© 2005 Pearson Education Canada Inc. 6.1 Chapter 6 Production and Cost: One Variable Input

© 2005 Pearson Education Canada Inc. 6.2 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 ).

© 2005 Pearson Education Canada Inc. 6.3 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.

© 2005 Pearson Education Canada Inc. 6.4 Figure 6.1 Finding a production function

© 2005 Pearson Education Canada Inc. 6.5 From Figure 6.1  The production function is: F(z 1 z 2 )=(1200z 1 z 2 ) 1/2 F(z 1 z 2 )=(1200z 1 z 2 ) 1/2  This is a Cobb-Douglas production function. The general form is given below where A, u and v are positive constants.

© 2005 Pearson Education Canada Inc. 6.6 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.

© 2005 Pearson Education Canada Inc. 6.7 Long-Run Cost Minimization  The goal is to choose quantities of inputs z 1 and z 2 that minimize total costs subject to being able to produce y units of output.  That is: 1. Minimize w 1 z 1 +w 2 z 2 (w 1,w 2 are input prices). 2. Choosing z 1 and z 2 subject to the constraint y=F(z 1, z 2 ).

© 2005 Pearson Education Canada Inc. 6.8 Production: One Variable Input  Total production function TP (z 1 ) (Z 2 fixed at 105) defined as: TP (z 1 )=F(z 1, 105)  Marginal product MP(z 1 )the rate of output change when the variable input changes (given fixed amounts of all other inputs).  MP (z 1 )=slope of TP (z 1 )

© 2005 Pearson Education Canada Inc. 6.9 Figure 6.3 From total product to marginal product

© 2005 Pearson Education Canada Inc 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.

© 2005 Pearson Education Canada Inc Figure 6.4 From total product to marginal product: another illustration

© 2005 Pearson Education Canada Inc Average Product  Average product (AP) of the variable input equals total output divided by the quantity of the variable input. AP(Z 1 )=TP(Z 1 )/Z 1

© 2005 Pearson Education Canada Inc Figure 6.5 From total product to average product

© 2005 Pearson Education Canada Inc Figure 6.6 Comparing the average and marginal product functions

© 2005 Pearson Education Canada Inc Marginal and Average Product 1. When MP exceeds AP, AP is increasing. 2. When MP is less than AP, AP declines. 3. When MP=AP, AP is constant.

© 2005 Pearson Education Canada Inc Costs of Production: One Variable Input  The cost-minimization problem is: Minimize W 1 Z 1 by choice of Z 1. Subject to constraint y=TP(z 1 ).  The variable cost, VC(y) function is: VC(y)=the minimum variable cost of producing y units of output.

© 2005 Pearson Education Canada Inc Figure 6.7 Deriving the variable cost function

© 2005 Pearson Education Canada Inc More Costs  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)

© 2005 Pearson Education Canada Inc Figure 6.8 Deriving average variable cost and short-run marginal cost

© 2005 Pearson Education Canada Inc Short-run Marginal Costs and Average Variable Costs 1. When SMC is below AVC, AVC decreases as y increases. 2. When SMC is equal to AVC, AVC is constant (its slope is zero). 3. When SMC is above AVC, AVC increases as y increases.

© 2005 Pearson Education Canada Inc Average Product and Average Cost AVC (y’)=w 1 /AP(z 1 ’)  The average variable cost function is the inverted image of the average product function.

© 2005 Pearson Education Canada Inc Marginal Product and Marginal Cost SMC (y’)=(w 1 Δz 1 )/(MP(z’))  The short-run marginal cost function is the inverted image of the marginal product function.

© 2005 Pearson Education Canada Inc Figure 6.9 Comparing cost and product functions

© 2005 Pearson Education Canada Inc Figure 6.10 Seven cost functions

© 2005 Pearson Education Canada Inc Figure 6.11 The costs of commuting

© 2005 Pearson Education Canada Inc Figure 6.12 Total commuting costs

© 2005 Pearson Education Canada Inc Figure 6.13 The allocation of commuters to routes