Cal Poly Pomona

EC 201 Lecture 7

Dr. Bresnock

EC 201

Cal Poly Pomona

Dr. Bresnock

Lecture 7

Production Theory

Basically we begin with a simple production relationship/function:

Q = f(N) where Q = Output

N = Input (i.e. Labor, Land, Capital, etc.)

How are Q and N related?

Let’s use L = Labor Input to keep things simple.

Do you expect Q to increase as L increases? In other words, if more workers are hired, do you expect output to increase?

The simple relationship between Q and L is usually direct, or positive. That is…

If L s then Q s

If L s then Q s

But the exact relationship may have 3 theoretical, functional forms or shapes…

Three Theoretical Production Forms

Let L = number of units of Labor Input

Q = number of units of Product or Output

TP = Q = Total Product or Total Output

AP = TP/L = Q/L = Average Product or Average Output (ex. output per worker)

MP = TP/L = Q/L = Marginal Product or Marginal Output

= the additional output per an additional unit of input

(ex. the additional output per an additional worker)

= the slope of the TP .

1)Linear -- demonstrates constant marginal returns, that is, as additional units of input are added to the production process, each additional unit of input adds an equal amount to the number of units of output/product produced.

L TP MP AP

0 0 Q TP

1 10 10 10

2 20 10 10 slope constant

3 30 10 10

4 40 10 10 10 MP = AP

5 50 10 10

0 1 L

2)Increasing-- demonstrates increasing marginal returns, that is, as additional units of input are added to the production process, each additional unit of input adds more and more to the number of units output/product produced.

L TP MP AP Q TP

0 0 slope ing

1 10 10 10

2 30 20 15 MP

3 60 30 20 AP

4 100 40 25

10

0 1 L

3)Decreasing-- demonstrates diminishing marginal returns, that is, as additional units of input are added to the production process, each additional unit of input adds less and less to the number of units of output/product produced.

Q

TP

L TP MP AP slope ing

0 0

1 200 200 200

2 350 150 175

3 450 100 150

4 525 75 131.25 200 AP

MP

L

0 1

The Typical Production Function -- A typical production function includes all the three theoretical cases presented on the previous page. The firm, whose objective is to maximize profits, will operate in the area of diminishing returns. (This result will be explained with additional comments from class lecture).

Graph 1: Typical Production Function

Three Stages of Production

Stage 1 = 0 – L1 Increasing Returns Stage. Here TP is increasing at an increasing rate. That increasing rate means that the MP is increasing. In this stage of production all workers should be hired as each additional worker adds more than the previous worker to total production.

Stage 2= L1 – L3 Decreasing Returns Stage. Here TP is increasing at a decreasing rate. That decreasing rate means that the MP is decreasing. In this state of production, aka “the economic region of production”, the firm will locate the profit maximizing amount of workers to hire.

Stage 3 = Beyond L3 Negative Returns Stage. Here TP is decreasing and the MP is negative. The firm should not hire workers past L3.

Two Equivalent Decision Rules for the Profit Maximizing Firm

(1) Hire L, the # of workers, such that the firm maximizes TOTAL profits. This occurs where

Max (Total Value of Output – Total Cost of Input) = Max Total Profit

(2) Hire L so that the marginal value product, MVP, is equal to the marginal cost, MC. (Marginal value product is also referred to as marginal revenue product.) That is…

MVP = MC where MVP = MP x Px (Px = Output Price)

Given the PX = Price of the output = $3, and the PL = price of the input, ie. labor = $75, and the following input and marginal product information, the following relationships are derived. Assume additionally that each laborer is paid the same amount, that is, the input cost of each additional worker is the same, or the marginal cost of each worker is the same, thus PL = MCL = $75.

This firm will hire 4 workers in order to maximize total profits.

Private Optimum

Determined by hiring the number of units, i.e. workers, so that Total Profit ismaximized, and the number of inputs so that the MVP = MCL.

Note : MVP = marginal value product = MP x PX. MVP = the value of the additional production created by an additional worker.

Graph 2 Private Optimum

Graph 3 Changes in the Marginal Cost

Graph 4 Changes in the Productivity and/or Output Prices

1