Theory of the Firm [-0.7Ex] Production and Cost in the Short

Circular Flow Diagram Business Economics

Wage Theory of the Firm LS Production and Cost in the Short Run LD Thomas & Maurice, Chapter 8 Working hours

Herbert Stocker Households Firms

[email protected] Price S Institute of International Studies Q University of Ramkhamhaeng & Department of Economics QD University of Innsbruck Quantity

Production and Technology A General Production Function

Production: Creation of goods and services from Production function: Maximum output, Q, that can inputs using a specific technology be obtained with any combination of inputs, given a specific technology Inputs Q = Q(L, K, E, M,...) Labor Capital Materials use ··· Energy Inputs (factors of production): labor (L), (physical) capital (K), energy (E), raw materials Firm (M) ... (Technology) There might also be different types of labor and capital, e.g., LA, LB , KA, KB ... Output(Q) Inputs and output are usually measured in flows (i.e., quantities used in a given period of time) Efficiency Fixed vs. Variable Inputs

Types of inputs Production function: Maximum Output with given Fixed inputs: Inputs for which the level of usage inputs and technology → maps inputs to technical cannot readily be changed and which must be efficient output. paid even if no output is produced Technical efficiency: Achieved when maximum Variable inputs: Inputs for which the level of amount of output is produced with a given usage may be changed quite readily combination of inputs. → Amount of output will vary when managers make Economic efficiency: Achieved when firm is decisions regarding amounts of variable input producing a given output at the lowest possible Quasi-fixed inputs: Inputs employed in a fixed cost. amount for any positive level of output that need not be paid if output is zero

Short- vs. Long-Run

Short-run Versus Long-run Production Decisions:

Not expressed in terms of calendar time, but in Production and Cost terms of ﬁxed and variable inputs! in the Short Run Short-run production function: involves at least one ﬁxed input. Long-run production function: production process in which all inputs are variable. ⇒ factor substitution ⇒ optimal factor allocation Short-Run Production Function Short-Run Production Function

¯ To simplify we assume only two inputs in what follows Q = Q(L, K)

Q = Q(L, K) Average product (AP): amount of output per unit of variable input (similar to a productivity) Short-run production decisions involve one ﬁxed factor Q of production, i.e., AP = L Q = Q(L, K¯ )= Q(L), Marginal product (MP): the additional output produced with an additional unit of that variable i.e., the only way to change a ﬁrm’s output is to input: change its amount of labor employed. dQ ∆Q Change in Output MP = ≈ = dL ∆L Change in Labor Input K=const.

Short-Run Production Function Short-Run Production Function

Production- Properties of production functions function Marginal- Labor Output product The slope of the production function measures the ∆Q Q = Q(L) LQ MPL = marginal product of an input (e.g., labor) ∆L 00 - Q − Marginal product of an input declines as the 60 0 200 1 60 1−0 = 60 quantity of that input is increased. 110−60 2 110 − = 50 ⇒ 2 1 100 Diminishing Marginal Product 3 150 40 Example: As more and more workers are hired at a firm, each additional worker contributes less and less to production because the firm has a limited amount of 4 180 30 0 equipment 5 200 20 0 2 4 6 L When the marginal product declines, the 6 210 10 Marginal product: ∆Q MPL = production function becomes flatter ∆L Diminishing Marginal Product Total and Marginal Product

Example: Farm production Generally additional units of variable input produce less and less additional output. Occurs because capital input and technologies are held constant.

There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs ﬁxed, leads to a decline in the marginal product of that input. Notice: Increasing land input (assumed constant in the short-run) each worker can produce more wheat.

Production and Cost Marginal Product and Marginal Cost

Firm has to pay for variable and ﬁxed inputs. Production Marginal- Labor Fixed Total- Marginal- Total Cost are the sum of the cost for ﬁxed factors Labor Output product cost cost cost cost (FC) and the cost for variable factors (VC) ∆TC LQ MPL VC FC TC ∆Q = MC TC = FC + VC 0 0 - 03030 - 40−30 1 60 60 10 30 40 60−0 =0.17 Marginal Cost (MC) are the cost for an 50−40 2 110 50 20 30 50 110−60 =0.20 additional unit of output (the cost of the last unit 60−50 3 150 40 30 30 60 150−100 =0.25 of output). 70−60 4 180 30 40 30 70 180−150 =0.33 ∆TC Change in total cost 80−70 MC = = 5 200 20 50 30 80 200−180 =0.50 ∆Q Change in quantity 90−80 6 210 10 60 30 90 210−200 =1.00 There is a close relation between marginal product and marginal cost. Marginal Product and Marginal Cost Production and Cost

Diminishing MP ⇒ Increasing MC! These tables show two fundamental concepts of L Q TC MC TC 90 economics: 0 0 30 - 80 The columns Q and L in the preceding table 1 60 40 0.17 70 represent a short-run production function, the 2 110 50 0.20 60 3 150 60 0.25 50 maximum output that can be produced with given 4 180 70 0.33 40 inputs. 30 The columns TC and Q in the preceding table 5 200 80 0.50 20

6 210 90 1.00 10 represent a short-run cost function, the

0 minimum cost to produce a given output. MC =∆TC/∆Q 0 50 100 150 200 Q

Discrete vs. Continious Marginal Cost Production and Cost

C =9+ Q2, dC =2Q: dQ Cost function: shows relationship between MC MC opportunity cost of production and level of output. discr. cont. C Opportunity cost: reflects use of resources in one Q C ∆C dC ∆Q dQ activity while foregoing another; consist of 09 - 0 bc Explicit cost: payment to an individual that is 110 1 2 bc ∆C recorded in an accounting system. ∆Q Implicit costs: value of using a resource that is not 213 3 4 bc 318 5 6 explicitly paid out, is often difficult to measure, and dC not recorded in an accounting system. 425 7 8 dQ Economic profit is based on opportunity cost, not 5 34 9 10 Q 6 45 11 12 on accounting cost! Economic vs. Accounting Profit Production and Cost

Economists Accounting Avoidable vs. Sunk Costs View View Avoidable costs: Input costs the firm can recover or avoid paying should Economic it no longer wish to employ that input Profit Reflect the opportunity costs of resource use and Accounting should NOT be ignored! Profit Revenue ) Opportunity Q Implicit Sunk Cost: Costs ×

Costs Payment for an input that, once made, cannot be P ( Revenue recovered should the ﬁrm no longer wish to employ Explicit Explicit that input Costs Costs No opportunity cost, should be ignored for decision making purposes! ⇒ Historic cost is most times irrelevant for decisions; the relevant opportunity cost is the cost of replacement.

Average Cost Average Cost

Average Cost cost of an average unit of output. Total cost (TC) are the sum of total variable cost Average Fixed Cost (AFC): total ﬁxed cost per unit of (VC) and total ﬁxed cost (FC) output FC AFC = TC = VC + FC Q Average Variable Cost (AVC): total variable cost per Average Cost (ATC or simply AC): cost of an unit of output VC average unit of output AVC = Q TC VC FC Marginal Cost cost of an additional unit of AC ≡ = + Q Q Q output. ∆TC AC AVC AFC MC = |{z} |{z} |{z} ∆Q Cost with Decreasing MP Typical Shapes of the Cost Curves

L Q MP VC AVC FC AFC TC AC MC Average ﬁxed cost (AFC) always decrease with 00 - 0 -30 - 30 - - output: Since FC are constant, AFC must decline 1 60 60 10 0.17 30 0.50 40 0.67 0.17 as output increases 2 110 50 20 0.18 30 0.27 50 0.45 0.20 Average variable cost (AVC) can fall initially, but 3 150 40 30 0.20 30 0.20 60 0.40 0.25 ﬁnally increase 4 180 30 40 0.22 30 0.17 70 0.39 0.33 ⇒ Average total cost (AC) initially fall and then 5 200 20 50 0.25 30 0.15 80 0.40 0.50 increase (if MP is diminishing) 6 210 10 60 0.29 30 0.14 90 0.43 1.00 ⇒ U-shaped AC-curve

Typical Shapes of the Cost Curves Typical Shapes of the Cost Curves

. AC (for the production function Q =4L0 5) 5 Notice that ... MC 4 1 marginal cost (MC) is upward sloping 2 average variable cost (AVC) also is upward sloping ATC 3 3 average ﬁxed cost (AFC) is downward sloping 2 AVC because of the spreading eﬀect, and 4 the marginal cost curve (MC) intersects the 1 AFC average total cost curve (AC) from below, crossing it at its lowest point 0 0 2 4 6 8 1012141618 Q Marginal and Average Cost The Relation between Marginal & Average Cost

Proof that the marginal cost curve intersects the Intuition behind property 4: Example average total cost curve always from below, crossing it Imagine, you wrote already three quick tests and at its lowest point: AC = C(Q)/Q got an average of 70% Then you write a forth quick test (this is the C(Q) dC marginal quick test) and get 90%. Will your dAC d( ) Q − C = Q = dQ average increase or decrease? dQ dQ Q2 Assume you got only 50%, would your average of 1 dC C = − 70% have had increased or decreased? Q dQ Q 1 = (MC − AC) Q

The Relation between Typical Shapes of the Cost Curves Marginal & Average Cost

A necessary condition for a minimum of the AC curve is that dAC =0 dQ Therefore dAC 1 = (MC − AC) = 0 dQ Q will only be fullﬁlled for MC = AC! Source: Krugman/Wells Typical Shapes of the Cost Curves Typical Shapes of the Cost Curves

Does the MC-curve always slope upward? MC-curves often slope downward at very low production levels, and slope upward only at higher levels of production Initially, the MC-curve often slopes downward because ﬁrms employ too few workers to reap the beneﬁts of specialization of labor Once there are enough workers to permit specialization, however, diminishing returns set in

Source: Krugman/Wells

Typical Shapes of the Cost Curves Production and Cost

Summary: Relationship between MC and MP: Consider VC=wL. Then, marginal cost are given by Three Important Properties of Cost Curves dC d(wL) Marginal cost eventually rises with the quantity of MC = = output. dQ dQ The average-total-cost curve is usually U-shaped dL 1 = w = w (e.g. because of ﬁxed cost and ﬁnally decreasing dQ dQ dL returns to scale). w = The marginal-cost curve crosses the MP average-total-cost curve always at the minimum of average total cost. Example before: Since ∆L = 1, ∆VC = 10 = w L 10 . At, e.g., =5: MC= 20 = 0 5 Production and Cost

Relationship between AC and AP: VC wL w w Any questions? AC = = = = Q Q Q/L AP Thanks! w L 10 . Example before: = 10. At, e.g., = 5: AC = 40 = 0 4 Interpretation If ∆MP > 0 (< 0), then ∆MC < 0 (> 0) If ∆AP > 0 (< 0), then ∆AC < 0 (> 0)