Lecture 28.April 2008 Microeconomics Esther Kalkbrenner:

Transcription

1 Lecture 28.April 2008 Microeconomics Esther Kalkbrenner: Supply and Demand Familiar Concepts Supply and Demand (Chapter 2) Applying the Supply and Demand Model (Chapter 3) Consumers Choice Consumer Choice (Chapter 4) Applying Consumer Theory (Chapter 5) Midterm 16. April 2008 Firms Production And Costs Firms and Production (Chapter 6) Minimizing Costs (Chapter 7) Market Setting For Interaction Btw. Consumers and Firms Competitive Firms and Markets (Chapter 8) Applying the Competitive Model (Chapter 9) Midterm 28. May 2008 Market Power and Market Structure Monopoly (Chapter 11) Pricing (Chapter 12) Oligopoly (Chapter 13) Final 27.June 2008

2 Lecture 28. April 2008 Microeconomics Esther Kalkbrenner Previously: We looked at production possibilities of a firm Today: How do costs determine the production decision? 1. measuring costs and different cost concepts (variable and fix costs, etc.) 2. SR cost minimization cost curves differ in SR and LR 3. LR cost minimization 4. costs are lower in LR Reason to study costs : understanding relationship between costs of inputs and production helps us determine least costly way to produce relationship between output and costs determines nature of an industry how many firms are in the industry how high price is relative to cost

3 Different Cost Concepts: Cost vocabulary Business costs: Economic costs: Opportunity costs: Only explicit costs e.g. workers wages, material costs Explicit and Implicit Costs (e.g. time of working owner) = Opportunity Costs = the value of the best alternative use of the resources What have you given up to do something SR Cost measure: Fixed Costs (FC) = production expenses that do not vary with output Variable Costs (VC) = production expenses that do vary with output Total Costs = VC + F Sunk fixed costs: Marginal costs: Average costs: Expenditure that cannot be recovered cost of producing the last unit = C/ Q or dc/dq average fixed costs AFC = F/Q average variable costs AVC=VC/Q average total costs AC=C/Q=AFC + AVC

4 SR Cost Curves: Cost, $ 400 C VC Total Cost Curve = VC + F B A F Cost per unit, $ Quantity, q, Units per day MC AC and AVC curves fall if MC < AC rise if MC > AC MC curve cuts AC and AVC at their minimum points b a AC AVC 8 AFC Quantity, q, Units per day

5 Different Cost Concepts: A profit maximizing firm needs to know how costs vary with output. SR cost function: C = q + q2 Determine the SR costs: Fixed cost = F = 125 Variable cost = VC = 2q + q2 Average cost = AC = C/q = 125/q q Average fixed cost = AFC = 125/q Average variable cost = AVC = 2 + q Marginal cost = MC = 2 + 2q

6 Shape of production function determines cost functions The production function determines the shape of a firm s cost curves. Production function indicates the amount of inputs needed to produce a given level of output e.g. number of employees * wage (= labor inputs) + capital * cost of capital = total costs Relationship btw. Production function and cost curves: If Input prices are constant, K fixed Production Function Cost Function: Q = F( K, L) C ( q) = rk + wl SR Fix Costs (K fixed): SR Variable Cost: FC ( q) = VC ( q) = rk wl Shape of VC Curve = Shape of Total Product of Labor Shape of MC Curve: ΔVC ΔL MC = = w produce extra output Δq Δq How much more L do we need to produce extra Q? w Therefore: MC = MP L MP L = Δq ΔL

7 Shape Production Shape Cost Curve Q and VC MP(L) and MC AP(L) and AVC Total Product of L = Q Relation Q and L as K fixed MP(L) = Q/ L L to produce add. unit of Q AP(L)=Q/L VC: VC=wL as K is fixed MC = VC/ Q= L/ Q AVC=VC/Q=wL/Q Relation C and L Cost to produce add. unit of Q Relation between them Example Assume: w= 5$ Quantity L less than in proportion Q = flattening of total product of L at higher levels of L = diminishing marginal returns This causes the VC more than in proportion as Q 6 5 Double L does not double Q Double Q costs more than double VC Q and VC in SR are the same w MC = MP L SR to produce add.q use add L As K is fixed MP(L) how much more L is needed to produce add. Q If Q=5 and L=20 get 1 more Q MP(L)=1/4 MC=5/MP(L)=20 MP(L) and MC move opposite Total product of Labor Variable Cost = same curve Cost AVC = w AP If Q=6 and L=24 AP(L)=6/24 AVC =5/1/4=20 AP(L) and AVC move opposite L AC MC AVC FC L, Hours of Labor Quantity VC = wl, variable Cost

8 LR costs LR firms can adjust all its inputs such that cost of production is as low as possible LR not only L is variable also K therefore F=0 LR Total cost = LR variable cost = VC Input Choice: Firm will choose from all technological efficient combinations of inputs such that it receives an optimal output. Isocost Line tells the firm all combinations of inputs that cost the same If if cost: C = wl + rk then isocost is C = wl+ rk, where C is a fixed level of cost

9 Family of Isocost Lines: K, Units of capital per year 15 = 10 = 5 = $150 $10 $100 $10 $50 $10 e Isocost Lines show all combinations of K and L such that costs remain the same 1. Slope: ΔK/ΔL = -w/r indicates rate of substitution btw. K and L holding costs constant d 2. Cross points X-axis: c $50 isocost b Y-axis: C/ w C/ r 3. Isocosts farther away from origin have higher costs $100 isocost C w K = L r r $150 isocost $50 $5 = 10 a $100 $5 = 20 $150 = 30 $5 L, Units of labor per year

10 Cost Minimization: K, Units of capital per year Graphical Example: Combining Production Possibilities and Cost Information: Equivalent Cost Minimizing Rules = to pick lowest-cost combination of inputs to produce a given level of output 303 3,000-kr isocost 2,000-kr isocost 1. lowest-isocost rule: pick bundle of inputs where lowest isocost line touches isoquant 2. tangency rule: MRTS = ratio of the input prices = w/r 3. last-dollar rule: y last dollar spent on one input produces as much extra output as last dollar spent on any other input MRTS MP L = = MPK w r 100 1,000-kr isocost x MP w L = MP r K 28 0 cost minimizing: output maximizing: 24 q = 100 isoquant z L what is the lowest cost, C*, at which the firm can produce output q*? what is the most output, q*, that can be produced at cost C*?

11 Effect if Input Prices change Change in Factor Prices: K, Units of capital per year Original isocost, 2,000 kr Change in Factor Prices cause firm to change the mix of inputs used firm substitutes relatively less expensive inputs for more expensive Example: r = 8 kr stays the same original wage = 24 kr, so w/r = 3 new wage = 8 kr, so w/r = 1 New isocost, 1,032 kr Change in w does not affect technological efficiency isoquant does not shift but move along isoquant isocost becomes flatter (darker blue in graph) 100 x v 52 q = 100 isoquant L, Workers per year

12 Shape of LR costs curves: LR cost vary with output X, Y, Z are the lowest-cost factor combination for various levels of output Expansion path: = cost-minimizing combination of L and K for each Q curve through tangency points is LR expansion path expansion path shows same relationship between LR cost and output as the LR cost curve LR cost Curve X-axis: Q Y-axis: C Expansiion Path: X-axis: L Y-axis: Q

13 Effect of a change of Factor Price on Expansion Path: Effect of Factor Prices: w decreases, r constant w therefore Isocost Line becomes flatter at each output level Expansion Path becomes flatter too What if w increases relative to r?

14 Shape of LR Cost Curves: (a) Cost Curve Cost, $ C Shape of LR Curve determines: Shape of AC curve Shape of MC curve Typical Firm has a U-shaped MC and AC curve Meaning: decrease at first, increase after (Note: Other Shape f. MC and AC could be straight) Q<Q* LR cost curve rises less rapidly than output (b) Marginal and Average Cost Curves q* q, Quantity per day Q>Q* LR cost curve rises more rapidly than output Cost per unit, $ MC Slope tangent to LR cost curve at Q* = MC and AC at Q* LR cost curve falls if MC<AC rises if MC>AC AC q* q, Quantity per day

15 Difference in SR and LR costs curves: The explanation why AC is U-shaped different in SR than in LR: SR: SR AC initially downward sloping because AFC is downward sloping Meaning: Spreading the fixed costs over more units of output lowers the average costs per unit SR AC later upward sloping because of diminishing returns Meaning: Marginal Product of L becomes smaller, the more L a firm employs; causes AVC, AC to rise LR: no fixed cost in LR (usually) no diminishing marginal returns as all factors can be varied in LR production function returns to scale (relationship btw. Output and Inputs) explain the LR AC shape CRS, IRS or DRS determine shape of cost curves e.g. IRS = costs double but output triples, the AC fall This means that the cost function exhibits economies of scale Economies of scale no Economies of scale Dis-Economies of scale AC as output AC does not change as output AC when output

16 Economies of Scale & SR costs > LR costs Why do Economies of Scale exist? Production Returns to Scale Economies of Scale not necessarily: returns to scale in production function sufficient condition for AC economies of scale but not necessary condition LR firm may change ratio of K/L as it expands output, possible to have economies of scale in costs without increasing returns to scale in production Economies of Scale Production Returns to Scale: The Shape of AC curve determines if the production process has economies or diseconomies of scale LR, firm chooses optimal plant size level to minimize its LR cost given q because the firm cannot vary its capital in SR but can in LR SR cost LR cost SR cost > LR cost if the "wrong" level of capital is used in SR Why SR cost LR cost: Firms have more flexibility in LR than in SR Technical process might lower cost over time Learning by doing: productive skills and knowledge increases

17 LR cost curve and SR cost curve Example: 3 different plant sizes Average cost, $ SRAC 3 LRAC SRAC 1 SRAC SRAC a b c d e 0 q 1 q 2 q, Output per day

18 LR and SR expansion path: Land LR Expansion Path: L and K can be adjusted x and z are optimal production points where costs are minimized I 3 SR Expansion Path: only L can be adjusted and K is fixed y yields the same output as z but costs are larger as K cant be adjusted I 2 Long-run expansion path I 1 z fixed land x y Short-run expansion path q 2 isoquant q 1 isoquant 0 Other inputs

19 Learning by doing and Economies of Scope Learning by doing: Economies of Scale: Learning by doing: q1 < q2 < q3 produce q2 costs B on AC1 in t produce q2 costs b on AC2 in t+1 Production of multiple goods: Economies of Scope = Ít is less expensive to produce both goods together Than to produce each good separately Production Possibility Frontier (PPF) = straight line no economies of scope = concave (bowed away from origin) economies of scope

20 Summary Lecture 28. April 2008 Microeconomics Esther Kalkbrenner Today: How do costs determine the production decision? 1. measuring costs and different cost concepts (variable and fix costs, etc.) economic cost = explicit + implicit costs opportunity cost = value of next best alternative use of inputs 2. SR cost minimization cost curves differ in SR and LR as some factors are fixed in SR costs vary with the variable (=non fixed) inputs 3. LR cost minimization all factors can be varied, so all costs are variable AC=AVC costs are minimized where: lowest isocost touches the relevant isoquant isocost is tangent to isoquant last $ spent on any input increases output by as much as last $ spent on any other input 4. costs are lower in LR more flexibility in the LR technological progress learning by doing Concept of Economies of Scale: producing more of one good decreases costs Concept of Economies of Scope: producing both goods together decrease costs