Chapter 6 Firms And Production Firms’ Goal

chapter 6: firms and production =============================== * firms’ goal is to maximize their profit. * profit function: π= r –

Chapter 6: Firms and Production
===============================
* Firms’ goal is to maximize their profit.
* Profit function: π= R – C = P*Q – C(Q)
* where R is revenue, C is cost, P is price, and Q is quantity
* Production function: the relationship between the quantities of
inputs used and the maximum quantity of output that can be
produced. It summarizes the technology of transforming inputs into
outputs. e.g.) q = f(L,K)
* Fixed input vs. variable input
Short-Run: At least one factor of production is fixed
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* For production function: q = f(L,K)
* Average product of labor (AP) = q/L
* Marginal product of labor (MP) = △q/△L
* AP increases when MP exceeds AP and decreases when MP is exceeded
by AP.
Diminishing Marginal Returns (or diminishing marginal product)
==============================================================
* If a firm keeps adding one more unit of input, holding all other
inputs and technology constant, the extra output it obtains will
become smaller eventually.
* Why?
* Too many workers per machine
* Increases the cost of managing labors, etc.
Example: A Cobb-Douglas Function
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* Production Function:
* Capital (K) is fixed. Only labor (L) is variable.
* The marginal product of Labor is
* The second derivative of q w.r.t. L is
* which is negative: Concave function.
*
* Assume that K is fixed at 100. Draw the production function and
the marginal product of Labor.
Long-Run: All inputs are variable
=================================
* Firms can vary input mix to achieve the most efficient production.
* Isoquant: a curve that shows the efficient combinations of labor
and capital that can produce a single level of output (similar to
indifference curve)
* Marginal Rate of Technical Substitution (MRTS):
* the extra units of one input needed to replace one unit of
another input that allows a firm to produce the same level of
output
* slope of an isoquant (i.e., )
Diminishing marginal rate of technical substitution
===================================================
* Diminishing marginal rate of technical substitution
Unique Isoquants
================
MRTS and Marginal Products
==========================
* By definition of isoquant:
* To see the small change in q, totally differentiate an isoquant:
*
* Marginal increase in output from increasing L
* Change in L
* Total increase in output from increasing L by dL
Example: A Cobb-Douglas Function
================================
* Production Function:
* Capital (K) is not fixed (long-run).
* The marginal product of Labor is
* The marginal product of Capital is
* The marginal rate of technical substitution (MRTS) is
* Draw the isoquant curve.
*
Returns to Scale
================
* How much output changes if a firm increases all its inputs
proportionately.
* Long-run concept
* Constant Returns to Scale (CRS):
* t * f(x1, x2) = f(tx1, tx2)
* Increasing Returns to Scale (IRS):
* t * f(x1, x2) < f(tx1, tx2)
* Decreasing Returns to Scale (DRS):
* t * f(x1, x2) > f(tx1, tx2)
Reasons for increasing or decreasing returns to scale
=====================================================
* Increasing Returns to Scale (IRS):
* A larger plant may allow for greater specializations of inputs.
*
* Decreasing Returns to Scale (DRS):
* Management problems may arise when the production scale is
increased, e.g., cheating by workers.
* Large teams of workers may not function as well as small teams.
*
For a Cobb-Douglas production function:
=======================================
* If we double all inputs,
* CRS if
* IRS if
* DRS if
Productivity and Technical Change
=================================
* Technical change:
* Neutral technical change
* q = A*f(L,K)
* Non-neutral technical change
* e.g. from labor-using to labor-saving
Illustration of Neutral Technical Change
========================================
* K
* L
* q = 30 → q = 45
* q = 20 → q = 30
* q = 10 → q = 15
* Isoquants
Illustration of Non-neutral or Biased Technical Change
======================================================
* K
* L
* K-using or L-saving
* L-using or K-saving
* Original isoquants