1. Production

2. What Owners Want
We focus on for-profit firms in the private sector in this course.
We assume these firms’ owners are driven to maximize profit.
Profit is the difference between revenue (R), what it earns from selling its product, and cost (C), what it pays for labor, materials, and other inputs.
where R = pq.
To maximize profits, a firm must produce as efficiently as possible, where efficient production means it cannot produce its current level of output with fewer inputs.

3. Production Function
The Production Function measures the maximum possible output that the firm can produce from a given amount of inputs (such as labor, capital, land, raw materials, etc) by given technology..

4. Short-Run vs Long-Run
A firm can more easily adjust its inputs in the long run than in the short run.
The short run is a period of time so brief that at least one factor of production cannot be varied (the fixed input). We can also call it Production with One Variable.
The long run is a long enough period of time that all inputs can be varied. We can also call it Production with Two Variables.

5. Production with One Variable: Labor Input (SR Production)
In the short run (SR), we assume that capital is a fixed input and labor is a variable input.
SR Production Function:
q is output, but also called total product; the short run production function is also called the total product of labor

6. Average (AP) vs Marginal Productivity (MP) of Labor
Average product : Output per unit of a particular input.
Marginal product: Additional output produced as an input increased by one unit, while the other inputs’ level stay the same.

7. Production with One Variable Input (Labor) - SR
TABLE 6.1
PRODUCTION WITH ONE VARIABLE INPUT
AMOUNT OF LABOR (L)
AMOUNT OF CAPITAL (K)
TOTAL OUTPUT (q)
AVERAGE PRODUCT
MARGINAL PRODUCT 10 — 1 2 30 15 20 3 60 4 80 5 95 19 6
108 18 13 7
112 16 8 14 9 12 -4
100 -8

8. The Slopes of the Production Curve
Figure 6.1 (1 of 2)
PRODUCTION WITH ONE VARIABLE INPUT
The total product curve in (a) shows the output produced for different amounts of labor input.
The average and marginal products in (b) can be obtained (using the data in Table 6.1) from the total product curve.
At point A in (a), the marginal product is 20 because the tangent to the total product curve has a slope of 20.
At point B in (a) the average product of labor is 20, which is the slope of the line from the origin to B.
The average product of labor at point C in (a) is given by the slope of the line 0C. 20

9. The Slopes of the Product Curve
Figure 6.1 (2 of 2)
PRODUCTION WITH ONE VARIABLE INPUT
To the left of point E in (b), the marginal product is above the average product and the average is increasing; to the right of E, the marginal product is below the average product and the average is decreasing.
As a result, E represents the point at which the average and marginal products are equal, when the average product reaches its maximum.
At D, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product.
When the marginal product is greater than the average product, the average product is increasing.
Similarly, when the marginal product is less than the average product, the average product is decreasing. 20

10. The Average Product of Labor Curve
In general, the average product of labor is given by the
slope of the line drawn from the origin to the corresponding point on the total product curve.
The Marginal Product of Labor Curve
In general, the marginal product of labor at a point is given by the slope of the total product at that point.
THE RELATIONSHIP BETWEEN THE AVERAGE AND MARGINAL
PRODUCTS
Note the graphical relationship between average and marginal products in Figure 6.1 (a). When the marginal product of labor is greater than the average product, the average product of labor increases.
At C, the average and marginal products of labor are equal.
Finally, as we move beyond C toward D, the marginal product falls below the average product. You can check that the slope of the tangent to the total product curve at any point between C and D is lower than the slope of the line from the origin.

11. The Law of Diminishing Marginal Returns
● law of diminishing marginal returns Principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease.
Figure 6.2
THE EFFECT OF TECHNOLOGICAL IMPROVEMENT
Labor productivity (output per unit of labor) can increase if there are improvements in technology, even though any given production process exhibits diminishing returns to labor.
As we move from point A on curve O1 to B on curve O2 to C on curve O3 over time, labor productivity increases.

12. Production Function with Two Variable Inputs (LR)
In the long run (LR), we assume that both labor and capital are variable inputs.
The freedom to vary both inputs provides firms with many choices of how to produce (labor-intensive vs. capital-intensive methods).

13. LR Production Isoquants
A production isoquant graphically summarizes the efficient combinations of inputs (labor and capital) that will produce a specific level of output. (i.e. Contour Map of Production Function at the given quntity level)

14. Figure 6.5
PRODUCTION WITH TWO VARIABLE INPUTS
A set of isoquants, or isoquant map, describes the firm’s production function.
Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D),
to isoquant q2 (75 units per year at points such as B), and
to isoquant q3 (90 units per year at points such as C and E).
By drawing a horizontal line at a particular level of capital—say 3, we can observe diminishing marginal returns. Reading the levels of output from each isoquant as labor is increased, we note that each additional unit of labor generates less and less additional output.

15. Diminishing Marginal Returns
Input Flexibility
Isoquants show the flexibility that firms have when making production decisions: They can usually obtain a particular output by substituting one input for another. It is important for managers to understand the nature of this flexibility.
Diminishing Marginal Returns
Even though both labor and capital are variable in the long run, it is useful for a firm that is choosing the optimal mix of inputs to ask what happens to output as each input is increased, with the other input held fixed.
Because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter when labor is added in place of capital.
There are also diminishing marginal returns to capital. With labor fixed, the marginal product of capital decreases as capital is increased.

16. Isoquants Properties of isoquants:
The farther an isoquant is from the origin, the greater the level of output.
Isoquants do not cross.
Isoquants slope downward.
The shape of isoquants (curvature) indicates how readily a firm can substitute between inputs in the production process.

17. Special LR Production Functions
Perfect Substitutes: ( q =f(L,K)= AL + BK ), where A and B are positive constants.

18. Figure 6.7 ISOQUANTS WHEN INPUTS ARE PERFECT SUBSTITUTES
When the isoquants are straight lines, the MRTS is constant. Thus the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being used.
Points A, B, and C represent three different capital-labor combinations that generate the same output q3.

19. Special LR Production Functions
Fixed-proportion: q = =f(L,K)= min{aL, bK} , where a and b are positive constants

20. Figure 6.8 FIXED-PROPORTIONS PRODUCTION FUNCTION
When the isoquants are L-shaped, only one combination of labor and capital can be used to produce a given output (as at point A on isoquant q1, point B on isoquant q2, and point C on isoquant q3). Adding more labor alone does not increase output, nor does adding more capital alone.

21. Special LR Production Functions
Cobb-Douglas: q =f(L,K)= A La Kb , where A, a and b are positive constants.

22. Marginal Productivities (MP)
The marginal product of an input is the change in output that results from a small change in an input holding the levels of other inputs constant.

23. Marginal Rate of Technical Substitution (MRTS)
Marginal Rate of Technical Substitution (MRTS) of labor for capital is the rate at which K must be given up as L level is increased so as not to change the output level.
OUTCOME: MRTS is the negative slope of the isoquant curve.

24. MRTS & Marginal Productivities
A small change (dL, dK) in the inputs causes a change to the output level of (i.e. total differential of the production function):
df = 0 since there is to be no change to the output level (on the same isoquant), so the changes dx1 and dx2 to the input levels must satisfy

25. MRTS & Marginal Productivities
By rearranging equation (A),

26. Returns to Scale
Returns to scale helps us to understand how output will respond to the increases in all inputs together
Suppose that all inputs are doubled, would the output double?
There are three types of returns to scales: for t>1
Increasing Returns to Scale (IRS):
Constant Returns to Scale (CRS):
Decreasing Returns to Scale (DRS):

27. Figure 6.10 RETURNS TO SCALE
When a firm’s production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are equally spaced as output increases proportionally.
However, when there are increasing returns to scale as shown in (b), the isoquants move closer together as inputs are increased along the line.

28. Production Function & Utility Function
Output from inputs
Preference level from consumption
Isoquant Curve
Indifference Curve
Marginal Rate of Technical Substitution (MRTS)
Marginal Rate of Substitution (MRS)
Marginal Productivities
Marginal Utilities