and average products when Jabot chooses L* to minimize Cost of Qo, given fixed Ko. MP* and AP* are functions of w, r, and Qo. The Jabot company's production function is: Q(L, K) = L²K² %D a. Rewrite the equation of the long run total cost from Problem (4d). Derive the equations of long run average and marginal cost: LTC: wL* +vヒ* LAC: LTC リa LTC = _dra CAC: LTC Qr'aw LAC = 2r"a w ar! da 2,V2 w'lail こ b. Suppose K is fixed at Ko. Solve the production function for L to find the short run cost equations as functions of Q with parameters w, r, and Ko: LMc= ditz 2r LML= LMC = Stcz wL trk, wi CQ/ko) v.ko STC = (+rk. wQ/kotr Ko /Q %3D 1メ+ wQ Ko SAC = to Ko KFr.ko AVC = Ko Smc= d u SMC =
and average products when Jabot chooses L* to minimize Cost of Qo, given fixed Ko. MP* and AP* are functions of w, r, and Qo. The Jabot company's production function is: Q(L, K) = L²K² %D a. Rewrite the equation of the long run total cost from Problem (4d). Derive the equations of long run average and marginal cost: LTC: wL* +vヒ* LAC: LTC リa LTC = _dra CAC: LTC Qr'aw LAC = 2r"a w ar! da 2,V2 w'lail こ b. Suppose K is fixed at Ko. Solve the production function for L to find the short run cost equations as functions of Q with parameters w, r, and Ko: LMc= ditz 2r LML= LMC = Stcz wL trk, wi CQ/ko) v.ko STC = (+rk. wQ/kotr Ko /Q %3D 1メ+ wQ Ko SAC = to Ko KFr.ko AVC = Ko Smc= d u SMC =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:> Suppose that, in the short run, Jabot's input L is variable and input K is fixed at
> Also find the marginal and average products when Jabot chooses L* to minimize
6.
Jabot Company II: SR Cobb-Douglas Production
Ko. Find expressions for average cost, variable cost, and marginal cost.
oubo
ot bei
the total cost of Qo, given fixed Ko. MP,* and AP* are functions of w, r, and Qo.
> The Jabot company's production function is:
Q(L, K) = L½K½
a. Rewrite the equation of the long run total cost from Problem (4d). Derive the
equations of long run average and marginal cost:
LTC= WL* +r k*
LAC:
リa
arw
しtC
LTC =
LAC =
CAC- LTC ar'awリス@
Q
due ar Va w/la Q
LMC = dr
LML=
こ
b. Suppose K is fixed at Ko. Solve the production function for L to find the short run
cost equations as functions of Q with parameters w, r, and Ko:
Stcz wL trk,
wiCQ%/Ko) r.ko
STC =
w Q/katr Ko /Q
wQ +r Ko
to Ko
SAC =
wQ
Ko
Ko
AVC =
AVC:
SMC =
Ko
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