Chapter 6 production and cost one variable input
Download
1 / 27

Chapter 6 Production and Cost: One Variable Input - PowerPoint PPT Presentation


  • 104 Views
  • Uploaded on

Chapter 6 Production and Cost: One Variable Input. Production Function. The production function identifies the maximum quantity of good y that can be produced from any input bundle (z 1 , z 2 ). Production function is stated as: y=F(z 1 , z 2 ). Production Functions.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Chapter 6 Production and Cost: One Variable Input' - blaze-winters


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Chapter 6 production and cost one variable input
Chapter 6Production and Cost: One Variable Input


Production function
Production Function

  • The production function identifies the maximum quantity of good y that can be produced from any input bundle (z1, z2).

  • Production function is stated as: y=F(z1, z2).


Production functions
Production Functions

  • In a fixed proportions production function, the ratio in which the inputs are used never varies.

  • In a variable proportion production function, the ratio of inputs can vary.



From figure 6 1
From Figure 6.1

  • The production function is:

    F(z1z2)=(1200z1z2)1/2

  • This is a Cobb-Douglas production function. The general form is given below where A, u and v are positive constants.


Costs
Costs

  • Opportunity cost is the value of the highest forsaken alternative.

  • Sunk costs are costs that, once incurred, cannot be recovered.

  • Avoidable costs are costs that need not be incurred (can be avoided).

  • Fixed costs do not vary with output.

  • Variable costs change with output.


Long run cost minimization
Long-Run Cost Minimization

  • The goal is to choose quantities of inputs z1 and z2 that minimize total costs subject to being able to produce y units of output.

  • That is:

  • Minimize w1z1+w2z2 (w1,w2 are input prices).

  • Choosing z1 and z2 subject to the constraint y=F(z1, z2).


Production one variable input
Production: One Variable Input

  • Total production function TP (z1) (Z2 fixed at 105)defined as:

    TP (z1)=F(z1, 105)

  • Marginal product MP(z1)the rate of output change when the variable input changes (given fixed amounts of all other inputs).

  • MP (z1)=slope of TP (z1)



Diminishing marginal productivity
Diminishing Marginal Productivity

  • As the quantity of the variable input is increased (all other input quantities being fixed), at some point the rate of increase in total output will begin to decline.



Average product
Average Product illustration

  • Average product (AP) of the variable input equals total output divided by the quantity of the variable input.

    AP(Z1)=TP(Z1)/Z1


Figure 6 5 from total product to average product
Figure 6.5 From total product to illustrationaverage product



Marginal and average product
Marginal and Average Product functions

  • When MP exceeds AP, AP is increasing.

  • When MP is less than AP, AP declines.

  • When MP=AP, AP is constant.


Costs of production one variable input
Costs of Production: One Variable Input functions

  • The cost-minimization problem is:

    Minimize W1Z1 by choice of Z1.

    Subject to constraint y=TP(z1).

  • The variable cost, VC(y) function is:

    VC(y)=the minimum variable cost of producing y units of output.



More costs
More Costs functions

  • Average variable cost is variable cost per unit of output. AV(y)=VC(y)/y

  • Short-run marginal cost is the rate at which costs increase in the short-run. SMC(y)=slope of VC(y)



Short run marginal costs and average variable costs
Short-run Marginal Costs and Average Variable Costs marginal cost

  • When SMC is below AVC, AVC decreases as y increases.

  • When SMC is equal to AVC, AVC is constant (its slope is zero).

  • When SMC is above AVC, AVC increases as y increases.


Average product and average cost
Average Product and Average Cost marginal cost

AVC (y’)=w1/AP(z1’)

  • The average variable cost function is the inverted image of the average product function.


Marginal product and marginal cost
Marginal Product and Marginal Cost marginal cost

SMC (y’)=(w1Δz1)/(MP(z’))

  • The short-run marginal cost function is the inverted image of the marginal product function.







ad