Economic Analysis for Managers (ECO 501) Fall:2012 Semester Khurrum S. Mughal

Theme of the Lecture Production Theory Introduction The Production Function Production with One Variable Input Production with Two Variable Input Returns to Scale

Production Production refers to the transformation of inputs or resources into outputs of goods and services

Production INPUTS CAPITAL LABOR Land & Natural Entrepreneur Structures Resources Entrepreneur Workers Machinery plant & equipment

Short Run- At least one input is fixed Factors of Production Short Run- At least one input is fixed Long Run - All inputs are variable The length of long run depends on industry.

Output = Total inputs(variable inputs) Level and Scale of Production Level of production can be altered changing the proportion of variable inputs Output = Fixed inputs + Variable inputs Scale of production can be altered by changing the supply of all the inputs (only in the long run) Output = Total inputs(variable inputs)

Production Function General equation for Production Function: Q = f (K,L), where L = Labour K = Capital Maximum rate of output per unit of time obtainable from given rate of Capital and Labour An engineering concept: Relates out puts and inputs

Production Function with Two Inputs Devoid of economics 6 10 24 31 36 40 39 5 12 28 42 4 3 23 33 2 7 18 30 1 8 14 Q = f(L, K) Capital (K) Labor (L) Substitutability between factors of production Returns to Scale vs Returns to Factor

Theme of the Lecture Production Theory Introduction The Production Function Production with One Variable Input Production with Two Variable Input Returns to Scale

Production or Output Elasticity Production With One Variable Input Q = f (K,L), where K is fixed Total Product TP = Q = f(L) Marginal Product MPL = TP L Average Product APL = TP L Production or Output Elasticity Q/Q L/L Q/ L Q/L = EL MPL APL

Total, Marginal, and Average Product of Labor, and Output Elasticity Production With One Variable Input Total, Marginal, and Average Product of Labor, and Output Elasticity

Total, Marginal, and Average Product of Labor, and Output Elasticity Production With One Variable Input Total, Marginal, and Average Product of Labor, and Output Elasticity L Q MP AP E - 1 3 2 8 5 4 1.25 12 14 3.5 0.57 2.8 6 -2 -1

Law of Diminishing Returns and Stages of Production Stage II of Labor Stage III of Labor Stage I of Labor Total Product 16 D E 14 C F TP 12 I 10 B 8 G 6 A 4 2 Marginal & Average Product 1 2 3 4 5 6 Labor 7 6 5 B’ C’ A’ D’ E’ F’ 4 3 AP 2 1 1 2 3 4 5 6 7 -1 MP Labor -2 -3

Relationship Among Production Functions 1: Marginal product reaches a maximum at L1 (Point of Inflection G). The total product function changes from increasing at a increasing rate to increasing at a decreasing rate. 2: MP intersects AP at its maximum at L2. 3: MP becomes negative at labor rate L3 and TP reaches its maximum.

Marginal Revenue Product of Labor Optimal use of the Variable Input Marginal Revenue Product of Labor MRPL = (MPL)(MR) Optimal Use of Labor MRPL = w

Optimal use of the Variable Input MP MR = P L 2.50 4 $10 3.00 3 10 3.50 2 10 4.00 1 10 4.50 10 Assumption : Firm hires additional units of labor at constant wage rate = $20

Use of Labor is Optimal When L = 3.50 Optimal use of the Variable Input L MP MR = P MRP w L L 2.50 4 $10 $40 $20 3.00 3 10 30 20 3.50 2 10 20 20 4.00 1 10 10 20 4.50 10 20 Assumption : Firm hires additional units of labor at constant wage rate Use of Labor is Optimal When L = 3.50

Optimal use of the Variable Input $ 40 30 20 10 w = $20 dL = MRPL 2.5 3.0 3.5 4.0 4.5 Units of Labor Used

Optimal use of the Variable Input Production function of global electronics: Q=2k0.5L0.5 Compute Optimal use of labor when K is fixed at 9, Price is Rs. 6 per unit and wage rate is Rs. 2 per unit

Theme of the Lecture Production Theory Introduction The Production Function Production with One Variable Input Production with Two Variable Input Returns to Scale

Production with Two Variable Input Isoquants show combinations of two inputs that can produce the same level of output. K Q 6 10 24 31 36 40 39 5 12 28 42 4 3 23 33 2 7 18 30 1 8 14 L

Marginal Rate of Technical Substitution K

_ (MPL) = MRTS (MPK) Marginal Rate of Technical Substitution A movement down an Isoquant the gain in out put from using more labor equals loss in output from using less capital MRTS: Slope of the Isoquant _ (MPL) = MRTS (MPK)

ISOCOST Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

Isocost Line AB C = $100, w = r = $10 slope = -w/r = -1 Capital AB C = $100, w = r = $10 10 8 6 4 2 A slope = -w/r = -1 vertical intercept = 10 1K 1L B Labor 2 4 6 8 10

Isocost Line Capital Labor A’ 14 10 8 4 Isocost Lines AB C = $100, w = r = $10 A’B’ C = $140, w = r = $10 AB* C = $100, w = $5, r = $10 A B B’ B* Labor 4 8 10 12 14 16 20

MRTS = w/r Optimal Combination of Inputs Isocost Lines AB C = $100, w = r = $10 A’B’ C = $140, w = r = $10 A’’B’’ C = $80, w = r = $10 MRTS = w/r

Optimal Employment of Two Inputs Optimal combination is where slope of Iso Cost and that of Isoquant are equal: MPL = w MPK r MPL = MPK w r

Profit Maximization MPL = w MPL = MPK w r MPK r To maximize Profits, each input must be hired at the efficient input rate MRPL = w = (MPL)(MR) MRPK = r = (MPK)(MR) Profit Maximizing follows that the firm must be operating efficiently MPL = MPK w r MPL = w MPK r

Expansion Path

Theme of the Lecture Production Theory Introduction The Production Function Production with One Variable Input Production with Two Variable Input Returns to Scale

Production Function Q = f(L, K) Economies of Scale - Returns to Scale Production Function Q = f(L, K) Q = f(hL, hK) If  = h, constant returns to scale. If  > h, increasing returns to scale. If  < h, decreasing returns to scale.

Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale

Cobb-Douglas Production Function Returns to Scale in An Empirical Production Function Cobb-Douglas Production Function Q = AKaLb If a + b = 1, constant returns to scale. If a + b > 1, increasing returns to scale. If a + b <1, decreasing returns to scale.

Sources of Increasing Returns to Scale Technologies that are effective at larger scale of production generally have higher unit costs at lower level of production Labor Specialization Labor may specialize in their specific tasks and perform it efficiently Inventory economies Larger firms have lesser need for machine inventory backup

Sources of Decreasing Returns to Scale Managerial Issues due to large size of the firm Increased Transportation costs Larger labor costs due to requirement of increased wages to attract labor from farther areas

Economies of Scope Using facility for producing additional products E.g. Daewoo Bus Service for passenger and cargo movement Using unique skills or comparative advantage Proctor & Gamble using its existing sales staff and production capabilities for marketing various products as substitutes and complements

Measuring Productivity Total Factor Productivity