Production in addition to Cost Chapter 5 Todays agenda General Ideas Short run production & cost The Soprano Garbage Company Short Run Costs using isoquant data
Jones, Richard, Morning Show Host has reference to this Academic Journal, PHwiki organized this Journal Production in addition to Cost Chapter 5 Productivity => Cost => Profitability Todays agenda Collect Assignment 1 Status of first half of applied managerial economics How much to produce Marginal analysis applied to choice of price in addition to quantity How to produce Output maximization in addition to cost minimization What to produce Competitive Strategy Ch. 8 For whom to produce Consumer behavior in addition to Ch. 7 pricing Production & Cost concepts short run Returns to an input & cost functions Profit maximization Marginal product in addition to marginal revenue product long run Optimal input mix output maximization in addition to cost minimization Economies of scale General Ideas Production functions show how output varies as input usage varies Cost functions show different cost measures & how they vary as output varies What can you do to improve productivity Lower costs Link to profits
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Short run production & cost Short run some inputs held fixed while other(s) vary Production Returns to an input x is sensitivity of output to the input x Total product TP = output (Q) produced per period Average Product AP = output per unit of input x = TP / x Marginal Product MP = change in output per unit increase in input x = D TP / D x Cost Fixed cost in addition to variable cost per period shown as functions of output TFC + TVC = TC which varies with output (Q) Per unit costs each total cost measure per unit of output e.g. AVC = TVC/Q AVC + AFC = ATC Marginal cost = change in TC per unit increase in output = D TC/ D Q Production functions Isoquants An isoquant map is a method to display production functions in graphical as long as m Short in addition to long run applications Definition: An isoquant shows the set of all input combinations that produce the same level of output. The Soprano Garbage Company Short Run Costs using isoquant data The Soprano Garbage Company hires labor in addition to capital to produce dumpsters. The price of labor is $3. The rental rate of capital is $2 per unit. In the short run, the Sopranos have 5 units of capital. Given the isoquant map shown, calculate & draw this firms short-run total cost curve, short-run average cost curve, short-run average variable cost curve, short-run average fixed cost curve, in addition to marginal cost curve.
The Soprano Garbage Company Short run production & cost classic case Diminishing returns to the variable input Concave TP curve Diminishing MP curve Increasing MC curve (if single variable input) Marginals influence averages If MP falls below AP, it pulls AP down Bad game pulls batting average down If MC rises above AVC, it pulls AVC up Short Run Production & Cost Classic case
Short run production & cost: discussion What causes diminishing returns to a variable input Pick a good/service your org. produces. Could you double production next month If so would your marginal costs increase How do the Soprano’s cost functions compare with classic case What can you infer about differences in productivity patterns Profit maximization / Loss-Minimization in the short run Total profit = TR – TC To maximize total profit or minimize total loss A firm should increase output as long as marginal revenue exceeds marginal cost A firm should not increase output if marginal cost would exceed marginal revenue At the profit-maximizing level of output, (approx) MR=MC Fixed costs are irrelevant as long as determining this level of output Loss-Minimization: Short run shut-down case Shutting down production producing zero output while continuing to pay fixed cost Minimize loss by shutting down if TR < TVC e.g. $50 < $60 with TFC = $10 if operate then loss is $20 if shut down then loss is $10 why Equivalently, shut down if P < AVC. Where is Sopranos shut down point What is the Sopranos output if competitive market price is $1 $3 Resulting profit Long-run production in addition to cost In future a manager could Change levels of fixed inputs Substitute capital as long as labor Increase the entire scale of operations We will look at three ways to possibly reduce costs Substituting one input as long as another (optimal input mix) Increasing scale (extra capital & other inputs) Increasing scope (additional related products) Increasing learning (feedback from more output) Long run: Optimal input mix Many inputs have some degree of substitutability Degree of automation people vs. machines Different metals in automobile parts Different types of labor e.g. skilled vs. unskilled Great hitting versus taking walks Blazing fastball versus deceptive ball movements Cost Minimization Problem Choice variables levels of inputs Objective minimize total cost of producing a target output level Dual Problem: Output maximization as long as a given level of cost Objective maximize output as long as a given target level of expenditures Optimal input mix Isoquants Each isoquant shows different combinations of inputs (metals) that will produce a given amount of output (auto parts) Isoquants portray technical combination of inputs to produce a given level of output Slope = marginal rate of technical substitution of one input as long as the other = ratio of marginal products of the two inputs Optimal input mix example Isoquants: differing input substitutability Curvature of isoquants reflects degree of substitutability of inputs In our example, steel & aluminum have substitute AND complement characteristics Perfect substitutes would have straight-line isoquants Cost Minimization Problem Many inputs have some degree of substitutability Degree of automation man vs. machine Different metals in automobile parts Different types of labor e.g. skilled vs. unskilled Great hitting versus taking walks Blazing fastball versus deceptive ball movements Cost Minimization Problem Choice variables levels of inputs Objective minimize total cost of producing a target output level Mr. Burns Principle Dual Problem: Output maximization as long as a given level of cost Objective maximize output as long as a given target level of expenditures Cost Minimization Problem Isocost lines Isocost lines portray combinations of inputs that entail the same cost Isocost lines change as input prices change TC = PXX + PYY Slope of isocost is Isocost lines changes in input prices The optimal choice of inputs is where Slope of the isoquant = Slope of isocost line "optimal input mix" rule Input Y per week TC1 TC2 TC3 q1 Y Input X per week X 0 Excellent! MRTS=Relative Price of Inputs Optimal Input Mix Change in input prices If price of steel rises then Ps/Pa goes up in addition to isocosts get steeper => Change cost minimizing input mix to more aluminum, less steel
Discussion: The Oakl in addition to As in addition to Cost minimization How did the As produce more at a lower cost Specifically how did the management change the As mix of inputs What will Beane do if the relative prices of different types of baseball talent changes Additional questions Optimal Input Mix Derivation of Long run cost curves The Sopranos The Soprano Garbage Company hires labor in addition to capital to produce dumpsters. The price of labor is $3. The rental rate of capital is $2 per unit. In the long-run, the Sopranos can vary both the amount of labor in addition to capital they use. The expansion path shows the tangencies between various isocost lines in addition to isoquants. Calculate & draw this firms long-run total cost curve, long-run average cost curve, in addition to marginal cost curve. How do these costs compare with the short-run counterparts Why Optimal Input Mix Derivation of long run cost curves The Sopranos
Long Run Supply Cost Minimization Problem Example: Labor substitutability Choose high school or college educated reps Compare relative productivities with relative wage rates Minimize labor cost by choosing most favorable cost/productivity ratio Other considerations Cost Minimization Problem – Example Choose between skilled in addition to unskilled sales workers to minimize total wage cost of achieving a target level of sales revenue
Economies of Scale Scaling up levels of all inputs due to higher production scale can alter ATC patterns. The fixed costs are higher but savings in AVC may offset. Economies of scale as long as plant sizes 1,2,3 on graph but diseconomies of scale thereafter Many companies have constant returns to scale, which means that lowest ATC doesnt vary with expansion. The dark, lower envelope of the SR average cost curves is the long run average cost curve: lowest achievable unit costs as long as different scales when you can vary all inputs. Looking Forward Assignment 2 on Blackboard Due on October 14,18, or 19 Read Managerial Economics Chapters 6 in addition to 8 Wal-Mart, p. 221 Going as long as the Gold in addition to Pineapple Acid Test, WSJ What are/were the barriers to entry into the premium pineapple market What is/will be the market structure of that market Profitability Note on the Structural Analysis of Industries Michael Porter Pick a market/industry with which you are familiar. Based on your text reading, how would you describe its market structure in addition to why How narrowly/broadly are you defining the market (e.g. does Coke compete in all beverages or bottled soft drinks) How would you characterize barriers to entry to this market
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