Session 5: Production and Optimal Input Combinations Business Economics Session 5: Production and Optimal Input Combinations Faculty: Sunitha Raju Session Date: 22.10.2016

Economics of Production Decisions Decision Problem what is the most efficient and cheapest means of producing quantities of output demanded by consumers Efficient Production Decisions - understanding the fundamentals of Production functions and Production process - selection of Production technique and resource inputs - relationship between technology, inputs and output Contd…

Basis for Production Decisions Economic principles underlying input-output relationships Conditions for achieving peak production efficiency Optimising the mix of resource inputs in short run and long run Provides the foundation for estimating production costs and for selecting the most economical production technique

Short Run Production Function A production function defines all technical efficient input-output combinations Any improvement in technology results in new production function. Q= f (Xₐ, Xb, Xc, Xd, ………. Xn ) Q = f (L, K ) Q= f (Xₐ, Xb, │Xc, Xd ,………. Xn )

Basic Production Concepts Defining Production Function Production is physical transformation of input resources into goods & services Inputs → Process → Output Production function defines the technical relationship between production inputs and output Contd…

Basic Production Concepts 2. Defining Production Process A product can be produced by various techniques/methods of production A method in which various inputs are combined is defined by a ‘Process’ or ‘Technique’ (P) P1 P2 P3 L 2 3 5 K 3 2 4 Output is same but methods of input combination differs. Contd…

Basic Production Concepts Technically efficient process P1 P2 L 2 3 K 3 3 P1 is technically efficient as less L used compared to P2 L 2 1 K 3 4 P1 and P2 are not comparable and both considered as technically efficient Contd…

Basic Production Concepts Economic Efficient process Amongst the technically efficient processes, the least cost process is defined as Economically efficient process. Contd…

Basic Production Concepts 3. Inputs Based on relationship with output, broadly categorise all inputs into Fixed inputs (Capital) : same level of input irrespective of output level (eg : Machinery) Variable input (Labour) : Varies with output level Q= f (L, K) how do changes in input level influence the changes in output level Contd…

Basic Production Concepts 4. Long Run vs Short Run Short run When Production decisions are defined by a given capacity/capital/technology Fixed and variable inputs together production determine production. decision relates to how much to produce under a given capacity Contd…

Basic Production Concepts Long run When Production decisions are not constrained by a given technology/capacity Number of technological options exist. As such, no fixed inputs Production decision relates to identifying optimum capacity/scale of operation.

Short Run Production Function A production function defines all technical efficient input-output combinations Any improvement in technology results in new production function. eg: better equipment, productivity enhancing training

Short Run Production Decisions 1. Case of one variable input Decision on output/input level defining technically efficient level of output defining economically efficient level of output Together (a), (b) & (c) will determine ‘how much’ output (Q) to produce and ‘how much’ inputs to use. Q = f (L, K )

ABC Company: Average and Marginal Products of Labour Amount of Machine Tools (Fixed) (K) Amount of Labour (L) Total Output 5 1 12 2 27 3 42 4 56 68 6 76 7 8 74

Production Function : Economic Principles 1. Production Function Characteristics Given a fixed amount of capital and managerial capability, behaviour of output with alternate amounts of variable input Technically most feasible output Operating below the production function-what does it mean? Nature of production function defined by nature of change in output to changes in variable input Alternate types of production function General type of Production function (S shaped) Total output and relationship with Average Product (APL) and Marginal Product (MPL)of Variable input Principle of Diminishing Marginal returns

ABC Company: Average and Marginal Products of Labour Amount of Machine Tools (Fixed) Amount of Labour Total Output Average Products of Labour Marginal Product of Labour 5 - 1 12 12.0 2 27 13.5 15 3 42 14.0 4 56 14 68 13.6 6 76 12.7 8 7 10.9 74 9.2 -2 Increasing returns to variable input More than proportional increase to variable input MP > AP Decreasing returns to Variable input Less than proportional increase to variable input MP<AP Maximum Output level MP=0 Declining AP

Production Efficiency and Production Costs Stages of Production Stage I (Rising APL) Increasing returns to variable input Efficiency of input use rising (Fixed vs Variable input) Efficiency of additional use of variable input positive Stage II ( Declining APL, MPL Max Q ) Decreasing return to variable input (greater than zero) Efficiency of fixed input rises (Output continues to rise) Additional units of variable input adds to efficiency of fixed input but diminish the efficiency of variable input Stage III (Declining Q) Efficiency of fixed input reaches peak More variable input leads to fall in Q MPL negative

Production Efficiency and Production Costs Optimum Stage of Production From standpoint of Efficiency and Cost, Stage II is Optimum Rate of variable input and fixed input use depends on prices Profit maximising output in Stage II, assuming no change in output prices In Stage I unit costs are declining. Hence, more inputs to produce output Profit max output can occur in this stage when output prices are falling (Recession) In Stage III, Output is declining. Hence irrational to operate

Total Marginal and Average Product Curves

P Q TR = D . Decision on how much Q to produce As long as MPL is positive Marginal Revenue Product (MRPL) → MRPL ≥ = PL = MRPL = = MRL . MPL = PL Corresponds to Q = 68 and L = 5 L P Q TR = D .

ABC Company: Average and Marginal Products of Labour Assume MR = 5 PL = 60 Amount of Machine Tools (Fixed) Amount of Labour Total Output Average Products of Labour Marginal Product of Labour MRPL 5 - 1 12 12.0 60 2 27 13.5 15 75 3 42 14.0 4 56 14 70 68 13.6 6 76 12.7 8 40 7 10.9 74 9.2 -2

Problem Solving 1 Tax Advisors Inc. has an office for processing tax returns in Pennsylvania. The following table shows how many tax returns are processed per hour as the number of CPA (Certified Public Accountants) employed increases CPAs (L) Tax returns processed / hour 1 0.2 2 1.0 3 2.4 4 2.8 5 3.0 6 2.7 1. Should the firm engage the 4th CPA? What should be the optimum number of CPAs to be engaged? 2. If the CPA’s earn $35 per hour and the revenue for each tax return processed is $100, should the firm employ the 4th CPA.

Production Decisions : Dimensions 1. Given a production function Under conditions of recession (output prices are falling), a firm decides to produce where APL max Under conditions of boom (output prices are rising), a firm produces until MRPL ≥ PL Conceptualize the rising managerial salaries Contd…

Production Decisions : Dimensions 2. Case of more than one variable input Efficient combination of inputs Methodology used is Isoquant

Short run Production Function : Efficient Combination of Inputs Isoquants L1 6 10 24 31 42 39 5 12 28 36 40 40 4 12 28 36 40 36 3 10 23 33 36 33 2 7 18 28 30 28 1 3 8 12 14 12 L2 1 2 3 4 5 6 Isoquants show combination of two inputs that can produce same level of outputs

Isoquants L1 6 10 24 31 42 39 5 12 40 40 28 36 4 12 40 36 28 36 3 10 23 33 33 36 2 7 18 28 30 28 1 3 8 12 14 12 L2 1 2 3 4 5 Isoquants show combinations of two inputs that can produce same level of outputs

L1 Substitution between L1 and L2 is determined by marginal productivities of L1 and L2 Marginal rate of technical substitution (MRTS) = = The rate of substitutability between inputs is defined by the shape of Isoquant (ratio of MPL) Q3 Q2 Q1 L2

Isoquant L1 L1 L1 L2 L2 L2 L1 and L2 are not perfect substitutes L1 and L2 are perfect substitutes L1 and L2 are complementary

Isocost Isocost show the different combinations of inputs (at given prices) For the same cost outlay. L1 L2 Any point on Isocost reflects the price ratio of L1 and L2

Efficient Combination of Inputs .

Efficient Combination of inputs Effect of a change in Input Price L1 L1 L1 Q2 L2 L2 L2

Problem Solving Medical Testing Labs, Inc., provides routine testing services for blood banks in the Los Angeles area. Tests are supervised by skilled technicians using equipment produced by two leading competitors in the medical equipment industry. Records for the current year show an average of 27 tests per hour being performed on the Test logic-1 and 48 tests per hour on a new machine, the Accutest-3. The Testlogic-1 is leased for $18,000 per month and the Accutest-3 is leased at $32,000 per month. On average, each Machine is operated 25 days of 8 hours each. Does the Lab usage reflect optimal mix of Testlogic-1 and Accutest-3. 2. If the price of tests conducted at the Lab is $6, should the company lease more machines.

Long Run Production Function Scale of operation is another source for cost minimization Identifying optimal scale of operation for a given demand conditions

Long Run Production Function Q = f (L, K) Where scale increases, then output increases (Increasing Returns to Scale) by a greater proportion output increases (Constant Returns to Scale) by the same proportion output increases (Decreasing Returns to Scale) by a lesser proportion

Long Run Production Function Production Function Q = f(L, K) Q = f (hL, hK) If  = h, then f has constant returns to scale. If  > h, then f has increasing returns to scale. If  < h, the f has decreasing returns to scale.