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# AP ECON 2300 F2012 Session 11.doc

14 Pages
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School
Department
Economics
Course
ECON 2300
Professor
Wai Ming Ho
Semester
Fall

Description
AP ECON 2300 F2012 Session 11 Instructor: Dr. David K. Lee Department of Economics York University Topic: Cost and Supply Curve Reading: Chapters 21 and 22 Announcement: Review materials for the final exam will be posted by the next week. Ch 21: Cost: Fixed, Variable & Total Cost Functions • F is the total cost to a firm of its short-run fixed inputs. F, the firm’s fixed cost, does not vary with the firm’s output level. • cv(y) is the total cost to a firm of its variable inputs when producing y output units. c (y) vs the firm’s variable cost function. • cv(y) depends upon the levels of the fixed inputs. • c(y) is the total cost of all inputs, fixed and variable, when producing y output units. c(y) is the firm’s total cost function; c( y) = F + c v y). \$ c(y) c (y) v F F y © 2010 W. W. Norton & Company, Inc. 10 Av. Fixed, Av. Variable & Av. Total Cost Curves • The firm’s total cost function is c( y) = F + c v y). • For y > 0, the firm’s average total cost function is Page 1 of 14 F cv(y) AC(y)= + y y = AFC(y)+AVC(y). • What does an average fixed cost curve look like? F AFC ( y) = y • AFC(y) is a rectangular hyperbola so its graph looks like ... • In a short-run with a fixed amount of at least one input, the Law of Diminishing (Marginal) Returns must apply, causing the firm’s average variable cost of production to increase eventually. • And ATC(y) = AFC(y) + AVC(y) \$/output unit Since AFC(y) → 0 as y →∞ , ATC(y) → AVC(y) as y →∞. And since short -run AVC(y) must eventually increase, ATC(y) must eventually increase in a short -run. ATC(y) AVC(y) AFC(y) 0 y © 2010 W. W. Norton & Company, Inc. 21 Marginal Cost Function • Marginal cost is the rate-of-change of variable production cost as the output level changes. That is, ∂ cv( y) MC ( y) = ∂ y . • The firm’s total cost function is c( y) = F + cv( y) • and the fixed cost F does not change with the output level y, so ∂ cv( y) ∂ c( y) MC ( y) = = . ∂ y ∂ y • MC is the slope of both the variable cost and the total cost functions. • Since MC(y) is the derivative of cv(y), v (y) must be the integral of MC(y). That is, ∂ cv( y) y MC ( y) = ⇒ c v y) = ∫MC (z)dz . ∂ y 0 Page 2 of 14 Marginal and Variable Cost Functions \$/output unit MC(y) Area is the variable cost of making y’ units 0 y © 2010 W. W. Norton & Company, Inc. 25 • How is marginal cost related to average variable cost? cv(y) ∂ AVC (y) y × MC ( y) −1× c (v) AVC (y) = , = 2 . y ∂ y y > > > ∂ AVC ( y )= 0 y × MC ( y ) = c ( y ). MC ( y ) =c v y )= AVC ( y ). ∂ y v y < < < > MC ( y ) = AVC ( y ). < \$/output unit The short-run MC curve intersects the short-run AVC curve from MC(y) below at the AVC curve’s minimum. AVC(y) © 2010 W. W. Norton & Company, Inc. y 35 Page 3 of 14 c( y) ∂ ATC ( y) y × MC ( y) −1× c( y) ATC ( y) = y , = 2 . ∂ y y > ∂ ATC ( y = 0 > > ∂ y y × MC ( y ) = c ( y ).MC ( y ) = c ( y= ATC ( y ). < y < < \$/output unit as MC(y) ATC(y) y © 2010 W. W. Norton & Company, Inc. 39 • The short-run MC curve intersects the short-run AVC curve from below at the AVC curve’s minimum. • And, similarly, the short-run MC curve intersects the short-run ATC curve from below at the ATC curve’s minimum. Page 4 of14 \$/output unit MC(y) ATC(y) AVC(y) y © 2010 W. W. Norton & Company, Inc. 41 Short-Run & Long-Run Total Cost Curves • A firm has a different short-run total cost curve for each possible short-run circumstance. • Suppose the firm can be in one of just three short-runs; x2= x2’ or x = x ’’ x ’ < x ’’ < x ’’’. 2 2 2 2 2 or x2= x2’’’. \$ c sy;x ′2 F′ = w x 2 2 F′′ = w x 2 2 A larger amount of the fixed c sy;x ′2) input increases the firm’s fixed cost. F′′ F′ © 2010 W. W. Norton & Company, Inc. y 45 Page 5 of14 • MP i1 the marginal physical productivity of the variable input 1, so one extra unit of input 1 gives MP 1 extra output units. • Therefore, the extra amount of input 1 needed for 1 extra output unit is 1 / MP 1units of input 1. • Each unit of input 1 costs w1, so the firm’s extra cost from producing one extra unit of output is w1 MC = . is the slope of the firm’s total cost curve. MP 1 • If input 2 is a complement to input 1 then MP 1s higher for higher x2. Hence, MC is lower for higher x2. • That is, a short-run total cost curve starts higher and has a lower slope if2x is larger. • The firm has three short-run total cost curves. • In the long-run the firm is free to choose amongst these three since it is free to selec2 x equal to any of x 2, 2 ’’, o2 x ’’’. • How does the firm make this choice? \$ For 0 ≤ y ≤ y′, choose x 2 = x ′2 c (y;x ′) s 2 For y ′ ≤ y ≤ y′′, choose x 2 = x ′2. For y ′′ < y, choose x 2 = x ′2′ . c sy;x ′′2 c (y;x ′′′ ) s 2 c(y), the F′′′ firm’s long - run total F′′ F′ cost curve. © 2010 W. W. Norton & Company, Inc. y′′ y 61 • The firm’s long-run total cost curve consists of the lowest parts of the short-run total cost curves. The long-run total cost curve is the lower envelope of the short-run total cost curves. • If input 2 is available in continuous amounts then there is an infinity of short-run total cost curves but the long-run total cost curve is still the lower envelope of all of the short-run total cost curves. • For any output level y, the long-run total cost curve always gives the lowest possible total production cost. • Therefore, the long-run av. total cost curve must always give the lowest possible av. total production cost. • The long-run av. total cost curve must be the lower envelope of all of the firm’s short-run av. total cost curves. • The firm’s long-run average total cost curve is the lower envelope of the short-run average total cost curves ... Q: Is the long-run marginal cost curve the lower envelope of the firm’s short-run marginal cost curves? A: No. Page 6 of14 \$/output unit MC (y;x ′) MC (y;x ′′) s 2 s 2 AC (y;x ′′′ ) s 2 AC (y;x ′) s 2 AC (s;x ′′2
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