Production and Cost: A Short Run Analysis

1. Production and Cost:A Short Run Analysis

2. Production

3. The Organization of Production Production: transformation of resources into output of goods and services. Inputs:Labour Machinery LandRaw Materials Output:goods and services

4. The Production Function Q = f ( L, K, R, T )Simplifying, Q = f (L, K) The Short Run The Long Run One of the factors is fixedSay K is fixed at KoQ = f ( L, Ko ) ALL factors are variable Q = f ( L, K )

5. The Short Run Production Function Q = f ( L, Ko )….. Only L is variable Production Q c As Labour input is raised while keeping capital constant output rises. But beyond a point (point c) output starts to fall as capital becomes over-utilized. 10 9 d b 5 a 3 0 Labour L 1 2 3 4

6. Constant Returns to Factor Production Q d CRF: If Labour input is raised x times output is exactly raised x times at all levels of L. Example: photocopying, writing software codes etc. 20 c 15 b 10 a 5 0 1 2 3 4 Labour L

7. Increasing Returns to Factor Production Q IRF: If Labour input is raised output is raised at an increasing rate. Example: Heavy industrial production (metals etc) etc. d 20 c 10 b 5 a 2 0 1 2 3 4 Labour L

8. Decreasing Returns to Factor Production Q DRF: If Labour input is raised output is raised at a decreasing rate. Example: subsistence agricultural production etc. d 23 c 21 b 17 a 10 0 1 2 3 4 Labour L

9. A typical manufacturing industry production function Most manufacturing production functions exhibit both IRF and DRF. Stage I : IRF Stage II : DRF Stage III : diminishing production Production Q b a 0 Lb Labour L La STAGE I STAGE II STAGE III

10. Average Product of Labour APL = Q / L Marginal Product of Labour MPL = ∆Q / ∆L

11. Exercise 1 Find the Marginal Products for production functions with a) Constant Returns to Factorb) Increasing Returns to Factorc) Decreasing Returns to Factor

12. Constant Returns to Factor Q d 20 c 15 For Production functions with CRF MP is constant. b 10 a 5 L 0 1 2 3 4 MPL a’ b’ c’ d’ 5 L 0 1 2 3 4

13. Q Increasing Returns to Factor d 20 c 10 For Production functions with IRF MP is rising. b 5 a 2 L 0 1 2 3 4 MPL d’ 10 c’ 5 b’ 3 a’ 2 L 0 1 2 3 4

14. Decreasing Returns to Factor Q d 23 21 21 c For Production functions with DRF MP is diminishing. 17 b a a 10 L 0 1 2 3 4 MPL a’ 10 b’ 7 c’ 4 d’ 2 L 0 1 2 3 4

15. MPL for a typical manufacturing industry production function MPL is rising in stage I, falling in stage II and negative in Stage III Q, MPL b Q STAGE I a STAGE II STAGE III 0 Lb Labour L La MPL

16. Find the Average Products for the manufacturing production functions Exercise 2

17. APL for a typical manufacturing industry production function APL is rising upto point c.At point c MPL = APLNote that the blue line showing the APis also tangent to the production curve. Q, MPL b c Q STAGE I STAGE II STAGE III a 0 Lb Labour L La

18. APL for a typical manufacturing industry production function APL is falling beyond point c.But APL is never negative Q, MPL b c Q STAGE I STAGE II STAGE III a 0 Lb Labour L La

19. MPL for a typical manufacturing industry production function Q, MPL b c Q STAGE I STAGE II STAGE III a APL 0 Lb Labour L La

20. MPL and APL for a typical manufacturing industry production function Q, MPL b c Q STAGE I a STAGE II STAGE III APL 0 Lb Labour L La MPL

21. APL & MPL for a typical manufacturing industry production function MPL is rising in stage I, falling in stage II and negative in Stage III c Q, MPL b a STAGE I STAGE II STAGE III APL 0 Lb Labour L La MPL

22. Exercise 3 Consider an improvement in production technology. How will this affect total, average and marginal products?

23. MPL and APL for a typical manufacturing industry production function B’ Q, MPL B A’ Q2 Q1 A 0 Lb Labour L La

24. APL & MPL for a typical manufacturing industry production function MPL is rising in stage I, falling in stage II and negative in Stage III Q, MPL APL2 MPL2 APL1 0 Labour L MPL1

25. Cost

26. Total cost = C = Cost of labour +Cost of Capital = [wage rate] . [ labour input] + [rental rate] . [Capital input] = [w.L] +[r. K] • In Short Run whe labour is the only variable input, capital is constant at Ko C = w.L + r.Ko Cost depends only on labour input.

27. Exercise 4 Mrs. Smith, the owner of a photocopying service is contemplating to open her shop after 4 PM until midnight. In order to do so she will have to hire additional workers. The additional workers will generate the following output. (Each unit of output = 100 pages). If the price of each unit of output is Rs.10 and each worker is paid Rs.40 per day, how many workers would Mrs. Smith hire?

29. Average and Marginal Costs

30. Short Run Costs • In the short run some inputs (K) are fixed and some inputs (L) are variable. So, Cost includes a fixed part and a variable part. Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC) TC = [ r. Ko ] + [ w. L ] • In the Short Run, K is fixed at Ko and r is also constant. • So as a Q ↑, fixed cost [r.Ko] is unchanged. • In the Short Run a Q ↑ must be due to a ↑ in L. • So as Q ↑ → L↑ → (w. L) ↑ → (TVC) ↑ • TVC = V(Q)

31. TC, TVC, TFC TC Explaining the shape of the TVC and TC: • The TC and TVC in this diagram relate to the manufacturing industry production. • TVC are rising with Q. Since TC = TVC + a constant, TC also takes the same shape. Up to point a TVC rises at a falling rate owing to Increasing Returns to Factors. • Between a and b, TVC rises at a rising rate owing to Decreasing Returns to Factors. • Beyond point b, TVC rises at a even faster rate owing to diminishing production. (the irrelevant part of the SR production function and hence of costs) TVC TFC b a Q

32. TC, TVC, TFC TFC and AFC TFC is fixed at [r.Ko] for the entire range of Q. AFC = TFC / Q • As Q ↑, the fixed cost gets distributed over a larger volume of production. Hence, AFC↓ as Q↑ TFC AFC AFC Q a b c

33. TC, TVC, TFC TC TVC TVC and TC and MC Marginal Cost = MC = ∆TC/∆Q = ∆TFC/∆Q + ∆TVC/∆Q = 0 + ∆[w. L] / ∆Q = ∆[w. L] / ∆Q = w. ∆L / ∆Q = w. [1/MPL] Or, MC = w/ MPL • That is MPL and MC are inversely related. A higher MPL implies a lower MC. • The range of Q for which MPL↑, MC would fall. (up to point a) • The range of Q for which MPL↓, MC would rise. (beyond point b) • The range of Q for which MPLis constant, MC would also be constant. (a very short span around point a) • The value of Q for which MPL is maximum, (Point a) MC would be minimum. MC,AVC, ATC MC Q a b c

34. TC, TVC, TFC TC TVC TVC and AVC Average Variable Cost = TVC/Q Or AVC = [w.L] / Q = w [L/Q] = w . [1/ APL] Thus AVC and APL are inversely related. Hence, AVC ↓ up to point c, reaching a minimum there and rising there after. At c , MPL = APL Hence AVC = MC MC,AVC, ATC MC AVC a b c Q

35. TC, TVC, TFC TC TVC ATC Average Total Cost = TC/Q The minimum of ATC corresponds to a point like point d. Note that at d, ATC = MC MC,AVC, ATC MC ATC a b c d Q

36. MC,AVC, ATC ATC = AVC + AFC The vertical distance between ATC and AVC is AFC. That’s it. ATC AVC AFC a b c d Q

37. MC,AVC, ATC MC The Cost Condition This diagram shows the AVC, ATC and the MC curves. Note that - • MC = AVC where AVC is minimum. • MC = ATC where ATC is minimum. ATC AVC a b c d Q