CAMS 2003 Economics of Input Substitution PDF

Economics of Input Substitution: Factor—Factor relationship Chapter 7 1 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP22-Jul-24  Topics of Discussion ▪ Concepts of i...

Economics of Input Substitution: Factor—Factor relationship Chapter 7 1 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP22-Jul-24  Topics of Discussion ▪ Concepts of isoquants and iso- cost line ▪ Least-cost use of inputs ▪ Long-run expansion of input use ▪ Economics of business expansion and contraction 2 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Concepts ▪ Output = f (labor | capital, land, and management) ▪ Output = f (labor, capital | land, and management) ▪ Labor-intensive, capital-intensive ▪ An isoquant captures unique combinations of two inputs that result in the same level of output. The prefix “iso” is the Greek word meaning equal. 3 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Isoquant means “equal quantity” Higher isoquants represent higher levels of output Output is identical along an isoquant Two inputs 4 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 ……..Equation 7.1 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. ……. Re-arrange −Δlabor × MPPlabor = +Δcapital × MPPcapital. Equation 7.1 5 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24 MRTS here is -4÷1= -4 6 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What is the slope over range B? The slope=-1 MRTS here is -1÷1= -1 7 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What is the slope over range C? The slope=-0.5 MRTS here is -.5÷1= -.5 8 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Imperfect substitutes Capital Labour ▪ Imperfect substitution shown in Fig. 7-1, implies decreasing MRTS one moves down the isoquants ▪ Perfect substitutes is a straight line, which implies a constant MRTS ▪ Perfect complements form 90-degree, implying that both capital & labor are required to produce a specific level of output (a certain 9 proportion of labor and capital to produce a product). 22-Jul-24  Plotting the Iso-Cost Line Introducing Input Prices Firm can afford 10 units of Capital 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 Labor 100 10 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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. We can also solve equation below for the use of capital). ($10 × use of labor)+($100 × use of capital)=$1,000 11 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 12 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 13 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Original iso-cost line Change in budget or both costs Change in wage rate 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… 14 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Original iso-cost line Change in budget or both costs Change in wage rate Change in rental 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… 15 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Decision Rule The least cost combination of two inputs (labor and capital in our example) occurs where the slope of the iso-cost line is tangent to the isoquant: MPPLABOR ÷ MPPCAPITAL = -(wage rate ÷ rental rate) Slope of an Slope of iso- isoquant cost line CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 16 22-Jul-24  Least Cost Decision Rule The least cost combination of labor and capital in our example also occurs where: MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate MPP per dollar MPP per dollar spent on labor = spent on capital 17 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Input Choice for 100 Units Iso-cost line for $1,000. Its slope reflects price of labor and capital. 18 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Input Choice for 100 Units We can determine this graphically by observing where these two curves are tangent…. 19 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 20 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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) 21 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 (7.4). 22 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Input Choice for 100 Units This therefore represents the cheapest combination of capital and labor to produce 100 units of output… 23 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Input Choice for 100 Units If I gave you the value of C1 and L1 and asked you for the value of A* and B*, how would you find them? 24 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 7 spending $1,300, or: $100×7+$10×60=$1,300 60 25 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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 7 units of labor, or: $1,300$10 = 130 60 130 26 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Input Choice for 100 Units And the rental rate is $100, then point A* must 13 represents 13 units of capital, or: $1,300 $100 = 13 7 60 130 27 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24 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 28 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Happens if Wage Rate Declines? Wage rate decline means that the firm can now afford B* instead of B… 29 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Happens if Wage Rate Declines? The new point of tangency occurs at H rather than G. 30 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Happens if Wage Rate Declines? As a consequence, the firm would desire to use more labor and less capital… 31 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Least Cost Combination of Inputs and Output for a Specific Budget What Inputs to Use for a Specific Budget? M An iso-cost line for a specific budget N Labor 32 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Inputs to Use for a Specific Budget? A set of isoquants for different levels of output… 33 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Inputs to Use for a Specific Budget? Firm can afford to produce only 75 units of output using C3 units of capital and L3 units of labor 34 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Inputs to Use for a Specific Budget? The firm’s budget is not large enough to operate at 100 or 125 units… 35 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  What Inputs to Use for a Specific Budget? Firm is not spending available budget here… 36 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  ECONOMICS OF BUSINESS EXPANSION 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. 37 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24 What can we say about the four firms in this graph? 38 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24 Size 1 would lose money at price P 39 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Firm size 2, 3 and 4 would earn a profit at price P…. Q3 40 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Firm #2’s profit would be the area shown below… Q3 41 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Firm #3’s profit would be the area shown below… Q3 42 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Firm #4’s profit would be the area shown below… Q3 43 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  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! 44 22-Jul-24 price might fall because the business give more economic profit , more firms joins, market supply increases  How to Expand Firm’s Capacity Optimal input combination for output=10 45 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  How to Expand Firm’s Capacity Two options: 1. Point B ? 46 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  How to Expand Firm’s Capacity Two options: 1. Point B? 2. Point C? 47 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Expanding Firm’s Capacity Optimal input combination for output=20 with budget FG Optimal input combination for output=10 with budget DE 48 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Expanding Firm’s Capacity This combination costs more to produce 20 units of output since budget HI exceeds budget FG 49 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24  Summary ▪ Concepts of iso-cost line and isoquants ▪ Marginal rate of technical substitution (MRTS) ▪ Least cost combination of inputs for a specific output level ▪ Effects of change in input price ▪ Level of output and combination of inputs for a specific budget ▪ Key decision rule …seek point where MRTS = ratio of input prices, or where MPP per dollar spent on inputs are equal 50 CAMS 2003: ECONOMIC OF INPUT SUBSTITUTION: FACTOR--FACTOR RELATIONSHIP 22-Jul-24