# Chapter 3. Production and cost

Production
• This is process by which inputs are transformed into ‘output’. Production is carried out by producers or firms.
• In order to acquire inputs a firm has to pay for them. It is known as cost of production.
• Cost refers to expenditure incurred by a producer on factor as well as non – factor inputs for a given output of a commodity.
• Once output has been produced, firm sell it in market and earns revenue.
• difference between revenue and cost is known as firm’s profit.

Production Function
• Production function is relation between a firm’s production [output] and material factors of production [input]. This is technological knowledge that determines maximum levels of output that can be produced using different combinations of inputs. production function of a firm is a relationship between inputs used and output produced by firm.
Qx = f [L, K]
• Where, Q is amount of wheat produced, K is area of land in hectares, • is number of hours of work done in a day.

Note: If either K or • increase, Q will increase. If technology improves, maximum levels of output obtainable for different input combinations increase.
• inputs that a firm uses in production process are known as factors of production.
Isoquant: This is set of all possible combinations of two inputs that yield same maximum possible level of output. Each isoquant represents a particular level of output and is labelled with that amount of output.

Short Run and Long Run
• Short run is a period of time when production can be increased only by increasing application of variable factors. Fixed factors remains constant.
• In order to vary output level, firm can vary only variable factors.
• factor that remains fixed is known as fixed factor.
• factor in which firm can vary is known as variable factor.
• In long run, all factors of production can be varied.

Total Product, Average Product and Marginal Product Total Product [TP]
• It refers to total amount [or volume] of output produced with a given amount of input during a period of time.
• It is known as total return of variable factor.

Average Product [AP]
• This is defined as output per unit of variable input. We calculate it as AP = TP/L

Marginal Product [MP]
• This is defined as change in output per unit of change in input when all other inputs are held constant. When capital is held constant, marginal product is: Marginal Product refers to change in TP when one more unit of variable factor is used.

Law of Diminishing Marginal Product and Law of Variable Proportions
• tendency of MP to first increase and then fall is known as law of variable proportions or law of diminishing marginal product.
• Law of variable proportions say that marginal product of a factor input initially rises with its employment level. But after reaching a certain level of employment, it starts falling. Note: TP increases as labour input increases. But rate at which it increases is not constant.
• law of variable proportion production can be divided into three distinct stages. These three stages of short run are: [i] Stage of Increasing Return [ii] Stage of Diminishing Return, and [iii] Stage of Negative Return.

Relation between TP and MP
• When TP rises at an increasing rate, MP rises as well.
• MP decreases as TP increases at a decreasing rate.
• When TP is at its maximum, MP equals zero.
• When TP starts to fall, MP becomes negative.

Shapes of Total Product, Marginal Product and Average Product Curves
• An increase in amount of one of inputs keeping all other inputs constant results in an increase in output. total product curve in input-output plane is a positively sloped curve.
• According to law of variable proportions, marginal product of an input initially rises and then after a certain level of employment, it starts falling. MP curve therefore, looks like an inverse ‘U’- shaped curve.
• Increase amount of input, MP rises. AP being average of marginal products, rises, but rises less than MP. Then, after a point, MP starts falling.
• However, as long as value of MP remains higher than value of AP, AP continues to rise. Once MP has fallen sufficiently, its value becomes less than AP and AP starts falling.
• So, AP curve is inverse ‘U’-shaped. As long as AP increases, it must be case that MP is greater than AP. Otherwise, AP cannot rise. Similarly, when AP falls, MP has to be less than AP. It follows that MP curve cuts AP curve from above at its maximum.

Costs
• cost function describes least cost of producing each level of output given prices of factors of production and technology.
• firm produces q amount of output using x1 amount of factor 1 and x2 amount of factor
(2) It is known as a Cobb-Douglas production function.

Note: when a + b > 1, production function exhibits IRS. When a + b < 1 production function exhibits DRS.

Short Run Costs
• These are costs over a period during which some factors are in fixed supply, like plant, machinery.
• total cost of production is divided into two parts: total fixed costs [TFC] and total variable cost [TVC].
• Adding fixed and variable costs, we get total cost [TC] of a firm TC = TVC + TFC

Note: In order to increase production of output, firm must employ more of variable inputs. As a result, total variable cost and total cost will increase. Therefore, as output increases, total variable cost and total cost increase.
• short run average cost [SAC] incurred by firm is defined as total cost per unit of output. SAC= T/ q
• average variable cost [AVC] is defined as total variable cost per unit of output. AVC= TV/ q
• Average fixed cost is defined as fixed cost of production per unit of commodity. Also, average fixed cost [AFC] is AFC = TFC/q
(1) SAC is sum of AVC and AFC. Initially, both AVC & AFC decreases as output increases. Therefore, SAC initially falls.
(2) After a certain level of output production, AVC starts rising, but AFC continues to fall. Initially fall in AFC is greater than rise in AVC and SAC is still falling.
(3) But, after a certain level of production, rise in AVC becomes larger than fall in AFC. From this point onwards, SAC is rising. SAC curve is therefore ‘U’-shaped.
• short run marginal cost [SMC] is defined as change in total cost per unit of change in output SMC =change in total cost change in output ∆TC q
(1) Marginal cost is additional cost that a firm incurs to produce one extra unit of output. According to law of variable proportions, initially, marginal product of a factor increases as employment increases, and then after a certain point, it decreases.
(2) This means initially to produce every extra unit of output, requirement of factor becomes less and less, and then after a certain point, it becomes greater and greater.
(3) As a result, with factor price given, initially SMC falls, and then after a certain point, it rises. SMC curve is, therefore, ‘U’-shaped.

Long Run Costs
• In long run, all inputs are variable. There are no fixed costs. total cost and total variable cost therefore, coincide in long run. Long run average cost [LRAC] is defined as cost per unit of output, i.e., LRAC = TC/q
• LRAC curve is a ‘U’-shaped curve.
• For first unit of output, both LRMC & LRAC are same.
• Then, as output increases, LRAC initially falls, and then, after a certain point, it rises.
• As long as average cost is falling, marginal cost must be less than average cost.
• When average cost is rising, marginal cost must be greater than average cost.
• LRMC curve is therefore a ‘U’-shaped curve. It cuts LRAC curve from below at minimum point of LRAC.

Returns to Scale or Shapes of Long Run Cost Curves
• When a proportional increase in all inputs results in an increase in output by same proportion, production function is said to display Constant Returns to Scale [CRS]. So, average cost remains constant as long as CRS operates.
• When a proportional increase in all inputs results in an increase in output by a larger proportion, production function is said to display Increasing Returns to Scale [IRS]
• Decreasing Returns to Scale [DRS] holds when a proportional increase in all inputs results in an increase in output by a smaller proportion.

Note: If output is less than doubled, then DRS holds, and if it is more than doubled, then IRS holds.