The Production Process and Costs By Asst. Prof. Kessara Thanyalakpark, Ph.D. 1
Production Analysis Production Function Q = F(K,L) The maximum amount of output that can be produced with K units of capital and L units of labor. Short-Run vs. Long-Run Decisions Fixed vs. Variable Inputs 2
Total Product Production Function Example: Q = F(K,L) = K.5 L.5 K is fixed at 16 units. Short run production function: Q = (16).5 L.5 = 4 L.5 Production when 100 units of labor are used? Q = 4 (100).5 = 4(10) = 40 units 3
Marginal Product of Labor MP L = DQ/DL Measures the output produced by the last worker. 4
Average Product of Labor AP L = Q/L Measures the output of an average worker. 5
Stages of Production Q Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns Q=F(K,L) MP L AP 6
The Law of Diminishing Marginal Returns As the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease. This law applies to a given production technology (assume technology constant) Technological Improvement may make it appear that there is not marginal returns when in fact there is 7
8 The Effect of Technological Improvement 8
Choice of Inputs : Production Isoquants Most production functions allow some substitution of inputs Suppose Q = K 1/2 L 1/2 ; to produce Q = 100, there are many combinations of K and L yield the result An isoquant shows all input combinations that produce the same quantity assuming efficient production. 9
10 Isoquants Substitution Unit of capital 50 40 20 10 0 T 15 20 40 Unit of labor 75 Q 3 = 300 Q 2 = 200 Q 1 = 100 Labors must be added for each unit of K eliminated, holding output constant.= -( K/ L) as K decreases, L increases : use more labor to compensate for one additional K 10
Slope and MP ( MP L, MP K ) output( Q) = (MP l ) x ( L) + (MP k ) x ( K) (Slope) = - ( K/ L) MP l = output / labor MP k = output/ capital In an isoquant curve, output is constant - hence Q = (MP l ) x ( L) + (MP k ) x ( K) = 0 Slope = - ( K/ L) = (MP l ) / (MP k ) 11
Returns to Scale Input substitution show what happen when a firm substitute one input for another while keeping output constant In long run, all input variable, one of the best ways to change output is to change the scale of operation (increase all inputs to production in proportion) 12
Returns to Scale Increasing Returns to Scale : output more than doubles when all inputs are doubled Constant Returns to Scale : output doubles when all inputs are doubled Decreasing Returns to Scale : output less than doubles when all inputs are doubled 13
Constant RTS 14
Increasing RTS 15
Isocost Line As we see,there are many ways to produce a given level of output, how does a firm choose its input mix? Depending on the costs of the inputs Cost is the sum of the quantities of each input used in the production process times their respective prices; TC = Wage x Labor + Rent x Capital 16
Capital 10 8 6 4 2 K A Total cost = wage (labor) + rent (capital) B Illustration of Isocost curve C K = a - b L 0 2 4 6 8 10 12 14 16 18 20 Labor Given TC is fixed, isocost can be expressed as : K = (TC/ r) - (wage/r) Labor Slope of isocost curve = - wage / rent ; slope is used to determine how much K must be given up if 1 more unit of labor is purchased. If TC increases - a parallel upward shift in the isocost curve because prices of inputs are constant D L 17
Isocost The combinations of inputs that cost the producer the same amount of money K For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slope of the isocost line K C 0 C 1 New Isocost Line for a decrease in the wage (price of labor). L L 18
Cost Minimization K Slope of Isocost = Slope of Isoquant Point of Cost Minimization Q L 19
Cost Minimization Marginal product per dollar spent should be equal for all inputs: MP w L = MP r K 20
Optimal Input Mix and Changes in Input Prices K B A High wage Low wage L 21
Optimal Input Mix When wage is low ; optimal input mix = A Once wage is high; optimal input mix = B Optimal input mix ( input combination yield a given output at the minimized cost) varies depending on relative prices It can be shown that the optimal input mix is at the point where ; MP w / Wage = MP r / Rent where slope of isoquant = slope of isocost 22
Cost Analysis Types of Costs Fixed costs (FC) Variable costs (VC) Total costs (TC) 23
Total Cost Curves It is a relationship between each possible level of output and its lowest cost possible. Basically, total cost is derived from the isoquant and isocost analysis 24
Short Run Versus Long Run There are two types of cost ; short run and long run Short run is the operating period during which at least one input is fixed in supply ( have fixed cost) Long run : periods where firm has complete flexibility - no inputs are fixed ( have only variable cost) 25
Short run Total and Variable Costs C(Q): Minimum total cost of producing alternative levels of output: $ C(Q) = VC + FC C(Q) = VC + FC VC(Q): Costs that vary with output FC: Costs that do not vary with output VC(Q) FC Q 26
Fixed Cost FC: Costs that do not change as output changes $ C(Q) = VC + FC VC(Q) FC Q 27
Average Total Cost ATC = AVC + AFC ATC = C(Q)/Q Average Variable Cost AVC = VC(Q)/Q Average Fixed Cost AFC = FC/Q Some Definitions $ MC ATC AVC Marginal Cost MC = C/ Q AFC Q 28
Fixed Cost $ Q 0 (ATC-AVC) = Q 0 AFC MC ATC = Q 0 (FC/ Q 0 ) AVC = FC AFC ATC AVC Fixed Cost Q 0 Q 29
Variable Cost $ Q 0 AVC = Q 0 [VC(Q 0 )/ Q 0 ] = VC(Q 0 ) MC ATC AVC AVC Variable Cost Q 0 Q 30
Total Cost $ Q 0 ATC = Q 0 [C(Q 0 )/ Q 0 ] MC ATC = C(Q 0 ) AVC ATC Total Cost Q 0 Q 31
Relation between Production Theory and Cost SMC = TVC/ Q = ( Wage x Labor) / Q = Wage ( Labor/ Output ) = Wage Payment / MP In the Short-Run, law of diminishing in MP apply to MC too. Law of diminishing MP eventually fall ( capital is fixed) MC rises 32
Long Run Cost Curve Long run curves - often referred to as planning curves In the long run, AVC always less than or equal to the short-run AVC It can be thought of as an envelop theorem 33
Long-run average cost envelope of short-run average cost curves 34
Long-run average and marginal cost curves 35
Economies of Scale $ LRAC Economies of Scale Diseconomies of Scale Output 36
Economies of Scale Greater Specialization in the use of capital and labor Learning curve effect Volume discounts in purchasing inputs Relatively cheaper cost of fund 37
Economies of Scale Overhead cost ( administrative costs management salaries, other indirect expenditures as heating and lighting expenses) Reserves of replacement parts and maintenance personal Distribution Marketing and sales promotions Research and development 38
Diseconomies of Scales Transportation cost (one plan distribute to all outlets) Problems of coordination and control encountered by management 39
Economies of Scope Costs of producing two or more products jointly by one firm is less than cost of producing these products separately by different plants or firms [TC(Q 1,0) + TC(0,Q 2 ) ] > TC(Q 1,Q 2 ) 40
Economics of Diversification Benefits Economies of Scope Promoting Complements Costs More expensive to manage Communication 41
A Faulty Reason to Diversify Should firm enter into a countercyclical industry to reduce earning volatility? It is true that diversification can reduce earning volatility. But the reduction in volatility need not increase a firm s value. 42
The costs of integrating diverse business within the same firm can be significant. Investors (shareholders) can diversify within their own investment portfolio at low cost. 43
When does Diversification create value? Economies of Scope is envisioned Likely to occur in related diversification. For example, when the businesses serve common markets or use related technologies. 44
Profit maximization A firm should increase output as long as marginal revenue exceeds marginal cost A firm should not increase output if marginal cost exceeds marginal revenue At the profit-maximizing level of output, MR=MC 45
Optimal output and changes in marginal cost 46