E501 Managerial Economics Fall 2012

Faculty: Dr. Syed Naimul Wadood

IBA DU, MBA Program

Lecture No. 9, Date: 27.09.2012

Topic 4: Theory of Production

(following Chapter 6 of Keat, Young and Banerjee (2011) and Chapter 6 of Salvatore (2005))

4.6 Concept: Output Elasticity of Labor

Production/Output Elasticity of Labor (EL) measures the percentage change in output divided by the percentage change in the quantity of labor used. That is,EL = % ∆Q/%∆L Rearranging this we findEL = (∆Q/Q) / (∆L/L) = (∆Q/∆L)/ (Q/L) = MPL/APL

In terms of calculus,EL = (∂Q/∂L)(L/Q)

4.7 Optimal Use of the Variable Input (Labor)

The extra revenue generated by the use of an additional unit of labor is called the marginal revenue product (MRPL). MRPL= MPL×MR

On the other hand, the extra cost of hiring an additional unit of labor is called the marginal cost of labor (MRCL). MRCL = ∆TC/∆L

Thus, a firm should continue to hire labor as long as MRPL>MRCL and until MRPL=MRCL. With perfectly competitive input and output markets, MRCL= w, P=MR, so MPL= w/P.

4.8 The Production Function with Two Variable Inputs

The Isoquant Curve (Inputs: Labor and Capital) The Isocost Lines The Marginal Rate of Technical Substitution (MRTS)

(the slope of the isoquant curve) The Optimal Combination of the Two Inputs. Special Cases: Perfect Substitutes and Perfect Complements Inputs.

4.9 The Long-Run Production Function: the Concept of Returns to Scale

EQ = Percentage change in Q/Percentage change in all inputsThus, If EQ>1, we have increasing returns to scale (IRTS)If EQ=1, we have constant returns to scale (CRTS)If EQ>1, we have decreasing returns to scale (DRTS).

Another way to express this is in terms of the production function:

Q= f(X, Y)

Suppose we increase all the inputs by some proportion k. Thus output Q is also expected to increase by some proportion (say, h) because of the increase of all the inputs. We express this as:

hQ= f(kX, kY)

If h>k, the firm experiences increasing returns to scale (EQ>1).If h=k, the firm experiences increasing returns to scale (EQ=1).If h<k, the firm experiences decreasing returns to scale (EQ<1).

4.10 The Various Forms of a Production Function

Short-run production function

Q = f(L)K (output is expressed in terms of a variable input, labor, whereas capital, K, is given)

Cubic production function:

Q = a + bL + cL2 – dL3

Quadratic production function:

Q = a + bL – cL2

Power function:

Q = aLb (this can be expressed as log Q = log a + blog L)

This can also be readily converted into a function with two or more independent variables:

Q = a X1b X2

c X3d…………Xn

m

(graphs of the abovementioned functions are in Keat, Young and Banerjee (2011), pp. 190,191)

Cobb-Douglas production function:

Q= a Lb Kc (or sometimes written as Q= a Lb K1-b)

Important properties of Cobb-Douglas production function: (1) Can easily exhibit IRS, CRS, DRS if b + c> 1, b+ c=1 and b+ c <1, respectively. (2) Marginal product of factors are MPk = bQ/L and MPL= cQ/K. (3) Elasticity of output for factor L is b and elasticity of output for factor K is c. (4) Can be extended to any number of input variables.

Short-comings of Cobb-Douglas production function: (1) It cannot show the marginal product going through all three stages of production (a cubic function can show it).(2) It cannot show a firm or industry passing through increasing, constant or decreasing returns to scale.