12/21/2015 Part 2- Contents Production in the Long-run Chapter Cost in the Long –run MICROECONOMICS Theories of Producer Behavior By Tran ThiKieu Minh, MSc 2015, FTU Kieu Minh 4.4 Production in the Long-run Production:Two Variable Inputs  Two Variable Inputs  The information can be represented graphically  Firm can produce output by combining using isoquants different amounts of labor and capital 2015, FTU Kieu Minh 2015, FTU Kieu Minh ◦ Curves showing all possible combinations of inputs that yield the same output 2015, FTU Kieu Minh 12/21/2015 Isoquant Map Capital per year Production:Two Variable Inputs  E A B C q3 = 90 D q2 = 75  Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant q1 = 55 Labor per year 2015, FTU Kieu Minh Substituting Among Inputs ◦ There is a trade-off between inputs allowing them to use more of one input and less of another for the same level of output ◦ Slope of the isoquant shows how one input can be substituted for the other and keep the level of output the same ◦ Positive slope is the marginal rate of technical substitution (MRTS) Ex: 55 units of output can be produced with 3K & 1L (pt A) OR 1K & 3L (pt D) 2015, FTU Kieu Minh Marginal Rate of Technical Substitution Production:Two Variable Inputs Capital per year  The marginal rate of technical substitution equals: Changein Capital input Changein Labor input MRTS   K (for a fixed level of q ) L MRTS  Slope measures MRTS MRTS decreases as move down the indifference curve 1 Q3 =90 2/3 1/3 Q2 =75 Q1 =55 2015, FTU Kieu Minh 2015, FTU Kieu Minh Labor per month 12/21/2015 MRTS and Isoquants Isoquants: Special Cases Diminishing MRTS occurs because of diminishing returns and implies isoquants are convex  There is a relationship between MRTS and marginal products of inputs If we are holding output constant  2015, FTU Kieu Minh Two extreme cases show the possible range of input substitution in production Perfect substitutes  B C 2015, FTU Kieu Minh 10 Q2 Q3 Extreme cases (cont.) Perfect Complements ◦ Fixed proportions production function ◦ There is no substitution available between inputs ◦ The output can be made with only a specific proportion of capital and labor ◦ Cannot increase output unless increase both capital and labor in that specific proportion Same output can be reached with mostly capital or mostly labor (A or C) or with equal amount of both (B) Q1 Same output can be produced with a lot of capital or a lot of labor or a balanced mix Isoquants: Special Cases  A MRTS is constant at all points on isoquant ◦ 2015, FTU Kieu Minh Perfect Substitutes Capital per month ◦ Labor per month 11 2015, FTU Kieu Minh 12 12/21/2015 Fixed-Proportions Production Function 4.5 Cost in the Long Run  Capital per month Same output can only be produced with one set of inputs   Q3 C B Q1 A Labor per month 2015, FTU Kieu Minh Assumptions ◦ Two Inputs: Labor (L) & capital (K) ◦ Price of labor: wage rate (w) ◦ The price of capital  r = depreciation rate + interest rate  Or rental rate if not purchasing  These are equal in a competitive capital market Q2 K1 In the long run a firm can change all of its inputs In making cost minimizing choices, must look at the cost of using capital and labor in production decisions L1 13 2015, FTU Kieu Minh 14 Isocost Line Cost in the Long Run Capital per year  Total cost of production C = wL + rK K2 or K = C/r - (w/r)L  The Isocost Line  r ◦ A line showing all combinations of L & K that can be purchased for the same cost Slope   w ◦ For each different level of cost, the equation shows another isocost line A K1 K3 C0 L2 2015, FTU Kieu Minh 15 2015, FTU Kieu Minh L1 C1 L3 C2 Labor per year 16 12/21/2015 Producing a Given Output at Minimum Cost Choosing Inputs  We will address how to minimize cost for a Capital per year given level of output by combining isocosts with isoquants  We choose the output we wish to produce and then determine how to that at minimum cost Q1 is an isoquant for output Q1 There are three isocost lines, of which are possible choices in which to produce Q1 K2 Isocost C2 shows quantity Q1 can be produced with combination K2L2 or K 3L3 However, both of these are higher cost combinations than K 1L1 A ◦ Isoquant is the quantity we wish to produce ◦ Isocost is the combination of K and L that gives a set cost K1 Q1 K3 C0 L2 2015, FTU Kieu Minh 17  The minimum cost combination can then be written as: production process? L  MPL Slope of isocost line  K 2015, FTU Kieu Minh MPK w r 18 Choosing Inputs  How does the isocost line relate to the firm’s MPL Labor per year 2015, FTU Kieu Minh Choosing Inputs MRTS  - K C2 C1 L3 L1 MPL MPK L  w ◦ r w  MPK r Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output when firmminimizes cost 19 2015, FTU Kieu Minh 20 12/21/2015 Ex Quiz  If w = $10, r = $20, and MPL = MP K, which input would be used more of? MPL MPK  10 20 2015, FTU Kieu Minh 21 A firm operates with the production function Q = K L The manager has been given a production target: Produce 8,000 units per day She knows that the daily rental price of capital is $400 per unit The wage rate paid to each worker is $200 day a) Currently the firm employs at 80 workers per day What is the firm’s daily total cost if it rents just enough capital to produce at its target? b) Compare the marginal product per dollar sent on K and on L when the firm operates at the input choice in part (a) What does this suggest about the way the firm might change its choice of K and L if it wants to reduce the total cost in meeting its target? c) In the long run, how much K and L should the firm choose if it wants to minimize the cost of producing 8,000 units of output day? What will the total daily cost of production be? 2015, FTU Kieu Minh 22 A Firm’s Expansion Path Cost in the Long Run  Cost minimization with Varying Output Levels Capital per year ◦ For each level of output, there is an isocost curve showing minimum cost for that output level ◦ A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output The expansion path illustrates the least-cost combinations of labor and capital that can be used to produce each level of output in the long-run 150 $3000 Expansion Path $200 100 C 75 ◦ Slope equals K/L B 50 300 Units A 25 200 Units 2015, FTU Kieu Minh 23 2015, FTU Kieu Minh 50 100 150 200 300 Labor per year 24 12/21/2015 A Firm’s Long-Run Total Cost Curve Expansion Path & Long-run Costs  Firms expansion path has same information as Cost/ Year long-run total cost curve  To move from expansion path to LR cost curve Long Run Total Cost F 3000 ◦ Find tangency with isoquant and isocost E ◦ Determine cost of producing the output level selected ◦ Graph output-cost combination 2000 D 1000 100 2015, FTU Kieu Minh 25 Long-Run Versus Short-Run Cost Curves  If input is doubled, output will double AC cost is constant at all levels of output 2015, FTU Kieu Minh Output, Units/yr 26 Increasing Returns to Scale Most important determinant of the shape of the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to cost Constant Returns to Scale ◦ ◦ 300 Long-Run Versus Short-Run Cost Curves Long-Run Average Cost (LAC) ◦ 200 2015, FTU Kieu Minh 27 ◦ ◦ If input is doubled, output will more than double AC decreases at all levels of output Decreasing Returns to Scale ◦ If input is doubled, output will less than double ◦ AC increases at all levels of output 2015, FTU Kieu Minh 28 12/21/2015 Long-Run Versus Short-Run Cost Curves Long-Run Versus Short-Run Cost Curves  In the long-run: ◦ Firms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped ◦ Source of U-shape is due to returns to scale rather than diminishing marginal returns to a factor of production ◦ Long-run marginal cost curve measures the change in long-run total costs as output is increased by unit  Long-run marginal cost leads long-run average cost: ◦ If LMC < LAC, LAC will fall ◦ If LMC > LAC, LAC will rise ◦ Therefore, LMC = LAC at the minimum of LAC  In special case where LAC if constant, LAC and LMC are equal 2015, FTU Kieu Minh 29 2015, FTU Kieu Minh Long-Run Average and Marginal Cost Long Run Costs  Cost ($ per unit of output 30 LMC As output increases, firm’s AC of producing is likely to decline to a point On a larger scale, workers can better specialize Scale can provide flexibility – managers can organize production more effectively LAC A Firm may be able to get inputs at lower cost if it can get quantity discounts Lower prices might lead to different input mix Output 2015, FTU Kieu Minh 31 2015, FTU Kieu Minh 32 12/21/2015 Long Run Costs  Long Run Costs At some point, AC will begin to increase  When input proportions change, the firm’s Factory space and machinery may make it more difficult for workers to their job efficiently Managing a larger firm may become more complex and inefficient as the number of tasks increase Bulk discounts can no longer be utilized Limited availability of inputs may cause price to rise  Economies of scale reflects input proportions 2015, FTU Kieu Minh expansion path is no longer a straight line ◦ Concept of return to scale no longer applies that change as the firm change its level of production  Unlike returns to scale, economies of scale allows inputs proportions vary 33 Economies and Diseconomies of Scale 34 Quiz  Economies of Scale ◦ Increase in output is greater than the increase in inputs  Diseconomies of Scale ◦ Increase in output is less than the increase in inputs  U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels 2015, FTU Kieu Minh 2015, FTU Kieu Minh 35 In the long run for Firm A, total cost is $105 when output is units and $120 when output is units Does Firm A exhibit economies or diseconomies of scale? a Diseconomies of scale, since total cost is rising as output rises b Diseconomies of scale, since average total cost is falling as output rises c Economies of scale, since total cost is rising as output rises d Economies of scale, since average total cost is falling as output rises 2015, FTU Kieu Minh 36 12/21/2015 Long-Run Versus Short-Run Cost Curves Average total cost in the short and long runs Average Total Cost  We will use short and long-run cost to ATC in short ATC in short run with run with small factory medium factory ATC in short run with large factory LAC determine the optimal plant size  We can show the short run average costs for different plant sizes  This decision is important because once built, $12,000 the firm may not be able to change plant size for a while 10,000 Economies of scale Constant returns to scale Diseconomies of scale 1,000 1,200 Quantity of Cars per Day Because fixed costs are variable in the long run, the average-total-cost curve in the short run differs from the average-total-cost curve in the long run 2015, FTU Kieu Minh 37 2015, FTU Kieu Minh 38 Average total cost in the short and long runs  Firm will always choose plant that minimizes the average cost of production  The long-run average cost curve envelopes the short-run average cost curves  The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels 2015, FTU Kieu Minh The firm experiences diseconomies of scale if it changes its level of output  a from Q1 to Q2  b from Q2 to Q3  c from Q3 to Q4  d from Q4 to Q5  39 2015, FTU Kieu Minh 40 10 ... long-run 15 0 $3000 Expansion Path $200 10 0 C 75 ◦ Slope equals K/L B 50 300 Units A 25 200 Units 2 0 15 , FTU Kieu Minh 23 2 0 15 , FTU Kieu Minh 50 10 0 15 0 200 300 Labor per year 24 12 / 21 /2 0 15 A Firm’s... cost, the equation shows another isocost line A K1 K3 C0 L2 2 0 15 , FTU Kieu Minh 15 2 0 15 , FTU Kieu Minh L1 C1 L3 C2 Labor per year 16 12 / 21 /2 0 15 Producing a Given Output at Minimum Cost Choosing... MRTS decreases as move down the indifference curve 1 Q3 =90 2/3 1/ 3 Q2 = 75 Q1 =55 2 0 15 , FTU Kieu Minh 2 0 15 , FTU Kieu Minh Labor per month 12 / 21 /2 0 15 MRTS and Isoquants Isoquants: Special Cases Diminishing