Theory and estimation of production

Chapter 6

The production function

• In economics and in business as in GF case, the analysis of cost begins with the study of production function.

• PF is a statement of the relationships between firm’s scarce resources (inputs) and the output. Mathematically Q = f(X1, X2,…Xk)

• For bottling company, input Xs would be raw materials (ie carbonated water, sweeteners, flavorings, labor, support staff and fixed assets such as plant and equipment)

• Short run PF shows the max quantity of goods produced by a set of inputs, assuming that one of inputs remains fixed.

Short run analysis of total, average and marginal product

• In the short run, marginal product (MP) and average product (AP) are important measures:– MPx = change in Q/ change in X,

holding other inputs constant– APx = Q/X

holding other inputs constant

• These can be seen better in the following tables (see photocopies attached)

Law of diminishing returns

• This law (economic doctrine) states that as additional units of variable input (labor) are combined with a fixed input, at some point, MP starts to diminish (see figure).

The case of multiple inputs• For multiple inputs, optimal employment of inputs is determined

where:– MP1 / W1 = MP2 / W2 = MPk / Wk

• Let’s consider India and Taiwan for production of computer parts for IBM. In production, one should not look only at input costs, but also marginal products. The figures are as follows:

– MPt = 36 Wt = 6 dollars– MPi = 12 Wi = 3 dollars

• How much to be produced in each manufacturing plant? Since labor is cheaper in India, you may be tempted to produce mostly in India. However, a closer look at MP/W ratios reveal the opposite.

– MPt / Wt > MPi / Wi or 36/6 > 12/3 but at the final decision, other factors, such as political stability, trade barriers, may be added to the final decision making.

Long run production function

• In the LR, all inputs are variable. As both inputs increase, total output increases at a rate called returns to scale. See table below:

• Insert here table return to scale• One way to measure return to scale is to use a

coefficient of output elasticity.• Eq = %change in Q / % change in all inputs

– If E>1 increasing return to scale– If E=1 constant return to scale– If E<1 decreasing return to scale

• In a production function of Q=f(X,Y)– If hQ = f(kX,kY)– If h>k increasing– If h=k constant– If h<k decreasing

• Example: Q=2X + 5Y when X=10, Y=10

• Q=70

• If both are doubled, Q=140 constant

Cobb-Douglas production function

• This is a special, functional production function suggested by Cobb (mathematician) and Douglas (economist) in 1928.

• It has important properties, such as • a)exhibits increasing, decreasing or constant returns.

Given:– Q=a Lb Kc if (b+c) > 1 increasing

» (b+c) = 1 constant» (b+c) < 1 decreasing

b) Permits to get MP for any factor.c) Exponents are the elasticity coefficients of production. Thus the

elasticity of L and K are constant.

International Call Centres

• Technology and falling costs of telecommunication have made it economically feasible for call centres to be located almost anywhere in the world. For example, Salt Lake City has become an attractive site for global call centres. In these service works, the input is labour at call centre and the output is the number of calls handled by customer representatives. Call centres are used by Credit Cards companies, hotels, etc.