The Cost Structure of Firms

The Cost Structureof Firms

Four classes of inputs • Intermediate products • Land • Labour • Capital

Production • The production function relates inputs of factor services to outputs. • It describes the technological relation between the inputs that a firm uses and the output that it produces. • q = ψ( f1 ,.... fm) q = quantity of output of some good /service F – quantities of m different inputs used in its production Expressed as rates per time

Costs and Profits • In addition to what firms count as their costs, economists include the imputed opportunity costs of owners’ capital. • This includes the pure return, what could be earned on a riskless investment, and a risk premium, what could be earned over the pure return on an equally risky investment.

Pure or economic profits are the difference between revenues and all these costs. • Pure profits play a key role in resource allocation. • Positive pure profits attract resources into an industry; negative pure profits induce resources to move elsewhere.

Costs in the Short Run • Short Run : period of time over which at least one significant input is fixed. • The inputs that can be varied in the short run are called variable inputs. • Short run variations in output are subject to the law of diminishing returns

Law of diminishing returns or the law of variable proportions - According to this relationship, in a production system with fixed and variable inputs (say factory size and labor), beyond some point, each additional unit of variable input yields less and less output 1 – Stage of increasing returns; Ex>1 2 – Stage of decreasing returns,0<Ex<1 3 – Stage of negative returns; Ex<0 O U T P U T 1 3 2 LABOR

Increasing return is the stage where with each additional unit of variable input employed, the marginal product increases. Diminishing returnis the stage where with each additional unit of variable input employed, the output increases but at a decreasing rate. The stage where with increase in variable input, the decreasing marginal product becomes negative, resulting in a decline of total output. It is the stage of negative returns. At this point the variable factor becomes counter productive. O U T P U T 1 3 1 – Stage of increasing returns; Ex>1 2 – Stage of decreasing returns,0<Ex<1 3 – Stage of negative returns; Ex<0 2 LABOR

Short Run Variations in Input Total Product (TP) : The total amount produced during some period of time by all the inputs that the firm is using at that time. Average Product (AP) : Total Product per unit of the variable input AP = TP/L Marginal product (MP) : Change in total product from using one more or one less unit of the variable input MP = ∆TP / ∆ L

Total, Average and Marginal Products in the Short Run Quantity of Labour (L) (1) 1 2 3 4 5 6 7 8 9 10 11 12 Total Product (TP) (2) 43 160 351 600 875 1152 1375 1536 1656 1750 1815 1860 Average Product (AP) (3) 43 80 117 150 175 192 196 192 184 175 165 155 Marginal Product (MP) (4) 43 117 191 249 275 277 220 164 120 94 65 45

Total, average and marginal product curves 2100 300 Point of diminishing marginal returns TP 1800 250 1500 200 Total product [T/P] AP 1200 150 Average product [AP] and marginal product [MP] 900 Point of diminishing average returns 100 600 MP 50 300 2 4 6 8 10 12 2 4 6 8 10 12 0 Quantity of Labour Quantity of labour [i] Total Product [ii] Average and Marginal Product

Total, average and marginal product curves (i): Total product curve • The TP curve shows the total product steadily rising, first at an increasing rate, then at a decreasing rate. (ii): Average and marginal product curves • The marginal product curves rise at first and then decline. • The level of output where marginal product reaches a maximum is called point of diminishing marginal returns. • First MP reaches its maximum at a lower level of L than does AP. • When AP is a Maximum ( point of diminishing average returns), MP=AP

Law of Diminishing Returns • The law of diminishing returns states that if increasing quantities of variable input are applied to a given quantity of a fixed input, the marginal product and the average product of the variable input will eventually decrease. • The law of diminishing returns is also called the law of variable proportions’ because it predicts the consequences of varying the proportions in which input types are used.

Short run variation in costs • Total cost (TC) : Total Cost of producing any given rate of output. Total Fixed cost( TFC), Total Variable Cost (TVC) • Average Total Cost ( ATC): Total Costs of producing any given output divided by the number of units produced i.e. cost per unit • Marginal Cost (MC): Increase in total cost resulting from raising the rate of production by one unit

Variation of Costs With Capital Fixed and Labour Variable Inputs Capital Labour [L] Total Cost Fixed Variable Total [TFC] [TVC] [TC] Average Cost Fixed Variable Total [AFC] [AVC] [ATC] Output [q] Marginal Cost [MC] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] 10 1 43 £100 £20 £120 £2,326 £0.465 £2,791 £0.465 10 100 140 0.625 0.250 0.875 160 40 0.171 2 10 351 60 160 0.285 0.171 0.456 0.105 3 100 Price of labour is £ 20 per unit ( worker hours) and the price of capital is £ 10 per unit ( machine hours)

Total, Average and Marginal Cost Curves 280 TC TVC 0.70 240 0.60 200 0.50 Cost per unit [[£] Cost [£] 160 MC 0.40 120 TFC 0.30 ATC 80 0.20 AVC 40 0.10 AFC 300 600 900 1200 1500 1800 2100 300 600 900 1200 1500 1800 2100 [i] Total cost curves [ii] Marginal and average cost curves Output Output

Total, Average and Marginal Cost Curves • Total fixed cost does not vary with output. • Total variable cost and the total of all costs, TC,(= TVC + TFC)rise with output, first at a decreasing rate, then at an increasing rate. • The total cost curves in the figure give rise to the average and marginal curves in this figure. • Average fixed cost (AFC)declines as output increases. • Average variable cost (AVC)and average total cost (ATC)decline and then rise as output increases. • Marginal cost (MC)does the same, intersecting the AVC and ATC curves at their minimum points. • Capacity output is defined as the minimum point of the ATC curve, which is an output of 1,500 in this example.

Short-run Average and Marginal Cost Curves are U-shaped, the rising portion reflecting Diminishing average and marginal returns. • The Marginal Cost curve intersects the Average Cost Curve at the latter’s minimum point, which is called the firm’s capacity output. • There is a family of Short-Run Average and Marginal cost curves, one for each amount of the fixed factor.

Isoquant • An isoquant is a curve on which every point satisfies the production function and thus, all combination of L and K on an isoquant are technically efficient combination with which the given level of output can be produced. • Each isoquant corresponds to a different level of output.

Isoquants • Graphical representation of production function • A curve drawn through the technically feasible combinations of inputs to produce a target level of output • Marginal rate of technical substitution is the substitution of one input for another. MRTS = - Change in K /Change in Labor

Properties of Isoquants They are downward sloping – That is as you employ more and more of the input on the X axis, you necessarily employ less of the input on the Y axis in order to maintain the same level of output. Employing more of both inputs would lead to a higher isoquant. They are convex to the origin – This happens as the power to substitute diminishes, called as the marginal physical product as we employ more and more of a factor. However, in case of perfect substitutes the isoquant is a downward sloping straight line with a constant slope, while for perfect complements the isoquant is a L shaped curve. They do not intersect each other

Applications of Isoquants Isoquants enable the decision maker to conceptualize the trade-offs involved in substitution between inputs. Managers consider the costs and benefits of substituting one input for another and select that one where the net benefits are maximised. Isoquant model helps the decision maker to figure out the increase /decrease in output with a change in input.

Cost curves show the money cost of producing various levels of output. The short-run cost curve is U-shaped because some inputs are being held constant and the law of diminishing returns applies to these that are allowed to vary. The long-run cost curve can take on various shapes depending on the scale effects when all inputs are allowed to vary at once. Costs in the very long run are altered by technical change.

Costs in the Long Run • In the long run, the firm can adjust all inputs to minimize the cost of producing any given level of output. • Cost minimization requires that the ratio of an input’s marginal product to its price be the same for all inputs. • The principle of substitution states that, when relative input prices change, firms will substitute relatively cheaper inputs for relatively more expensive ones.

Long-run cost curves are often assumed to be U-shaped, indicating decreasing average costs (increasing returns to scale) followed by increasing average costs (decreasing returns to scale). • The long-run cost curve may be thought of as the envelope of the family of short-run curves, all of which shift when factor prices shift.

The Very Long Run • In the very long run, innovations introduce new methods of production that alter the production function. • These innovations occur as response to changes in economic incentives such as variations in the prices of inputs and outputs. • These cause cost curves to shift downwards.

A simplified profit and loss account • Costs are divided between variable and fixed. • Total revenue minus total costs as measured by the firm give profits in the sense used by firms. • To the firm, profits include the opportunity cost of its capital - what it must earn to induce it to keep its capital in its present use.

Calculation of Pure Profits Profits as reported by the firm £150,000 Opportunity cost of capital Pure return on the firm’s capital -£100,000 Risk Premium -£40,000 Pure or economic rent £10,000

Calculation of pure profits • The economist’s definition of profits does not include the opportunity cost of capital. • To arrive at this figure the opportunity cost of capital must be deducted from what the firm regards as its capital.

A Long-run Average Cost-curve( LRAC) c2 LRAC c0 E0 E1 c1 Attainable levels of cost Cost per unit Unattainable levels of cost qm q0 q1 0 Output per period

A Long-run Average Cost-curve • The long-run average cost (LRAC) curve is the boundary between attainable and unattainable levels of cost. • Since the lowest attainable cost of producing q0 is c0 per unit, the point E0 is on the LRAC curve. • At output qm the firm attains its lowest possible per-unit cost of production for the given technology and factor prices.

Long-run Average Cost and Short-run Average Cost Curves Cost per unit SRATC LRAC c0 q0 qm Output per period

Long-run Average Cost and Short-run Average Cost Curves • The short-run average total cost (SRATC) curve is tangent to the long-run average cost (LRAC) curve at the output for which the quantity of the fixed factors is optimal. • The curves SRATC and LRAC coincide at output q0where the fixed plant is optimal for that level of output. • For all other outputs, there is too little or too much plant and equipment, and SRATC lies above LRAC.

Long-run Average Cost and Short-run Average Cost Curves • If some output other than q0is to be sustained, costs can be reduced to the level of the long-run curve when sufficient time has elapsed to adjust the size of the firm’s fixed capital. • The output qm is the lowest point on the firms long-run average cost curve. • It is called the firm’s minimum efficient scale (MES), and it is the output at which long-run costs are minimized.

The Envelope Long-run Average Cost Curve Cost per unit LRAC Output per period

The Envelope Long-run Average Cost Curve SRATC Cost per unit LRAC c0 q0 Output per period

The Envelope Long-run Average Cost Curve SRATC Cost per unit SRATC LRAC c0 q0 Output per period

The Envelope Long-run Average Cost Curve SRATC Cost per unit SRATC LRAC c0 q0 qm Output per period

The Envelope Long-run Average Cost Curve • Each short-run curve shows how costs vary if output varies, with the fixed factor held constant at the level that is optimal for the output at the point of tangency with LRAC. • As a result, each SRATC curve touches the LRAC curve at one point and lies above it at all other points. • This makes the LRAC curve the envelope of the SRATC curves.

The Cost Structure of Firms