Week 3 managerial economics

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I need assistance with the attached homework in managerial economics. Please explain answer. I have also attached supporting slides. Please assign asma. I need it by Wednesday April 10th 12 noon EST. Thank you

BUSN6120

HOMEWORK 3

Problem 1

The maker of a leading brand of low-calorie microwavable food estimates the following demand equation for its product using data from 26 supermarkets around the country for the month of April.

Q
=
– 5200 – 42P + 20PX + 5.2I + .20A + .25M

(2.002)
(17.5)
(6.2)
(2.5)
(0.09)
(0.21)

R2 = 0.55
n = 26
F = 4.88

Assume the following values for the independent variables:

Q
=
Quantity sold per month

P (in cents)
=
Price of the product = 500

PX (in cents)
=
Price of leading competitor’s product = 600

I (in dollars)
=
Per capita income of the standard metropolitan statistical area

(SMSA) in which the supermarkets are located = 5,500

A (in dollars)
=
Monthly advertising expenditures = 10,000

M
=
Number of microwave ovens sold in the SMSA in which the

supermarkets are located = 5,000

Using this information, answer the following questions:

a. Compute elasticities for each variable.

b. How concerned do you think this company would be about the impact of a recession on its sales? Explain. (Hint: Interpret income elasticity coefficient.)

c. Do you think that this firm should cut its price to increase its market share? Explain. (Hint: Refer to the price elasticity of demand.)

d. What portion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer? Explain. (Hint: Interpret R2 and F.)

Problem 2

You have the following data for the last 12 months’ sales for the PRQ Corporation (in thousands of dollars):

January
500

July
610

February
520

August
620

March
520

September
580

April
510

October
550

May
530

November
510

June
580

December
480

a. Calculate a 3-month centered moving average.

b. Use this moving average to forecast sales for January of next year.

c. If you were asked to forecast January and February sales for next year, would you be confident of your forecast using the preceding moving averages? Why or why not?

Chapter Five
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*
Chapter 5
Demand Estimation
and Forecasting
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Chapter Five
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*
Overview
Regression analysis
Hazards with use of regression analysis
Subjects of forecasts
Prerequisites of a good forecast
Forecasting techniques

Chapter Five
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*
Data collection
Data for studies pertaining to countries, regions, or industries are readily available

Data for analysis of specific product categories may be more difficult to obtain
buy from data providers (e.g. ACNielsen, IRI)
perform a consumer survey
focus groups
technology: point-of-sale, bar codes

Chapter Five
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*
Regression analysis
Regression analysis: a procedure commonly used by economists to estimate consumer demand with available data

Two types of regression:
cross-sectional: analyze several variables for a single period of time
time series data: analyze a single variable over multiple periods of time

Chapter Five
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*
Regression analysis
Regression equation: linear, additive

eg: Y = a + b1X1 + b2X2 + b3X3 + b4X4
Y: dependent variable
a: constant value, y-intercept
Xn: independent variables, used to explain Y
bn: regression coefficients (measure impact of
independent variables)
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Chapter Five
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*
Regression analysis
Interpreting the regression results:

coefficients:
negative coefficient shows that as the independent variable (Xn) changes, the variable (Y) changes in the opposite direction
positive coefficient shows that as the independent variable (Xn) changes, the dependent variable (Y) changes in the same direction
magnitude of regression coefficients is a measure of elasticity of each variable

Chapter Five
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*
Regression analysis
Statistical evaluation of regression results:
t-test: test of statistical significance of each estimated coefficient

b = estimated coefficient
SEb = standard error of estimated coefficient

Chapter Five
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*
Regression analysis
Statistical evaluation of regression results:

 ‘rule of 2’: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level
 if coefficient passes t-test, the variable has a true impact on demand
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Chapter Five
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*
Regression analysis
Statistical evaluation of regression results
R2 (coefficient of determination): percentage of variation in the variable (Y) accounted for by variation in all explanatory variables (Xn)
 R2 value ranges from 0.0 to 1.0
 the closer to 1.0, the greater the explanatory power of the regression
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Chapter Five
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*
Regression analysis
Statistical evaluation of regression results
F-test: measures statistical significance of the entire regression as a whole (not each coefficient)

Chapter Five
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*
Regression results

Steps for analyzing regression results
check coefficient signs and magnitudes
compute implied elasticities
determine statistical significance

Chapter Five
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*
Regression results

Example: estimating demand for pizza
demand for pizza affected by
1. price of pizza
2. price of complement (soda)
managers can expect price decreases to lead to lower revenue
tuition and location are not significant

Chapter Five
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*
Regression problems

Identification problem: the estimation of demand may produce biased results due to simultaneous shifting of supply and demand curves

 solution: use advanced correction techniques, such as two-stage least squares and indirect least squares
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Chapter Five
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*
Regression problems

Multicollinearity problem: two or more independent variables are highly correlated, thus it is difficult to separate the effect each has on the dependent variable

 solution: a standard remedy is to drop one of the closely related independent variables from the regression
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Chapter Five
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*
Regression problems
Autocorrelation problem: also known as serial correlation, occurs when the dependent variable relates to the Y variable according to a certain pattern
Note: possible causes include omitted variables, or non-linearity; Durbin-Watson statistic is used to identify autocorrelation

 solution: to correct autocorrelation consider transforming the data into a different order of magnitude or introducing leading or lagging data
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Chapter Five
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*
Forecasting
Examples: common subjects of business forecasts:
gross domestic product (GDP)
components of GDP
eg consumption expenditure, producer durable equipment expenditure, residential construction
industry forecasts
eg sales of products across an industry
sales of a specific product
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Chapter Five
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*
Forecasting

A good forecast should:
be consistent with other parts of the business
be based on knowledge of the relevant past
consider the economic and political environment as well as changes
be timely

Chapter Five
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*
Forecasting techniques

Factors in choosing the right forecasting technique:
item to be forecast
interaction of the situation with the forecasting methodology
amount of historical data available
time allowed to prepare forecast

Chapter Five
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*
Forecasting techniques

Approaches to forecasting
qualitative forecasting is based on judgments expressed by individuals or group
quantitative forecasting utilizes significant amounts of data and equations

Chapter Five
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*
Forecasting techniques

Approaches to forecasting

naïve forecasting projects past data without explaining future trends
causal (or explanatory) forecasting attempts to explain the functional relationships between the dependent variable and the independent variables

Chapter Five
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*
Forecasting techniques
Six forecasting techniques
expert opinion
opinion polls and market research
surveys of spending plans
economic indicators
projections
econometric models

Chapter Five
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*
Forecasting techniques
Expert opinion techniques
Jury of executive opinion: forecasts generated by a group of corporate executives assembled together Drawback: persons with strong personalities may exercise disproportionate influence

Chapter Five
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*
Forecasting techniques
Expert opinion techniques

The Delphi method: a form of expert opinion forecasting that uses a series of questions and answers to obtain a consensus forecast, where experts do not meet

Chapter Five
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*
Forecasting techniques

Opinion polls: sample populations are surveyed to determine consumption trends

may identify changes in trends
choice of sample is important
questions must be simple and clear

Chapter Five
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*
Forecasting techniques
Market research: is closely related to opinion polling and will indicate not only why the consumer is (or is not) buying, but also

who the consumer is
how he or she is using the product
characteristics the consumer thinks are most important in the purchasing decision

Chapter Five
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*
Forecasting techniques
Surveys of spending plans: yields information about ‘macro-type’ data relating to the economy, especially:
consumer intentions
Examples: Survey of Consumers (University of Michigan); Consumer Confidence Survey (Conference Board)
inventories and sales expectations

Chapter Five
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Forecasting techniques

Economic indicators: a barometric method of forecasting designed to alert business to changes in conditions

The Conference Board

leading, coincident, and lagging indicators
composite index: one indicator alone may not be very reliable, but a mix of leading indicators may be effective

Chapter Five
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*
Forecasting techniques
Leading indicators predict future economic activity
average hours, manufacturing
initial claims for unemployment insurance
manufacturers’ new orders for consumer goods and materials
vendor performance, slower deliveries diffusion index
manufacturers’ new orders, nondefense capital goods

Chapter Five
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*
Forecasting techniques
Leading indicators predict future economic activity

building permits, new private housing units
stock prices, 500 common stocks
money supply, M2
interest rate spread, 10-year Treasury bonds minus federal funds
index of consumer expectations

Chapter Five
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*
Forecasting techniques

Coincident indicators identify trends in current economic activity
employees on nonagricultural payrolls
personal income less transfer payments
industrial production
manufacturing and trade sales

Chapter Five
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*
Forecasting techniques

Lagging indicators confirm swings in past economic activity
average duration of unemployment, weeks
ratio, manufacturing and trade inventories to sales
change in labor cost per unit of output, manufacturing (%)

Chapter Five
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Forecasting techniques

Lagging indicators confirm swings in past economic activity

average prime rate charged by banks
commercial and industrial loans outstanding
ratio, consumer installment credit outstanding to personal income
change in consumer price index for services

Chapter Five
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*
Forecasting techniques
Economic indicators: drawbacks
leading indicator index has forecast a recession when none ensued
a change in the index does not indicate the precise size of the decline or increase
the data are subject to revision in the ensuing months

Chapter Five
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*
Forecasting techniques

Trend projections: a form of naïve forecasting that projects trends from past data without taking into consideration reasons for the change

compound growth rate
visual time series projections
least squares time series projection

Chapter Five
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*
Forecasting techniques
Compound growth rate: forecasting by projecting the average growth rate of the past into the future

provides a relatively simple and timely forecast

appropriate when the variable to be predicted increases at a constant %

Chapter Five
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*
Forecasting techniques
General compound growth rate formula:

E = B(1+i)n

E = final value
n = years in the series
B = beginning value
i = constant growth rate
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Chapter Five
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*
Forecasting techniques

Visual time series projections: plotting observations on a graph and viewing the shape of the data and any trends

Chapter Five
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*
Forecasting techniques

Time series analysis: a naïve method of forecasting from past data by using least squares statistical methods to identify trends, cycles, seasonality and irregular movements

Chapter Five
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*
Forecasting techniques
Time series analysis:

Advantages:
easy to calculate
does not require much judgment or analytical skill
describes the best possible fit for past data
usually reasonably reliable in the short run

Chapter Five
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*
Forecasting techniques
Time series data can be represented as:

Yt = f(Tt, Ct, St, Rt)

Yt = actual value of the data at time t
Tt = trend component at t
Ct = cyclical component at t
St = seasonal component at t
Rt = random component at t
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Chapter Five
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*
Forecasting techniques
Time series components: seasonality

need to identify and remove seasonal factors, using moving averages to isolate those factors
remove seasonality by dividing data by seasonal factor
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Chapter Five
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*
Forecasting techniques
Time series components: trend

to remove trend line, use least squares method
possible best-fit line styles:
straight Line: Y = a + b(t)
exponential Line: Y = abt
quadratic Line: Y = a + b(t) + c(t)2
choose one with best R2
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Chapter Five
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*
Forecasting techniques

Time series components: cycle, noise
isolate cycle by smoothing with a moving average

random factors cannot be predicted and should be ignored

Chapter Five
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*
Forecasting techniques
Smoothing techniques
moving average
exponential smoothing
 work best when:
no strong trend in series
infrequent changes in direction of series
fluctuations are random rather than seasonal or cyclical

Chapter Five
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*
Forecasting techniques
Moving average: average of actual past results used to forecast one period ahead

Et+1 = (Xt + Xt-1 + … + Xt-N+1)/N
Et+1 = forecast for next period
Xt, Xt-1 = actual values at their respective
times
N = number of observations included in
average
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Chapter Five
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*
Forecasting techniques
Exponential smoothing: allows for decreasing importance of information in the more distant past, through geometric progression

Et+1 = w·Xt + (1-w) · Et
w = weight assigned to an actual
observation at period t
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Chapter Five
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*
Forecasting techniques
Econometric models: causal or explanatory models of forecasting
regression analysis
multiple equation systems
endogenous variables: dependent variables that may influence other dependent variables
exogenous variables: from outside the system, truly independent variables

Chapter Five
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*
Forecasting techniques
Example: econometric model
Suits (1958) forecast demand for new automobiles
∆R = a0 + a1 ∆Y + a2 ∆P/M + a3 ∆S + a4 ∆X
R = retail sales
Y = real disposable income
P = real retail price of cars
M = average credit terms
S = existing stock
X= dummy variable
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Chapter Five
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Global application

Example: forecasting exchange rates
GDP
interest rates
inflation rates
balance of payments

t
=

Chapter Six
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*
Chapter 6
The Theory
and
Estimation of Production
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Chapter Six
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*
Overview
The production function
Short-run analysis of average and marginal product
Long-run production function
Importance of production function in managerial decision making

Chapter Six
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*
Learning objectives

define the production function
explain the various forms of production functions
provide examples of types of inputs into a production function for a manufacturing or service company

Chapter Six
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*
Learning objectives
understand the law of diminishing returns
use the Three Stages of Production to explain why a rational firm always tries to operate in Stage II

Chapter Six
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*
Production function
Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology

Q=f(X1, X2, …, Xk)
Q = level of output
X1, X2, …, Xk = inputs used in
production
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Chapter Six
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*
Production function
Key assumptions
given ‘state of the art’ production technology

whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level

Chapter Six
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*
Production function
For simplicity we will often consider a production function of two inputs:

Q=f(X, Y)
Q = output
X = labor
Y = capital
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Chapter Six
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*
Production function
Short-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged

Long-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used

Chapter Six
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*
Short-run analysis of Total,
Average, and Marginal product
Alternative terms in reference to inputs
‘inputs’
‘factors’
‘factors of production’
‘resources’

Alternative terms in reference to outputs
‘output’
‘quantity’ (Q)
‘total product’ (TP)
‘product’

Chapter Six
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*
Short-run analysis of Total,
Average, and Marginal product
Marginal product (MP) = change in output (Total Product) resulting from a unit change in a variable input

Average product (AP) = Total Product per unit of input used

Chapter Six
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*
Short-run analysis of Total,
Average, and Marginal product
if MP > AP then AP is rising

if MP < AP then AP is falling MP=AP when AP is maximized Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Law of diminishing returns: as additional units of a variable input are combined with a fixed input, after some point the additional output (i.e., marginal product) starts to diminish nothing says when diminishing returns will start to take effect all inputs added to the production process have the same productivity Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product The Three Stages of Production in the short run: Stage I: from zero units of the variable input to where AP is maximized (where MP=AP) Stage II: from the maximum AP to where MP=0 Stage III: from where MP=0 on Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product In the short run, rational firms should be operating only in Stage II Q: Why not Stage III?  firm uses more variable inputs to produce less output Q: Why not Stage I?  underutilizing fixed capacity, so can increase output per unit by increasing the amount of the variable input Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product What level of input usage within Stage II is best for the firm?  answer depends upon: how many units of output the firm can sell the price of the product the monetary costs of employing the variable input Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Total revenue product (TRP) = market value of the firm’s output, computed by multiplying the total product by the market price TRP = Q · P Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Marginal revenue product (MRP) = change in the firm’s TRP resulting from a unit change in the number of inputs used MRP = MP · P = Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Total labor cost (TLC) = total cost of using the variable input labor, computed by multiplying the wage rate by the number of variable inputs employed TLC = w · X Marginal labor cost (MLC) = change in total labor cost resulting from a unit change in the number of variable inputs used MLC = w Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Summary of relationship between demand for output and demand for a single input: A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input  MRP = MLC Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Short-run analysis of Total, Average, and Marginal product Multiple variable inputs Consider the relationship between the ratio of the marginal product of one input and its cost to the ratio of the marginal product of the other input(s) and their cost Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Long-run production function In the long run, a firm has enough time to change the amount of all its inputs The long run production process is described by the concept of returns to scale Returns to scale = the resulting increase in total output as all inputs increase Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Long-run production function If all inputs into the production process are doubled, three things can happen: output can more than double  ‘increasing returns to scale’ (IRTS) output can exactly double  ‘constant returns to scale’ (CRTS) output can less than double  ‘decreasing returns to scale’ (DRTS) Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Long-run production function One way to measure returns to scale is to use a coefficient of output elasticity: if EQ > 1 then IRTS
if EQ = 1 then CRTS
if EQ < 1 then DRTS Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Long-run production function Returns to scale can also be described using the following equation hQ = f(kX, kY) if h > k then IRTS
if h = k then CRTS
if h < k then DRTS Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter Six Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. * Long-run production function Graphically, the returns to scale concept can be illustrated using the following graphs Q X,Y IRTS Q X,Y CRTS Q X,Y DRTS Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall. X Q MP X D D = X Q AP X = X TRP D D k k w MP w MP w MP = = 2 2 1 1 inputs all in change Percentage Q in change Percentage = Q E

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