The functional relationship between physical inputs and physical output
3.
Production Function With One Variable Input Total Product Marginal Product Average Product Production or Output Elasticity TP = Q = f(L) MP L = TP L AP L = TP L E L = MP L AP L
4.
Production Function With One Variable Input Total, Marginal, and Average Product of Labor, and Output Elasticity
1. Production function for a firm is Q = 100L – 0.02L 2 . If 10 units of labor are used, What is the maximum average productivity of labor?
2. If the average product of labor (AP L ) is 30L – L 2 , What is the maximum possible total product (TP L ) ?
3. The Production function of a manufacturing unit, using only labor (L) as inputs in the production process, is estimated to be Q = 100 L 2 – L 3 . What is the number of labor input at which the firm can maximize average productivity ? and What is the maximum average productivity at that input level?
8.
Optimal Use of the Variable Input Marginal Revenue Product of Labor MRP L = (MP L )(MR) Marginal Resource Cost of Labor MRC L = Optimal Use of Labor MRP L = MRC L TC L
9.
Optimal Use of the Variable Input Use of Labor is Optimal When L = 3.50
11.
Production With Two Variable Inputs Isoquants show combinations of two inputs that can produce the same level of output. Firms will only use combinations of two inputs that are in the economic region of production , which is defined by the portion of each isoquant that is negatively sloped.
13.
Production With Two Variable Inputs Economic Region of Production
14.
Production With Two Variable Inputs Marginal Rate of Technical Substitution MRTS = - K/ L = MP L /MP K
15.
Production With Two Variable Inputs MRTS = -(-2.5/1) = 2.5
16.
Production With Two Variable Inputs Perfect Substitutes Perfect Complements
17.
Optimal Combination of Inputs Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.
18.
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 AB* C = $100, w = $5, r = $10
Budget constraint of the firm is Rs.720. The market going wage rate w = Rs.10 and cost of capital r = Rs.10
a.The optimum input quantities of Labour and Capital and the output at that input quantities
b.The optimum output if both the wage rate and cost of capital increase to Rs. 15.
2.Suppose the price of labour is Rs.10 and the price of capital is Rs.2.5
Use this information to determine the isocost equations corresponding to a total cost of Rs.200 and Rs.500
Plot these two iso-cost lines on a graph
If the price of labour falls from Rs.10 per unit to Rs. 8 per unit, determine the new Rs.500 iso-cost line and plot it on the same diagram used in part (b)
22.
Returns to Scale 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.
23.
Returns to Scale Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale
24.
Returns to Scale Returns to Scale Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale
Classify various firms in an industry under study by size groups or classes
Determine which size groups or classes are increasing or decreasing their share of the total output
If the share of a given size-class falls, that size class is relatively inefficient and in general, more inefficient the size group, more rapidly the share falls. Likewise, the size-class whose share in industry grows the most, is regarded as most efficient size- class or group
The technique gives the optimum size of a firm only and that too in terms of output range or the size group. Butit does not yield the cost function