cost records explicit costs only. Economic cost includes implicit costs as well, which is why economic profit is lower than accounting profit and why a firm can show an accounting profit while making an economic loss.

Fixed costs do not vary with output in the short run — rent, insurance, salaries of permanent staff. Variable costs vary with output — raw materials, wages of casual labour, power.

Sunk costs have already been incurred and cannot be recovered. They are irrelevant to future decisions, because no decision can now change them. This is examined regularly and is the practical application of opportunity cost reasoning.

The short-run cost curves

$TC=TFC+TVC$

$AFC=\frac{TFC}{Q},AVC=\frac{TVC}{Q},ATC=\frac{TC}{Q}=AFC+AVC$

$MC=\frac{\Delta TC}{\Delta Q}$

The shapes follow from the law of variable proportions:

• AFC falls continuously as output rises, since a fixed total is divided among more units. It approaches zero but never reaches it, so the AFC curve is a rectangular hyperbola.
• AVC, ATC and MC are U-shaped, falling initially because of increasing returns and rising later because of diminishing returns.
• MC is unaffected by fixed cost, since fixed cost does not change with output and therefore contributes nothing to the change in total cost.
• The gap between ATC and AVC narrows as output rises, because that gap is AFC, which is falling.

The relationship between AC and MC

This is the single most examined relationship in the chapter, and it is worth reasoning through rather than memorising.

• When MC < AC, AC is falling.
• When MC > AC, AC is rising.
• MC cuts AC at the minimum point of AC, and it does so from below.

The reason is arithmetical, not economic. An average is pulled in the direction of the marginal value. If the next unit costs less than the current average, it must pull the average down; if it costs more, it must pull the average up; and the average stops falling and starts rising exactly where the next unit costs the same as the current average.

A student's examination average behaves identically: a paper scored below the current average lowers it, one above raises it, and the average is at its lowest just before the first above-average paper.

The same reasoning gives the relationship between marginal and average product, and between marginal and average revenue.

Long-run cost

In the long run all factors are variable, so there are no fixed costs. The long-run average cost curve is the envelope of the short-run curves, showing the lowest attainable average cost for each output when plant size can be varied.

It is U-shaped for reasons different from the short-run curve. It falls because of economies of scale and rises because of diseconomies of scale, whereas the short-run curve is shaped by the law of variable proportions.

Internal economies arise within the firm from its own growth — technical, managerial, marketing, financial and risk-bearing. External economies arise from the growth of the industry as a whole and benefit every firm in it, such as a pool of skilled labour or shared infrastructure.

Diseconomies of scale arise principally from managerial difficulty: as an organisation grows, coordination becomes harder, communication slower and control weaker.

Revenue

$TR=P\times Q,AR=\frac{TR}{Q}=P,MR=\frac{\Delta TR}{\Delta Q}$

Note that AR equals price always, which follows directly from the definitions. The AR curve is therefore the demand curve facing the firm.

Under perfect competition, the firm is a price taker and can sell any quantity at the ruling price, so AR is constant and AR = MR = price. The demand curve facing the firm is horizontal.

Under imperfect competition, the firm must lower price to sell more, and because the lower price applies to all units, MR falls faster than AR and lies below it. For a straight-line AR curve, MR falls twice as steeply.

Price determination in different markets

Every firm maximises profit where MR = MC, with MC rising at that point. That condition is common to all market forms; what differs is the demand curve the firm faces.

Perfect competition

Its features: a very large number of buyers and sellers; a homogeneous product; free entry and exit; perfect knowledge; perfect mobility of factors; and no transport costs.

Because the product is homogeneous and there are many sellers, no firm can influence price. Each is a price taker facing a horizontal demand curve.

In the short run a firm may earn supernormal profit, normal profit or a loss, and it continues to produce in a loss as long as price covers average variable cost, since it is then contributing something towards fixed costs which must be paid anyway. The shut-down point is where price falls below AVC.

In the long run, free entry and exit eliminate supernormal profit. If profits are being made, new firms enter, supply rises and price falls; if losses are made, firms leave. Equilibrium is reached where price = MR = MC = minimum ATC, and every firm earns only normal profit.

Monopoly

A single seller with no close substitutes and barriers to entry. The monopolist is a price maker but not free of constraint: it faces the entire market demand curve, so it can set the price or the quantity but not both.

Its demand curve slopes downward and MR lies below AR. Equilibrium is where MR = MC, and price is read off the AR curve above that output — so price exceeds marginal cost, which is the source of the allocative inefficiency attributed to monopoly. Supernormal profit can persist in the long run because entry is blocked.

Price discrimination is charging different prices to different buyers for the same product where the difference is not justified by cost. Its conditions are that the seller must have monopoly power, the markets must be separable so that resale between them is impossible, and the elasticities of demand must differ — with the higher price charged in the less elastic market.

Monopolistic competition

Many sellers of differentiated products, with free entry and exit. Product differentiation may be real or merely perceived through branding and advertising.

Because products are differentiated, each firm faces a downward-sloping but highly elastic demand curve — it has some price-setting power, but a price rise sends most customers to close substitutes.

Selling costs — advertising and promotion — are a distinguishing feature of this market form and do not arise under perfect competition, where the product is homogeneous and every firm can sell all it wishes at the ruling price.

In the long run, free entry eliminates supernormal profit, so firms earn only normal profit. But equilibrium occurs where the demand curve is tangent to the ATC curve at a point to the left of minimum ATC, so firms operate with excess capacity — producing less than the output at which average cost would be lowest. This is the characteristic inefficiency of the form.

Oligopoly

A few large sellers, each of whose decisions materially affects the others. Interdependence is its defining feature, and it is what makes oligopoly analytically distinct: no firm can decide its price without predicting rivals' reactions.

The kinked demand curve explains observed price rigidity. Suppose a firm considers changing its price. If it raises the price, rivals will not follow, so it loses many customers — demand is elastic above the current price. If it cuts the price, rivals will follow to protect their share, so it gains few customers — demand is inelastic below it.

The demand curve therefore has a kink at the current price, and the MR curve has a discontinuity at that output. Marginal cost can move within that gap without changing the profit-maximising price, which is why oligopoly prices remain stable even as costs change.

Oligopolists may also collude, formally through a cartel or informally through price leadership, to escape the uncertainty of interdependence.

The comparison

The reliable examination question compares the four forms across named bases: the number of sellers, the nature of the product, the barriers to entry, the degree of price control, the elasticity of the demand curve facing the firm, the presence of selling costs, and long-run profit.

Perfect competition and monopoly are the two extremes; monopolistic competition and oligopoly lie between them and together describe most real markets.

How this chapter is examined

Expect questions on the stages of the law of variable proportions and which is rational; the distinction between the law of variable proportions and returns to scale; the relationship between AC and MC and where MC cuts AC; the irrelevance of sunk costs; the difference between accounting and economic profit; the shut-down condition in the short run; the conditions for price discrimination; the source of excess capacity in monopolistic competition; and the kinked demand curve as an explanation of price rigidity.

The recurring errors are confusing the short-run law with the long-run one, asserting that MC cuts AC at the minimum of MC rather than of AC, and forgetting that a firm in the short run continues producing so long as price covers average variable cost rather than average total cost.