LONG RUN PRODUCTION FUNCTION

1. PRODUCTION IN LONG-RUN

2. IN ECONOMICS TERM: PRODUCTION MEANS A PROCESS BY WHICH RESOURCES (MEN,MATERIAL,AND TIME ETC.) ARE TRANSFORMED INTO A DIFFERENT NAD MORE USEFUL COMMODITY OR SERVICE. INPUT: IT IS A GOOD OR SERVICE THAT GOES INTO A THE PROCESS OF PRODUCTION. OUTPUT: IT IS ANY GOOD OR SERVICE THAT COMES OUT IN PRODUCTION PROCESS. CONCEPT OF PRODUCTION

3. The Long –run production function which may also be termed as “returns to scale” describes the maximum quantity of good or service that can be produced by a set of inputs, assuming that the firm is free to adjust the level of all inputs. Mathematically it can be represent as: Q=F(K,L) INTRODUCTION OF THE LONG RUN

4. The term ‘iso-quant’ has been derived from the GREEK word ISO means “ EQUAL ” LATIN word QUANTUS means “ QUANTITY ” . An iso-quant curve shows all possible combinations of two inputs(capital and labou r ) yielding the same output ,i.e., the factors combinations are so formed that the substitution of one factor for the other leaves the output unaffected. ISO –QUANT CURVE

5. ISO- QUANT SCHEDULE combination Labour (L) Capital (K) Output (Q,units) A 1 12 200 B 2 08 200 C 3 05 200 D 4 03 200 E 5 02 200 A schedule showing various of two inputs (say labour and capital) at which a producer gets equal output is known as iso-quant schedule. The table depicts that all combinations A,B,C,D and E of labour and capital gives 2000units of output to a producer.

6. 12 8 5 3 2 The slope of Iso-quant indicates , how the quantity of one input can be traded off against the quantity of other While the OUTPUT is held constant. M.R.T.S = y2-y1 x2-x1 8-12 = -4 = -4 2-1 1 ISO-QUANT CURVE CAPITAL LABOUR 1 2 3 4 5 Q=200 X Y A(1,12) B(2,8) C(3,5) D(4,3) E(2,5) X1,y1 X2,y2

7. The term Iso-cost refers to “EQUAL COST OF PRODUCTION” An Iso-cost is a line showing all the combinations of the two factors(say labour and capital) that can be purchased for a given expenditure outlay by the firm. An Iso-cost denotes a particular level of total cost for a given level of production changes,the total cost changes and thus the iso-cost curve moves upward and vice-versa. ISO-COST LINE

8. ISO-COST SCHEDULE COMBINATIONS CAPITAL(K) LABOUR (L) TOTAL OUTPUT (A , B) 03 01 100 (C , D) 02 04 150 (E , F) 01 07 200

9. A CAPITAL LABOUR B C D E F IN THIS ISO- COST LINE THE PRODUCER HAS THREE DIFFERENT COMBINATIONS OF (LABOUR AND CAPITAL). IF THERE IS AN INCREASE IN INPUTS THEN THE TOTAL OUTPUT ALSO INCRESES . BUT THE PRODUCER ALWAYS PREFERS TO GO FOR THE COMBINATION WHICH GIVES HIM THE COST MINIMIZATION 1 2 3 1 4 7 ISO-COST LINE

10. IN COST MINIMIZATION THE PRODUCER ALWAYS PREFERS TO CHOOSE THE INPUT COMBINATONS THAT MINIMIZE A FIRM’S TOTAL COST OF PRODUCTION. HENCE , THE COMPANY CHOOSES TO PRODUCE AN OUTPUT WHERE A COST-MINIMIZATION “SLOPE OF ISO-QUANT = SLOPE OF ISO-COST ”

11. Cost-minimization can be explained with the help of an example. Suppose a transportation company wants to satisfy the demand of its passengers and provides cargo service per year. The company is having a wide combinations of vehicles and workers for producing the desired level of output. The annual cost of a vehicle is (1,50,000) The annual cost of a worker is (4,000). Now the company has to optimally decide the combination that would yield the desired production at reduced cost. UNDERSTANDING COST-MINIMIZATION

12. combinations vehicles workers Total cost 1 6 1500 69,00,000 2 7 1400 66,50,000 3 A 8 1320 64,80,000 4 B 9 1270 64,30,000 5 C 10 1240 64,60,000 The annual cost of ONE vehicle is (1,50,000) The annual cost of ONE worker is (4,000 ). Therefore at first combination the total cost =6*1,50,000+1500*4000 (9,00,000)+(60,00,000) The every combination is optimal than its above combination till the fourth combination because of cost reduction .And at fifth combination there is no cost reduction The firm would save (1,20,000) in case of workers but it has to incur (1,50,000) in vehicle expenses at fifth combination , which is (30,000)more than fourth combination. Hence , the firm would go for the fourth combination . (15,00,000)+(49,60,000) (13,50,000)+(50,80,000) (12,00,000)+(52,80,000) (10,50,000)+(56,00,000) (9,00,000) +(60,00,000)

13. E A B C VEHICLES LABOUR K1 K0 K2 L0 L1 L2 DIFFERENT ISO-COSTS & ISO-QUANTS CURVES SHOWS DIFFERENT LEVELS of EXPENDITURE THAT CAN BE USED TO SHOW THE PRICE LEVELS OF VEHICLE AND LABOUR AS (K0 L0,K1 L1,K2 L2) . EQUILIBRIUM POINT IS REPRESENTED BY “E” WHERE the iso-quant showing the desired output is represented by tangent to the iso-cost. m.r.t.s = mp l = k mp k l