Economics of Input and Product Substitution Chapter 7

Economics of Input and Product Substitution Chapter 7

Topics of Discussion üConcepts of isoquants and iso-cost line üLeast-cost use of inputs üLong-run expansion of input use üEconomics of business expansion and contraction üProduction possibilities frontier üProfit maximizing combination of products

Physical Relationships

Isoquant means “equal quantity” Output is identical along an isoquant Two inputs Page 133

Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS = Capital ÷ labor Page 133

Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS = Capital ÷ labor If output remains unchanged along an isoquant, the loss in output from decreasing labor must be identical to the gain in output from adding capital. Page 133

MRTS here is -4÷ 1= -4 Page 133

What is the slope over range B? Page 133

What is the slope over range B? MRTS here is -1÷ 1= -1 Page 133

What is the slope over range C? Page 133

What is the slope over range C? MRTS here is -. 5÷ 1= -. 5 Page 133

Introducing Input Prices

Plotting the Iso-Cost Line Capital Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1, 000 10 100 Labor Page 136

Plotting the Iso-Cost Line Capital Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1, 000 10 Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1, 000 100 Labor Page 136

Slope of an Iso-cost Line The slope of an iso-cost in our example is given by: Slope = - (wage rate ÷ rental rate) or the negative of the ratio of the price of the two Inputs. See footnote 5 on page 179 for the derivation of this slope based upon the budget constraint (hint: solve equation below for the use of capital). ($10 × use of labor)+($100 × use of capital)=$1, 000 Page 135

Original iso-cost line Change in budget or both costs Line AB represents the original iso-cost line for capital and labor… Change in wage rate Change in rental rate Page 136

Original iso-cost line Change in budget or both costs The iso-cost line would shift out to line EF if the firm’s available budget doubled (or costs fell in half) or back to line CD if the available budget halved (or costs doubled. Change in wage rate Change in rental rate Page 136

Original iso-cost line Change in wage rate Change in budget or both costs Change in rental rate If wage rates fell in half, the line would shift out to AF. The iso-cost line would shift in to line AD if wage rates doubled… Page 136

Original iso-cost line Change in wage rate The iso-cost line would shift out to line BE if rental rate fell in half while the line would shift in to line BC if the rental rate for capital doubled… Change in budget or both costs Change in rental rate Page 136

Least Combination of Inputs

Least Cost Decision Rule The least combination of two inputs (labor and capital in our example) occurs where the slope of the iso-cost list is tangent to the isoquant: MPPLABOR ÷ MPPCAPITAL = -(wage rate ÷ rental rate) Slope of an isoquant Slope of isocost line Page 139

Least Cost Decision Rule The least combination of labor and capital in out example also occurs where: MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate MPP per dollar spent on labor = MPP per dollar spent on capital Page 139

Least Cost Decision Rule This decision rule holds for a larger The least combination of labor and capital in out example alsoof occurs where: as well… number inputs MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate MPP per dollar spent on labor = MPP per dollar spent on capital Page 139

Least Combination of Inputs to Produce a Specific Level of Output

Least Cost Input Choice for 100 Units Iso-cost line for $1, 000. Its slope reflects price of labor and capital. Page 138

Least Cost Input Choice for 100 Units We can determine this graphically by observing where these two curves are tangent…. Page 138

Least Cost Input Choice for 100 Units We can shift the original iso-cost line from AB out in a parallel fashion to A*B* (which leaves prices unchanged) which just touches the isoquant at G Page 138

Least Cost Input Choice for 100 Units At the point of tangency, we know that: slope of isoquant = slope of iso-cost line, or… MPPLABOR ÷ MPPCAPITAL = - (wage rate ÷ rental rate) Page 138

Least Cost Input Choice for 100 Units At the point of tangency, therefore, the MPP per dollar spent on labor is equal to the MPP per dollar spent on capital!!! See equation (8. 5) on page 181, which is analogous to equation (4. 2) back on page 76 for consumers. Page 138

Least Cost Input Choice for 100 Units This therefore represents the cheapest combination of capital and labor to produce 100 units of output… Page 138

Least Cost Input Choice for 100 Units If I told you the value of C 1 and L 1 and asked you for the value of A* and B*, how would you find them? Page 138

Least Cost Input Choice for 100 Units If I told you that point G represents 7 units of capital and 60 units of labor, and that the wage rate is $10 and the rental rate is $100, then at point G we must be spending $1, 300, or: 7 $100× 7+$10× 60=$1, 300 60 Page 138

Least Cost Input Choice for 100 Units If point G represents a total cost of $1, 300, we know that every point on this iso-cost line also represents $1, 300. If the wage rate is $10, then point B* must represent 130 units of labor, or: $1, 300 $10 = 130 7 60 130 Page 138

Least Cost Input Choice for 100 Units And the rental rate is $100, then point A* must represents 13 units of capital, or: 13 $1, 300 $100 = 13 7 60 130 Page 138

What Happens if the Price of an Input Changes?

What Happens if Wage Rate Declines? Assume the initial wage rate and cost of capital results in the iso-cost line AB Page 140

What Happens if Wage Rate Declines? Wage rate decline means that the firm can now afford B* instead of B… Page 140

What Happens if Wage Rate Declines? The new point of tangency occurs at H rather than G. Page 140

What Happens if Wage Rate Declines? As a consequence, the firm would desire to use more labor and less capital… Page 140

Least Combination of Inputs and Output for a Specific Budget

What Inputs to Use for a Specific Budget? Capital M An iso-cost line for a specific budget N Labor Page 141

What Inputs to Use for a Specific Budget? A set of isoquants for different levels of output… Page 141

What Inputs to Use for a Specific Budget? Firm can afford to produce only 75 units of output using C 3 units of capital and L 3 units of labor Page 141

What Inputs to Use for a Specific Budget? The firm’s budget is not large enough to operate at 100 or 125 units… Page 141

What Inputs to Use for a Specific Budget? Firm is not spending available budget here… Page 141

Economics of Business Expansion

The Planning Curve The long run average cost (LAC) curve reflects points of tangency with a series of short run average total cost (SAC) curves. The point on the LAC where the following holds is the long run equilibrium position (QLR) of the firm: SAC = LAC = PLR where MC represents marginal cost and PLR represents the long run price, respectively. Page 145

What can we say about the four firms in this graph? Page 145

Size 1 would lose money at price P Page 145

Firm size 2, 3 and 4 would earn a profit at price P…. Q 3 Page 145

Firm #2’s profit would be the area shown below… Q 3 Page 145

Firm #3’s profit would be the area shown below… Q 3 Page 145

Firm #4’s profit would be the area shown below… Q 3 Page 145

If price were to fall to PLR, only size 3 would not lose money; it would break-even. Size 4 would have to down size its operations! Page 145

How to Expand Firm’s Capacity Optimal input combination for output=10 Page 146

How to Expand Firm’s Capacity Two options: 1. Point B ? Page 146

How to Expand Firm’s Capacity Two options: 1. Point B? 2. Point C? Page 146

Expanding Firm’s Capacity Optimal input combination for output=20 with budget FG Optimal input combination for output=10 with budget DE Page 146

Expanding Firm’s Capacity This combination costs more to produce 20 units of output since budget HI exceeds budget FG Page 146

Production Possibilities The goal is to find that combination of products that maximizes revenue for the maximum technical efficiency on the production possibilities frontier.

Shows the substitution between two products given the most efficient use of firm’s resources Page 149

Slope of the PPF The slope of the production possibilities curve is referred to as the Marginal Rate of Product Transformation, or MRPT. The value of the MRPT in our example is given by: MRPT = canned fruit ÷ canned vegetables Page 148

Slope over range between D and E is – 1. 30, or: -13 10 Drops from 108 to 95 Increases from 30 to 40 Page 149

95, 000 - 108, 000 -13, 000 ÷ 40, 000 - 30, 000 10, 000 = - 1. 30 Page 148

Inefficient use of firm’s resources Page 149

Level of output unattainable with firm’s existing resources Inefficient use of firm’s existing resources Page 149

Accounting for Product Prices

Plotting the Iso-Revenue Line Canned fruit 30, 000 cases of canned fruit required at price of $33. 33/case to achieve A TARGET revenue of $1 million 40, 000 Canned vegetables Page 150

Plotting the Iso-Revenue Line Canned fruit 30, 000 cases of canned fruit required at price of $33. 33/case to achieve revenue of $1 million 30, 000 40, 000 cases of canned vegetables required at price of $25. 00/case to achieve revenue of $1 million 40, 000 Canned vegetables Page 150

Original iso-revenue line Changes in income or both prices Line AB is the original iso-revenue line, indicating the number of cases needed to reach a specific sales target. Change in price of fruit Change in price of vegetables Page 150

The iso-revenue line would Original iso-revenue line shift out to line EF if the revenue target doubled (or prices fell in half) while the line would shift in to line CD if revenue targets fell in half or prices doubled. Change in price of fruit Changes in income or both prices Change in price of vegetables Page 150

Original iso-revenue line Change in price of fruit Changes in income or both prices The iso-revenue line would Change in price of vegetables shift out to line BC is the price of fruit fell in half but shift in to line BD if the price of fruit doubled Page 150

Original iso-revenue line The iso-revenue line would Change in price of fruit shift out to line AD if the price of vegetables fell in half but shift in to line AC is the price of fruit doubled. Changes in income or both prices Change in price of vegetables Page 150

Profit Maximizing combination of Product Prices

Combination of Products The profit maximizing combination of two products is found where the slope of the production possibilities frontier (PPF) is equal to the slope of the iso-revenue Curve, or where: Canned fruit Price of vegetables = – Canned vegetables Price of fruit Slope of an PPF curve Slope of isorevenue line. Page 152

Assume Line AB represents revenue for $1 million. Page 153

We want to find the profit maximizing combination to “can” given the current prices of canned fruit and vegetables. Page 153

Canned fruit Canned vegetables = – Price of vegetables Price of fruit Shifting line AB out in a parallel fashion holds both prices constant at their current level Page 153

125, 000 cases of fruit 18, 000 cases of vegetables MRPT equals -0. 75 Page 152

Price ratio = -($25. 00 ÷ $33. 33) = - 0. 75 125, 000 cases of fruit 18, 000 cases of vegetables MRPT equals -0. 75 Page 152

Price ratio = -($25. 00 ÷ $33. 33) = - 0. 75 125, 000 cases of fruit 18, 000 cases of vegetables Canned fruit Canned vegetables = – MRPT equals -0. 75 Price of vegetables Price of fruit Page 152

Doing the Math… Let’s assume the price of a case of canned fruit is $33. 33 while the price of a case of canned vegetables is $25. 00. If point M represents 125, 000 cases of fruit and 18, 000 cases of vegetables, then total revenue at point M is: Revenue = 125, 000 × $33. 33 + 18, 000 × $25. 00 = $4, 166, 250 + $450, 000 = $4, 616, 250

Doing the Math… At these same prices, if we instead produce 108, 000 cases of fruit and 30, 000 cases of vegetables, then total revenue would fall to: Revenue = 108, 000 × $33. 33 + 30, 000 × $25. 00 = $3, 599, 640 + $750, 000 = $4, 349, 640 which is $266, 610 less than the $4, 616, 250 earned at point M.

Effects of a Change in the Price of One Product

If the price of canned fruit fell in half, the firm must sell twice as many cases of canned fruit to earn $1 million if it focused solely on fruit production. Page 153

This gives us a new isorevenue curve… line CB. Page 153

To see the effects of this price change, we can shift the new iso-revenue curve out to the point of tangency with the PPF curve…. Page 153

Shifting the new isorevenue curve in a parallel fashion out to a point of tangency with the PPF curve, we get a new combination of products required to maximize profit. Page 153

The firm would shift from point M on the PPF to point N as a result of the decline in the price of fruit. That is, to maximize profit, the firm would cut back its production of canned fruit and produce more canned vegetables. Page 153

Summary #1 ü Concepts of iso-cost line and isoquants ü Marginal rate of technical substitution (MRTS) ü Least combination of inputs for a specific output level ü Effects of change in input price ü Level of output and combination of inputs for a specific budget ü Key decision rule …seek point where MRTS = ratio of input prices, or where MPP per dollar spent on inputs are equal

Summary #2 ü Concepts of iso-revenue line and the production possibilities frontier ü Marginal rate of product transformation (MRPT) ü Concept of profit maximizing combination of products ü Effects of change in product price ü Key decision rule – maximize profits where MRPT equals the ratio of the product prices

Chapter 8 focuses on market equilibrium conditions under perfect competition….