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Economic Analysis for Business Session XI: The Costs of Production Instructor Sandeep Basnyat 9841892281 [email protected] Objectives of the firms Varieties of objectives: 1. Profit maximization 2. Sales Revenue maximization 3. Utility maximization 4. Corporate growth maximization 5. Etc… Most Important economic Objective- Profit Maximization ◦ The economic goal of the firm is to maximize profits. Profit = Total revenue – Total cost the amount a firm receives from the sale of its output the market value of the inputs a firm uses in production Sequence of Presentation Understanding Costs, Production functions and their relationship Derive various cost curves A concept of Revenue How firms behave if they are in different market structures? Costs: Explicit vs. Implicit Explicit costs – require an outlay of money, e.g. paying wages to workers Accounting profit = total revenue minus total explicit costs Implicit costs (Opportunity Costs) – do not require a cash outlay e.g. the cost of the owner’s time Economic profit = total revenue minus total costs (including explicit and implicit costs) The Production Function A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good. It can be represented by a table, equation, or graph. Simple Example: Production Function Q (no. of (bushels workers) of wheat) 3,000 Quantity of output L 2,500 0 0 1 1000 2 1800 3 2400 500 4 2800 0 5 3000 2,000 1,500 1,000 0 1 2 3 4 No. of workers 5 Properties of Production Functions: Returns to Scale Increasing Returns to Scale When inputs are increased by m, output increases by more than m. Eg: A 10% increase in labour/capital increases the output by more than 10% Constant Returns to Scale When inputs are increased by m, output increases by exactly m. Decreasing Returns to Scale When inputs are increased by m, output increases by less than m. Note: Assuming that the value of multiplier >1 (positive) Properties of Production Functions: Returns to Scale Find if the followings production functions have increasing, constant or decreasing returns to scale. (i) Q = 3L (ii) Q = L0.5 (iii) Q = L2 Q = 3L = 3 (mL) = m . 3L = m. Q (Constant) Q = L0.5 = (mL)0.5 = m0.5L0.5 = m0.5Q (Decreasing) Q = L2 = (mL)2 = m2L2 = m2Q (Increasing) Marginal Product The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant. ∆Q Marginal product of labor (MPL) = ∆L ∆Q = change in output, ∆L = change in labor EXAMPLE :Marginal Product L Q (no. of (bushels workers) of wheat) ∆L = 1 0 1 ∆L = 1 ∆L = 1 ∆L = 1 ∆L = 1 2 3 4 5 0 MPL ∆Q = 1000 1000 ∆Q = 800 800 ∆Q = 600 600 ∆Q = 400 400 ∆Q = 200 200 1000 1800 2400 2800 3000 Relationship between Production Function and MPL Q 3,000 (no. of (bushels MPL workers) of wheat) 0 0 1000 1 1000 800 2 1800 Quantity of output L 2,500 2,000 1,500 1,000 600 3 4 5 2400 2800 3000 500 400 0 200 0 1 2 3 4 No. of workers Diminishing MPL: This property explains why Production Function flatters as output increases. 5 Why MPL Diminishes Diminishing marginal product: the marginal product of an input declines as the quantity of the input increases (other things equal) E.g.: Output rises by a smaller and smaller amount for each additional worker. Why? If the number of workers increased but not land, the average worker has less land to work with, so will be less productive. In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.). Deriving Costs curves FC VC TC 0 $100 $0 $100 1 100 70 170 2 100 120 220 3 100 160 260 4 100 210 310 5 100 280 380 FC $700 VC TC $600 $500 Costs Q $800 $400 $300 $200 $100 6 7 100 380 100 520 Example: FC = Cost of land VC = Wages to labor 480 620 $0 0 1 2 3 4 Q 5 6 7 Marginal Cost curve TC MC 0 $100 1 2 3 4 5 6 7 170 220 260 310 380 480 620 $70 50 40 50 70 100 140 $200 Marginal Cost (MC) is $175 the change in total cost from producing one more unit: $150 ∆TC MC = ∆Q $100 Usually, MC rises as Q rises, due $75 to diminishing marginal product. Costs Q $125 $50 Sometimes, MC falls before rising. $25 (In rare cases, MC may be $0 constant.) 0 1 2 3 4 Q 5 6 7 EXAMPLE : Rising Marginal Cost Curve 0 $12 TC MC $1,000 $2.00 1000 $3,000 $2.50 1800 $5,000 $3.33 2400 $7,000 $5.00 2800 $9,000 3000 $11,000 $10.00 $10 Marginal Cost ($) Q (bushels of wheat) $8 $6 $4 $2 $0 0 1,000 2,000 Q 3,000 Average Fixed Cost curve FC 0 $100 1 100 AFC n.a. $100 2 100 3 100 33.33 4 100 25 5 100 20 6 50 100 16.67 Average fixed cost (AFC) $200 is fixed cost divided by the $175 quantity of output: $150 AFC = FC/Q Costs Q $125 $100 $75 $50 $25 $0 7 100 14.29 0 1 2 3 4 Q 5 6 7 Average Variable Cost curve VC AVC 0 $0 n.a. 1 70 $70 2 120 60 3 160 53.33 4 210 52.50 5 280 56.00 6 380 63.33 7 520 74.29 $200 Average variable cost (AVC) is$175 variable cost divided by the quantity of output: $150 Costs Q AVC $125 = VC/Q $100 As$75 Q rises, AVC may fall initially. In most cases, AVC will $50 eventually rise as output rises. $25 $0 0 1 2 3 4 Q 5 6 7 Average Total Cost curve Q TC 0 $100 ATC AFC AVC n.a. n.a. n.a. 1 170 $170 $100 $70 2 220 110 50 60 3 260 86.67 33.33 53.33 4 310 77.50 25 52.50 5 380 76 20 56.00 6 480 80 16.67 63.33 7 620 88.57 14.29 74.29 Average total cost (ATC) equals total cost divided by the quantity of output: ATC = TC/Q Also, ATC = AFC + AVC Average Total Cost Curves Q TC 0 $100 ATC $200 Usually, the ATC curve is U$175 shaped. n.a. 170 $170 $150 2 220 110 $125 3 260 86.67 4 310 77.50 5 380 76 Costs 1 $100 $75 $50 $25 6 480 80 7 620 88.57 $0 0 1 2 3 4 Q 5 6 7 Why ATC Is Usually U-shaped As Q rises: $200 Initially, falling AFC pulls ATC down. $175 Costs Eventually, rising AVC pulls ATC up. $150 $125 $100 $75 $50 $25 $0 0 1 2 3 4 Q 5 6 7 The Various Cost Curves Together $200 $175 ATC AVC AFC MC Costs $150 $125 $100 $75 $50 $25 $0 0 1 2 3 4 Q 5 6 7 Important Economic Relation: ATC and MC When MC < ATC, ATC is falling. $175 $150 ATC is rising. $125 Costs When MC > ATC, The MC curve crosses the ATC curve at the ATC curve’s minimum. ATC MC $200 $100 $75 $50 $25 $0 0 1 2 3 4 Q 5 6 7 ACTIVE LEARNING 3: Costs Fill in the blank spaces of this table. Q VC 0 1 10 2 30 TC AFC AVC ATC $50 n.a. n.a. n.a. $10 $60.00 80 3 16.67 4 100 5 150 6 210 150 20 12.50 36.67 8.33 $10 30 37.50 30 260 MC 35 43.33 60 24 ACTIVE LEARNING 3: Answers Q VC TC AFC AVC ATC 0 $0 $50 n.a. n.a. n.a. 1 10 60 $50.00 $10 $60.00 2 30 80 25.00 15 40.00 3 60 110 16.67 20 36.67 4 100 150 12.50 25 37.50 5 150 200 10.00 30 40.00 6 210 260 8.33 35 43.33 MC $10 20 30 40 50 60 25 Numerical Problem on Costs Given the cost function: TC = 1000 + 10Q - 0.9Q2 + 0.04Q3 Find: 1) MC, TVC, AVC functions 2) Discarding the previous TC function, consider that the existing AVC function became the ATC function for the firm. Find Q when AVC is minimum. Worked out Problem TC = 1000 + 10Q - 0.9Q2 + 0.04Q3 1) MC = ΔTC / ΔQ = d(TC) / dQ = 10-1.8Q+ 0.12Q2 2) TVC = TC –TFC = 1000 + 10Q - 0.9Q2 + 0.04Q3 – 1000 = 10Q - 0.9Q2 + 0.04Q3 3) AVC = TVC / Q =(10Q - 0.9Q2 + 0.04Q3 )/Q = 10 - 0.9Q + 0.04Q2 4) Since AVC function is the ATC function, Q at Minimum AVC when: AVC = MC 10 - 0.9Q + 0.04Q2 = 10-1.8Q+ 0.12Q2 Or, - 0.08Q2 + 0.9Q =0 Or, Q(- 0.08Q+ 0.9) =0 Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC) Costs in the Short Run & Long Run Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC. Long run: All inputs are variable (e.g., firms can build more factories, or sell existing ones) LRATC with 3 Factory Sizes Firm can choose from 3 factory sizes: S, M, L. Each size has its own SRATC curve. The firm can change to a different factory size in the long run, but not in the short run. Avg Total Cost ATCS ATCM ATCL Q EXAMPLE 3: LRATC with 3 Factory Sizes To produce less than QA, firm will choose size S in the long run. To produce between QA and QB, firm will choose size M in the long run. To produce more than QB, firm will choose size L in the long run. Avg Total Cost ATCS ATCM ATCL LRATC QA QB Q A Typical LRATC Curve In the real world, factories come in many sizes, each with its own SRATC curve. ATC LRATC So a typical LRATC curve looks like this: Q How ATC Changes as the Scale of Production Changes Economies of scale: ATC falls as Q increases. ATC LRATC Constant returns to scale: ATC stays the same as Q increases. Diseconomies of scale: ATC rises as Q increases. Q The Revenue of a Competitive Firm Total revenue (TR) TR = P x Q Average revenue (AR) TR =P AR = Q Marginal Revenue (MR): The change in TR from selling one more unit. ∆TR MR = ∆Q How do firms behave in different market structures? 1. Perfectly Competitive Market 2. Monopoly Market 3. Oligopoly Market 4. Monopolistically Competitive Market Perfectly Competitive Market 1. Many buyers and many sellers 2. The goods offered for sale are largely the same. 3. Firms can freely enter or exit the market. Because of 1 & 2, each buyer and seller is a “price taker” – takes the price as given. Sample Data Q P TR = P x Q 0 $10 $0 AR = TR Q MR = ∆TR ∆Q n.a. $10 1 2 3 $10 $10 $10 Notice that $20 $10 MR = P $10 $30 $10 $10 $10 $10 $10 4 $10 $40 $10 $10 5 $10 $50 $10 36 MR = P for a Competitive Firm A competitive firm can keep increasing its output without affecting the market price. So, each one-unit increase in Q causes revenue to rise by P, i.e., MR = P. MR = P is only true for firms in competitive markets. Profit Maximization What Q maximizes the firm’s profit? If increase Q by one unit, revenue rises by MR, cost rises by MC. If MR > MC, then increase Q to raise profit. If MR < MC, then reduce Q to raise profit. Profit Maximization (continued from earlier exercise) At any Q with MR > MC, increasing Q raises profit. At any Q with MR < MC, reducing Q raises profit. Q TR TC 0 $0 $5 –$5 1 10 9 1 2 20 15 5 3 30 23 7 4 40 33 7 5 50 45 Profit MR MC 5 Profit = MR – MC $10 $4 $6 10 6 4 10 8 2 10 10 0 10 12 –2 MC and the Firm’s Supply Decision Rule: MR = MC at the profit-maximizing Q. At Qa, MC < MR. So, increase Q to raise profit. At Qb, MC > MR. So, reduce Q to raise profit. Costs MC MR P1 At Q1, MC = MR. Changing Q would lower profit. Q a Q1 Q b Q MC and the Firm’s Supply Decision If price rises to P2, then the profitmaximizing quantity rises to Q2. The MC curve determines the firm’s Q at any price. Hence, Costs MC P2 MR2 P1 MR the MC curve is the firm’s supply curve. Q1 Q2 Q Market Structure Problems Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price is $10 per unit for a firm in the competitive market. Calculate the profit maximizing output (Q) and economic profit. Market Structure Problems Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price is $10 per unit for a firm in the competitive market. Calculate the profit maximizing output (Q) and economic profit. Solution: MC = dTC /dQ = 2+0.02Q In a perfectly competitive market, profit maximizing output is at where MR = P = MC 10 = 2+0.02Q Therefore, Q = 400 Economic Profit = TR –TC = 10(400) – (1000 + 2(400) + 0.01(4002)) =$600 When would the firms Shutdown, Exit or Enter? Shutdown: A short-run decision not to produce anything because of market conditions. Exit: A long-run decision to leave the market. A firm that shuts down temporarily must still pay its fixed costs. A firm that exits the market does not have to pay any costs at all, fixed or variable. A Firm’s Short-Run Decision to Shut Down If firm shuts down temporarily, ◦ revenue falls by TR ◦ costs fall by VC So, the firm should shut down if TR < VC. Divide both sides by Q: TR/Q < VC/Q So we can write the firm’s decision as: Shut down if P < AVC A Competitive Firm’s SR Supply Curve The firm’s SR supply curve is the portion of its MC curve above AVC. If P > AVC, then firm produces Q where P = MC. If P < AVC, then firm shuts down (produces Q = 0). Costs MC ATC AVC Q A Firm’s Long-Run Decision to Exit If firm exits the market, ◦ revenue falls by TR ◦ costs fall by TC So, the firm should exit if TR < TC. Divide both sides by Q to rewrite the firm’s decision as: Exit if P < ATC A New Firm’s Decision to Enter the Market In the long run, a new firm will enter the market if it is profitable to do so: if TR > TC. Divide both sides by Q to express the firm’s entry decision as: Enter if P > ATC Identifying a firm’s profit or Loss A competitive firm Determine if this firm’s total has profit/Loss? Identify the area on the graph that represents the firm’s profit or Loss. Costs, P MC MR ATC P = $10 $6 50 Q 49 Answers A competitive firm Costs, P profit per unit = P – ATC = $10 – 6 = $4 MC MR ATC P = $10 profit $6 Total profit = (P – ATC) x Q = $4 x 50 = $200 50 Q 50 Identifying a firm’s profit or loss. A competitive firm Determine if this firm has total profit or loss. Identify the area on the graph that represents the firm’s profit or loss. Costs, P MC ATC $5 MR P = $3 30 Q 51 Answers A competitive firm Costs, P MC Total loss = (ATC – P) x Q = $2 x 30 = $60 ATC $5 P = $3 loss loss per unit = $2 MR 30 Q 52 Demand Curve for Individual firm’s product In a competitive market, the market demand curve slopes downward. but the demand curve for any individual firm’s P product is horizontal at the market price. The firm can increase Q without lowering P, A competitive firm’s demand curve D so MR = P for the competitive firm. Price line represents the level of demand for the firm’s product Q Market Structure Problems Consider a firm which has a horizontal demand curve for its products. The firms Total Cost is given by the function: TVC = 150Q – 20Q2 +Q3. Below what price should the firm shut down operation? Market Structure Problems In the competitive market, the firm shut down only when P<AVC. The firm continue to operate until: P = AVC In competitive market, P =MC MC =dTVC / dQ = 150 -40Q +3Q2 AVC = TVC /Q = (150Q – 20Q2 +Q3) / Q = 150 -20Q +Q2 Equating, both equations: MC = AVC or 150 -40Q +3Q2 = 150 -20Q +Q2 Or, 2Q2 – 20Q = 0 or 2Q (Q – 10) = 0 Or, Q = 0 and Q = 10 Substituting Q = 10 into marginal cost, P = MC = 150 – 40(10) + 3 (100) = $50 Similarly, substituting Q = 0 in the marginal cost, P = $150 Therefore, if the price falls below $50, the firm shuts down. Firms behaviour in the Long RunProfit Condition In the LR, the number of firms can change due to entry & exit. If existing firms earn positive economic profit, ◦ ◦ ◦ ◦ New firms enter. SR market supply curve shifts right. P falls, reducing firms’ profits. Entry stops when firms’ economic profits have been driven to zero. Firms behaviour in the Long RunLoss Condition In the LR, the number of firms can change due to entry & exit. If existing firms incur losses, • Some will exit the market. • SR market supply curve shifts left. • P rises, reducing remaining firms’ losses. • Exit stops when firms’ economic losses have been driven to zero. SR & LR Effects of an Increase in Demand …but then an increase A firm begins in profits to zero …leadingeq’m… to…driving SR Over time, profits induce entry, in demand raises P,… long-run andfirm. restoring long-run eq’m. profits for the shifting S to the right, reducing P… P One firm Market P S1 MC Profit S2 ATC P2 P2 P1 P1 Q (firm) B A C long-run supply D1 Q1 Q2 Q3 D2 Q (market) Why Do Firms Stay in Business if Profit = 0? Recall, economic profit is revenue minus all costs – including implicit costs, like the opportunity cost of the owner’s time and money. In the zero-profit equilibrium, firms earn enough revenue to cover these costs. Distinction between The SR and LR Market Supply Curves Example: 1000 identical firms. At each P, market Qs = 1000 x (one firm’s Qs) P One firm MC P P3 P3 P2 P2 AVC P1 Market S P1 10 20 30 Q (firm) Q (market) 10,000 20,000 30,000 The LR Market Supply Curve The LR market supply curve is horizontal at P = minimum ATC. In the long run, the typical firm earns zero profit. P One firm MC P Market LRATC P= min. ATC long-run supply Q (firm) Q (market) The Zero-Profit Condition Long-run equilibrium: The process of entry or exit is complete – remaining firms earn zero economic profit. Zero economic profit occurs when P = ATC. Since firms produce where P = MR = MC, the zero-profit condition is P = MC = ATC. Recall that MC intersects ATC at minimum ATC. Hence, in the long run, P = minimum ATC. The Irrelevance of Sunk Costs Sunk cost: a cost that has already been committed and cannot be recovered Sunk costs should be irrelevant to decisions; you must pay them regardless of your choice. FC is a sunk cost: The firm must pay its fixed costs whether it produces or shuts down. So, FC should not matter in the decision to shut down. Thank you