PPA 723: Managerial Economics Lecture 10: Production

Managerial Economics, Lecture 10: Production Outline  Production Technology in the Short Run  Production Technology in the Long Run

Managerial Economics, Lecture 10: Production Production  A production process transform inputs or factors of production into outputs.  Common types of inputs:  capital (K): buildings and equipment  labor services (L)  materials (M): raw goods and processed products.

Managerial Economics, Lecture 10: Production Production Functions  A production function specifies:  the relationship between quantities of inputs used and the maximum quantity of output that can be produced  given current knowledge about technology and organization.  For example, q = f(L, K)

Managerial Economics, Lecture 10: Production Short Run versus Long Run  Short run: A period of time so brief that at least one factor of production is fixed.  Fixed input: A factor that cannot be varied practically in the short run (capital).  Variable input: a factor whose quantity can be changed readily during the relevant time period (labor).  Long run: A time period long enough so that all inputs can be varied.

Managerial Economics, Lecture 10: Production Total, Average, and Marginal Product of Labor  Total product: q  Marginal product of labor: MP L =  q/  L  Average product of labor: AP L = q/L  The graphs for these concepts appear smooth because a firm can hire a "fraction of a worker" (part time).

Managerial Economics Lecture 10: Production Output, q, Units per day B A C L, Workers per day Marginal product,MP L Average product,AP L L,MP L (a) b a c L, Workers per day (b) Figure 6.1 Production Relationships with Variable Labor AP L = Slope of straight line to the origin MP L = Slope of total product curve AP L = MP L at maximum AP L

Managerial Economics, Lecture 10: Production Effects of Added Labor  AP L  Rises and then falls with labor.  Equals the slope of line from the origin to the point on the total product curve.  MP L  First rises and then falls.  Cuts the AP L curve at its peak.  Is the slope of the total product curve.

Managerial Economics, Lecture 10: Production

Law of Diminishing Marginal Returns  As a firm increases an input, holding all other inputs and technology constant,  the marginal product of that input will eventually diminish,  which shows up as an MP L curve that slopes downward above some level of output.

Managerial Economics, Lecture 10: Production Long-Run Production: Two Variable Inputs  Both capital and labor are variable.  A firm can substitute freely between L and K.  Many different combinations of L and K produce a given level of output.

Managerial Economics, Lecture 10: Production Isoquant  An isoquant is a curve that shows efficient combinations of labor and capital that can produce a single (iso) level of output (quantity):  Examples:  A 10-unit isoquant for a Norwegian printing firm 10 = 1.52 L 0.6 K 0.4  Table 6.2 shows four (L, K) pairs that produce q = 24

Managerial Economics, Lecture 10: Production

Figure 6.2 Family of Isoquants K, Units of capital per day e b a d fc L, Workers per day q = 14 q = 24 q = 35

Managerial Economics, Lecture 10: Production Isoquants and Indifference Curves  Isoquants and indifference curves have most of the same properties.  The biggest difference:  An isoquant holds something measurable (quantity) constant  An indifference curve holds something that is unmeasurable (utility) constant

Managerial Economics, Lecture 10: Production Three Key Properties of Isoquants 1.The further an isoquant is from the origin, the greater is the level of output. 2.Isoquants do not cross. 3. Isoquants slope downward.

Managerial Economics, Lecture 10: Production The Shape of Isoquants  The slope of isoquant shows how readily a firm can substitute one input for another  Extreme cases:  perfect substitutes: q = x + y  fixed-proportions (no substitution): q = min(x, y)  Usual case: bowed away from the origin

Managerial Economics, Lecture 10: Production Figure 6.3a Perfect Substitutes: Fixed Proportions y, Idaho potatoes per day x, Maine potatoes per day q = 3q = 2q = 1

Managerial Economics, Lecture 10: Production Figure 6.3b Perfect Complements Boxes per day Cereal per day q = 3 q = 2 q = 1 45° line

Managerial Economics, Lecture 10: Production Figure 6.3c Substitutability of Inputs q = 1 K, Capital per unit of time L, Labor per unit of time

Managerial Economics, Lecture 10: Production Marginal Rate of Technical Substitution  The slope of an isoquant tells how much a firm can increase one input and lower the other without changing quantity.  The slope is called the marginal rate of technical substitution (MRTS).  The MRTS varies along a curved isoquant, and is analogous to the MRS.

Managerial Economics, Lecture 10: Production Figure 6.4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant K, Units of capital per year e b  K = – 18 –7 – 4 –2  L = 1 d c L, Workers per day q = 10 a

Managerial Economics, Lecture 10: Production The Slope of an Isoquant  If firm hires  L more workers, its output increases by MP L =  q/  L  A decrease in capital by  K causes output to fall by MP K =  q/  K  To keep output constant,  q = 0:  or

Managerial Economics, Lecture 10: Production Returns to Scale  Returns to scale (how output changes if all inputs are increased by equal proportions) can be:  Constant: when all inputs are doubled, output doubles,  Increasing: when all inputs are doubled, output more than doubles, or  Decreasing: when all inputs are doubled, output increase < 100%.

Managerial Economics, Lecture 10: Production K capital per year q = 100 q = 200 q = L, Units of labor per year (c) Concrete Blocks and Bricks: Increasing Returns to Scale, Units of