Units 2&3 prod. & cost functions

Production Analysis Factors of Production Land: materials and forces that nature gives to man—land, water, air, light, heat, etc. Renewable and non renewable; inelastic supply. Labour Time or service that individuals put into production Quantity of labour vs. quality of labour Division of labour. Capital: ‘ produced means of production’. Entrepreneurship

You run General Motors. List 3 different costs you have. List 3 different business decisions that are affected by your costs. A C T I V E L E A R N I N G Brainstorming the concept of costs

Total Revenue, Total Cost, Profit We assume that the firm’s goal is to maximize profit . Profit = Total revenue – Total cost 0 the amount a firm receives from the sale of its output the market value of the inputs a firm uses in production

Costs: Explicit vs. Implicit Explicit costs require an outlay of money, e.g. , paying wages to workers. Implicit costs do not require a cash outlay, e.g. , the opportunity cost of the owner’s time. Remember one of the Ten Principles: The cost of something is what you give up to get it . This is true whether the costs are implicit or explicit. Both matter for firms’ decisions. 0

Explicit vs. Implicit Costs: An Example You need $100,000 to start your business. The interest rate is 5%. Case 1: borrow $100,000 explicit cost = $5000 interest on loan Case 2: borrow $60,000, and use $40,000 of your savings explicit cost = $3000 (5%) interest on the loan implicit cost = $2000 (5%) foregone interest you could have earned on your $40,000. 0 In both cases, total (expl + impl) costs are $5000.

Economic Profit vs. Accounting Profit Economic profit = total revenue minus total costs (including explicit and implicit costs) Accounting profit = total revenue minus total explicit costs Accounting profit ignores implicit costs, so it’s higher than economic profit. 0

Economists versus Accountants How an Economist Views a Firm How an Accountant Views a Firm Revenue Total opportunity costs Revenue Economic profit Implicit costs Explicit costs Explicit costs Accounting profit

The equilibrium rent on office space has just increased by $500/month. Compare the effects on accounting profit and economic profit if a. you take your office space on rent b. you own your office space A C T I V E L E A R N I N G Economic profit vs. accounting profit

The rent on office space increases $500/month. a. You take your office space on rent. Explicit costs increase $500/month. Accounting profit & economic profit each fall $500/month. b. You own your office space. Explicit costs do not change, so accounting profit does not change. Implicit costs increase $500/month (opp. cost of using your space instead of renting it out), so economic profit falls by $500/month. A C T I V E L E A R N I N G 2 Answers

Theory of Production Concepts of product: Total product : of a factor of production is the amount of total output produced by that factor, other factors being kept constant .

Concepts of product Average Product: of a factor of production is the total output produced per unit of the factor. AP = TP/(number of units of the factor) If the factor is L, AP L = Q/L [OR] AP L = TP/L

Concepts of product Marginal product (MP) of variable input: Change in output, (ΔQ) , resulting from a unit change of the variable input Holding all other inputs constant

Marginal Product If capital is the variable input: then marginal product of capital is If labor is the variable input: then marginal product of labour is MP is analogous to the concept of marginal utility, except that MP is a cardinal number. Distances between any levels of MP are of a known size measured in physical quantities like bushels, bottles, kilograms, litres, etc .

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. Can be represented by a table, equation, or graph. Q = f (L, K, D) Example 1: Farmer cultivating wheat Farmer Jack cultivates wheat. He has 5 acres of land. He can hire as many workers as he wants. 0

Example 1: Farmer Jack’s Production Function 0 0 500 1,000 1,500 2,000 2,500 3,000 0 1 2 3 4 5 No. of workers Quantity of output 3000 5 2800 4 2400 3 1800 2 1000 1 0 0 Q (bushels of wheat) L (no. of workers)

Marginal Product If Jack hires one more worker, his output rises by the marginal product of labor . The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant. Notation: ∆ (delta) = “change in…” Examples: ∆ Q = change in output, ∆ L = change in labor Marginal product of labor ( MP L ) = 0 ∆ Q ∆ L

EXAMPLE 1: Total & Marginal Product 200 400 600 800 1000 MP L 0 3000 5 2800 4 2400 3 1800 2 1000 1 0 0 Q (bushels of wheat) L (no. of workers) ∆ Q = 1000 ∆ L = 1 ∆ Q = 800 ∆ L = 1 ∆ Q = 600 ∆ L = 1 ∆ Q = 400 ∆ L = 1 ∆ Q = 200 ∆ L = 1

EXAMPLE 1: MP L = Slope of Prod Function MP L equals the slope of the production function. Notice that MP L diminishes as L increases. This explains why the production function gets flatter as L increases. 3000 5 200 2800 4 400 2400 3 600 1800 2 800 1000 1 1000 0 0 MP L Q (bushels of wheat) L (no. of workers) 0 0 500 1,000 1,500 2,000 2,500 3,000 0 1 2 3 4 5 No. of workers Quantity of output

Why MP L Is Important Recall one of the Ten Principles: ‘ Rational people think at the margin.’ When Farmer Jack hires an extra worker, his costs rise by the wage he pays the extra worker his output rises by MP L Comparing them helps Jack decide whether he would benefit from hiring the worker.

Why MP L Diminishes Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why? As Jack adds workers, the each worker has less land to work with, and so, will be less productive. In general, MP L diminishes as L rises, regardless of whether the fixed input is land or capital (equipment, machines, etc.). Diminishing Marginal Product : the marginal product of an input declines as the quantity of the input increases (other things being constant).

Units 2&3 prod. & cost functions

Production Function with One Variable Input Law of Variable Proportions (a.k.a. Law of Diminishing Returns) The law deals with the short run production function Explains the short-run changes in P Quantity of one factor of production is changed; other factors held constant Varying proportion of the factors--‘variable proportions’ “ As the proportion of one factor in a combination of factors is increased, first the marginal, and then the average product of that factor will diminish. ”

Law of Variable Proportions TP, MP, and AP in the 3 stages

Law of Variable Proportions The Optimum Stage of Production: Stage II is the choice of a rational producer. Stage I: Fixed factors too much in proportion to variable factor. Stage II: Fixed factors and variable factor in ideal proportion. Stage III: Fixed factor too little in proportion to variable factor.

Production Function with Two Variable Inputs Isoquant : “ An isoquant is the locus of different combinations of two factors of production, such that every combination yields the same quantity of output.” Each combination on an isoquant produces the same quantity of output. Iso-product curve, equal-product curve, production-indifference curve. Similar to indifference curve, but cardinal value used.

Production Function with Two Variable Inputs Factor Combinations Factor Combination Labour Capital A 1 12 B 2 8 C 3 5 D 4 3 E 5 2

Production Function with Two Variable Inputs Construct isoquant from the preceding table. Isoquant Map: Family of Isoquants Each isoquant represents a different quantity of output Therefore, an Isoquant map represents the production function of a product with two factors.

Production Function with Two Variable Inputs Marginal Rate of Technical Substitution: “ MRTS of labour for capital (MRTS LK ) is the number of units of capital that can be replaced by one unit of labour, the quantity of output remaining the same.” MRTS LK = ∆K / ∆L ∆ K / ∆L = MP L / MP K Therefore, MRTS LK = MP L / MP K

Production Function with Two Variable Inputs ∆ K / ∆L = MP L / MP K Proof: On an isoquant, Loss of output due to reduction of K = Gain in output due to addition of L (∆K * MP K ) = (∆L * MP L )  ∆ K / ∆L = MP L / MP K

Production Function with Two Variable Inputs Diminishing Marginal Rate of Technical Substitution : As we go on replacing K with L, the quantity of K that can be replaced by one additional unit of L goes on decreasing. This is due to: the principle of diminishing returns.

Production Function with Two Variable Inputs General Properties of Isoquants: Slope downward to the right Can’t touch or intersect one another Convex to the origin

Production Function with Two Variable Inputs Iso-Cost Line : Iso-cost line is the locus of different combinations of factors that a firm can buy with a constant outlay. Also known as outlay line.

Production Function with Two Variable Inputs Slope of the iso-cost line: slope of the isocost line = ratio of prices of the two factors Proof: C  Total Outlay (i.e., amount of money spent) r  Price of Capital; w  Price of Labour Maximum quantity of Capital = OB Maximum quantity of Labour = OL Therefore, slope of the Isocost line = OB/OL

Production Function with Two Variable Inputs If C is used to buy only Labour, C = OL * w OL = C / w If C is used to buy only Capital, C = OB * r OB = C / r

Production Function with Two Variable Inputs Therefore, OB/OL = (C/r) ÷ (C/w) (C/r) * (w/C) w/r Thus, OB / OL = w / r Slope of isocost line = Ratio of prices of the two factors

Production Function with Two Variable Inputs Shifts in Iso-Cost Line Three causes of shifts-- Shifts due to changes in cost of one factor at a time Shifts due to changes in cost of both factors Shifts due to changes in outlay

Production Function with Two Variable Inputs Two approaches to deciding output and cost of production: Maximising output for a given outlay. Minimising the outlay for a given quantity of output. (least-cost combination of factors) Both involve isoquants and iso-cost lines.

Production Function with Two Variable Inputs Maximising Output for a given outlay:

Production Function with Two Variable Inputs Minimising outlay for a given output:

Production Function with Two Variable Inputs Expansion Path : “ The expansion path is the locus of the various least-cost combinations of the two factors as the firm ‘expands’ its output.” Diagram of Expansion Path. Note that an expansion path only shows us the cheapest (i.e., most efficient) way of producing each level of output. It does not tell us where exactly on the path a producer is situated.

Production Function with Two Variable Inputs Returns to Scale ‘ Scale ’ refers to the proportion of the factors used. Proportional change in all the factors is called a change in the scale. Returns to scale refers to how output responds to an equiproportionate change in all inputs.

Production Function with Two Variable Inputs Returns to Scale Increasing Returns to Scale: If the change in output is in greater proportion than the change in input, returns to scale are said to be increasing. In other words, if an increase in scale leads to an increase in the output by a greater proportion, the returns to scale are said to be increasing. Diagram: (Q2/Q1) > (OA2/OA1)

Production Function with Two Variable Inputs Returns to Scale Constant Returns to Scale : If the change in output is equal in proportion to the change in input, returns to scale are said to be constant. If an increase in scale leads to an increase in the output by the same proportion, the returns to scale are said to be constant. Diagram: (Q2/Q1) = (OA2/OA1)

Production Function with Two Variable Inputs Returns to Scale Decreasing Returns to Scale: If the change in output is in a smaller proportion than the change in input, returns to scale are said to be decreasing. In other words, if an increase in scale leads to an increase in the output by a smaller proportion, the returns to scale are said to be decreasing. Diagram: (Q2/Q1) < (OA2/OA1)

Production Function with Two Variable Inputs Returns to Scale In reality, all three types of returns to scale are found in within a firm. Diagram

Cost-Benefit Analysis in an Advertisement

Cost Concepts Fixed Costs; Variable Costs; Total Cost Average Fixed Cost; Average Variable Cost; Average Total Cost [a.k.a. Average Cost] Marginal Cost

EXAMPLE 1: Farmer Jack’s Costs Farmer Jack must pay $1,000 per month for the land, regardless of how much wheat he grows. The market wage for a farm worker is $2,000 per month. So Farmer Jack’s costs are related to how much wheat he produces….

Fixed and Variable Costs Fixed cost ( FC ) – does not vary with the quantity of output produced. For Farmer Jack, FC = $1000 for his land Other examples: cost of equipment, loan payments Variable cost ( VC ) – varies with the quantity produced. For Farmer Jack, VC = wages he pays workers Other example: cost of materials Total cost ( TC ) FC + VC 0

EXAMPLE 1: Farmer Jack’s Costs Total Cost 3000 5 2800 4 2400 3 1800 2 1000 1 0 0 Cost of labor Cost of land Q (bushels of wheat) L (no. of workers) 0 $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000

EXAMPLE 1: Farmer Jack’s Total Cost Curve Q (bushels of wheat) Total Cost 0 $1,000 1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000

Marginal Cost Marginal Cost ( MC ): is the increase in Total Cost due the production of one more unit of the output. ∆ TC ∆ Q MC =

EXAMPLE 1: Total and Marginal Cost $10.00 $5.00 $3.33 $2.50 $2.00 Marginal Cost ( MC ) $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 Total Cost 3000 2800 2400 1800 1000 0 Q (bushels of wheat) ∆ Q = 1000 ∆ TC = $2000 ∆ Q = 800 ∆ TC = $2000 ∆ Q = 600 ∆ TC = $2000 ∆ Q = 400 ∆ TC = $2000 ∆ Q = 200 ∆ TC = $2000

EXAMPLE 1: The Marginal Cost Curve MC usually rises as Q rises, as in this example. $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 TC MC 3000 2800 2400 1800 1000 0 Q (bushels of wheat) $10.00 $5.00 $3.33 $2.50 $2.00

Why MC Is Important Farmer Jack is rational and wants to maximize his profit. To increase profit, should he produce more or less wheat? To find the answer, Farmer Jack needs to “think at the margin.” If the cost of producing additional wheat ( MC ) is less than the revenue he would get from selling it, then Jack’s profits rise if he produces more.

EXAMPLE 2 The next example is more general, applies to any type of firm, producing any good with any types of inputs.

Example 2: Costs 7 6 5 4 3 2 1 0 TC VC FC Q $0 $100 $200 $300 $400 $500 $600 $700 $800 0 1 2 3 4 5 6 7 Q Costs FC VC TC 0 620 480 380 310 260 220 170 $100 520 380 280 210 160 120 70 $0 100 100 100 100 100 100 100 $100

EXAMPLE 2: Marginal Cost Recall, Marginal Cost ( MC ) is the change in total cost from producing one more unit: Usually, MC rises as Q rises, due to diminishing marginal product. Sometimes (as here), MC falls before rising. (In other examples, MC may be constant.) 620 7 480 6 380 5 310 4 260 3 220 2 170 1 $100 0 MC TC Q 140 100 70 50 40 50 $70 ∆ TC ∆ Q MC =

EXAMPLE 2: Average Fixed Cost 100 7 100 6 100 5 100 4 100 3 100 2 100 1 $100 0 AFC FC Q Average fixed cost ( AFC ) is the fixed cost per unit of the quantity of output: AFC = FC / Q Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. 0 14.29 16.67 20 25 33.33 50 $100 n.a.

EXAMPLE 2: Average Variable Cost 520 7 380 6 280 5 210 4 160 3 120 2 70 1 $0 0 AVC VC Q Average variable cost ( AVC ) is the variable cost per unit of the output: AVC = VC / Q As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 0 74.29 63.33 56.00 52.50 53.33 60 $70 n.a.

EXAMPLE 2: Average Total Cost [a.k.a. Average Cost] ATC 620 7 480 6 380 5 310 4 260 3 220 2 170 1 $100 0 TC Q 0 Average total cost ( ATC ) is the total cost per unit of the output: ATC = TC / Q Also, ATC = AFC + AVC 88.57 80 76 77.50 86.67 110 $170 n.a. 74.29 14.29 63.33 16.67 56.00 20 52.50 25 53.33 33.33 60 50 $70 $100 n.a. n.a. AVC AFC

EXAMPLE 2: Average Total Cost Usually, as in this example, the ATC curve is U-shaped. 88.57 80 76 77.50 86.67 110 $170 n.a. ATC 620 7 480 6 380 5 310 4 260 3 220 2 170 1 $100 0 TC Q 0 $0 $25 $50 $75 $100 $125 $150 $175 $200 0 1 2 3 4 5 6 7 Q Costs

EXAMPLE 2: The Various Cost Curves Together 0 AFC AVC ATC MC $0 $25 $50 $75 $100 $125 $150 $175 $200 0 1 2 3 4 5 6 7 Q Costs

A C T I V E L E A R N I N G 3 : Costs Fill in the blank spaces of this table. 210 150 100 30 10 VC 43.33 35 8.33 260 6 30 5 37.50 12.50 150 4 36.67 20 16.67 3 80 2 $60.00 $10 1 n.a. n.a. n.a. $50 0 MC ATC AVC AFC TC Q 60 30 $10

First, deduce FC = $50 and use FC + VC = TC . A C T I V E L E A R N I N G 3 : Answers Use AFC = FC / Q Use AVC = VC / Q Use relationship between MC and TC Use ATC = TC / Q 210 150 100 60 30 10 $0 VC 43.33 35 8.33 260 6 40.00 30 10.00 200 5 37.50 25 12.50 150 4 36.67 20 16.67 110 3 40.00 15 25.00 80 2 $60.00 $10 $50.00 60 1 n.a. n.a. n.a. $50 0 MC ATC AVC AFC TC Q 60 50 40 30 20 $10

EXAMPLE 2: Why ATC Is Usually U-Shaped 0 As Q rises: Initially, falling AFC pulls ATC down. Eventually, rising AVC pulls ATC up. $0 $25 $50 $75 $100 $125 $150 $175 $200 0 1 2 3 4 5 6 7 Q Costs

EXAMPLE 2: ATC and MC 0 When MC < ATC , ATC is falling. When MC > ATC , ATC is rising. The MC curve crosses the ATC curve at the ATC curve’s minimum. That is, when MC=AC, ATC is at its minimum. ATC MC $0 $25 $50 $75 $100 $125 $150 $175 $200 0 1 2 3 4 5 6 7 Q Costs

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) In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q ( e.g ., the factory size with the lowest ATC ).

EXAMPLE 3: 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. ATC S ATC M ATC L Q Avg Total Cost

EXAMPLE 3: LRATC with 3 factory Sizes LRATC To produce less than Q A , firm will choose size S in the long run. To produce between Q A and Q B , firm will choose size M in the long run. To produce more than Q B , firm will choose size L in the long run. ATC S ATC M ATC L Q Avg Total Cost Q A Q B

A Typical LRATC Curve In the real world, factories come in many sizes, each with its own SRATC curve. So a typical LRATC curve looks like this: Q ATC LRATC

How ATC Changes As the Scale of Production Changes Economies of scale : ATC falls as Q increases. Constant returns to scale : ATC stays the same as Q increases. Diseconomies of scale : ATC rises as Q increases. LRATC Q ATC

How ATC Changes As the Scale of Production Changes Economies of scale occur when increasing production allows greater specialization: workers more efficient when focusing on a narrow task. More common when Q is low. Diseconomies of scale are due to coordination problems in large organizations. E.g ., management becomes stretched, can’t control costs. More common when Q is high.

Summary Implicit costs do not involve a cash outlay, yet are just as important as explicit costs to firms’ decisions. Accounting profit is revenue minus explicit costs. Economic profit is revenue minus total (explicit + implicit) costs. The production function shows the relationship between output and inputs.

Summary The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly. Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper. Variable costs vary with output; fixed costs do not.

Summary Marginal cost is the increase in total cost from an extra unit of production. The MC curve is usually upward-sloping. Average variable cost is variable cost divided by output. Average fixed cost is fixed cost divided by output. AFC always falls as output increases. Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.

Summary The MC curve intersects the ATC curve at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises. In the long run, all costs are variable. Economies of scale: ATC falls as Q rises. Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.

CONCLUSION Costs are critically important to many business decisions, including production, pricing, and hiring. These slides have introduced the various cost concepts. The following unit will show how firms use these concepts to maximize profits in various market structures.

Law of Diminishing Marginal Returns A firm’s costs will depend on Prices it pays for inputs Technology of combining inputs into output In short run firm can change its output by adding variable inputs to fixed inputs Output may at first increase at an increasing rate However, given a constant amount of fixed inputs, output will at some point increase at a decreasing rate Occurs because at first variable input is limited compared with fixed input As additional workers are added, productivity remains very high Output, or TP, increases at an increasing rate However, as more of variable input is added, it is no longer as limited Eventually, TP will still be increasing, but at a decreasing rate MP L will still be positive, but declining

Law of DMR Diminishing marginal returns starts at point A MP L is at a maximum To the left of point A there are increasing returns and at point A constant returns exist Between points A and B, where MP L is declining, diminishing marginal returns exist To the right of point B, marginal productivity is both diminishing and negative (MP L < 0), which violates Monotonicity Axiom

Law of DMR TP curve will at some point increase only at a decreasing rate (concave) due to Law of Diminishing Marginal Returns

Units 2&3 prod. & cost functions

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