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## Economics of Input and Product Substitution

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**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 • Production possibilities frontier • Profit maximizing combination of products**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**Plotting the Iso-Cost Line**Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000 Capital 10 Labor 100 Page 136**Plotting the Iso-Cost Line**Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000 Capital 10 Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1,000 Labor 100 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 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… Page 136**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… Page 136**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 list is tangent to the isoquant: MPPLABOR÷ MPPCAPITAL= -(wage rate÷ rental rate) Slope of an isoquant Slope of iso- cost line Page 139**Least Cost Decision Rule**The least cost 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 number of inputs as well… The least cost 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 Combination of Inputs to Produce aSpecific 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 C1 and L1 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: $100×7+$10×60=$1,300 7 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 7 130 60 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: $1,300 $100 = 13 13 7 130 60 Page 138**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 Cost Combination of Inputs and Outputfor a Specific**Budget**What Inputs to Use for a Specific Budget?**M An iso-cost line for a specific budget Capital 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 C3 units of capital and L3 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**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…. Q3 Page 145