Question 1: Consider a production function with two inputs, capital (k) and labor (1), given by f(k,1) = kP + Lº where p < 1,p # 0. Price per unit of each input is given by r for capital and w for labor. a. Compute the total cost function C(r,w,q) b. Now suppose p = Rewrite the total cost function C(r,w, q) for this case. Suppose inverse demand for output is given by p = 2000 -; 25 Consider the following different industry structures, but each firm in the industry has the same cost curve as in part (b) above. c. Suppose there is only one firm in the industry (monopoly). Find the profit-maximizing output, price, and profit. d. Suppose there are two firms in the industry (duopoly) competing as Cournot oligopolists. Find the profit-maximizing output, price, and profit for each firm. e. Suppose there are four firms in the industry competing as Cournot oligopolists. Find the profit-maximizing output, price, and profit for each firm. f. Compare industry price and total industry profit in each of the above three cases. Only PART C Mono 2000 - 1851-85 ろ onc %3D 2 Symmunir cot stuucturi 25 1 Propit is monimized when MC- MR P= 1425·92 2 Sinu (niwg) and firm's nerpers is : 2173- 91 - 0•04359, Prefit =pg-CC) =(1925 •926 X185)-85 1851· w ²+ n² Corng 9, =% in equation o /851852 6. MC= day Given p= 2000- 2カ。 Pard D > 2173.91 3 - 0•043591 9 Finm's pefit maseimization i T,=Pq, - c(q) 1004 3501 217391 ニ Total revenie > Pq =2000-9" 2000- 25 ス5 25 = 2173.91 2 MR TR - 2000 ー29 JT= 20009,2-4% 2. /•0435 25 25 ス5 2 20 83 · 333 At Equilibrium MC =MR 2000g, 234-4,9z 50 2000 - 29 25 25 P= 2000 (2083.39 + 2083.33 FOC: d7 - o Ą 2+ W2 25 For numvrical Answer , Lets cansidor W=r= ) Lets ccangidor W= r=1 ノ pa 1833:33 2083 -3 > 2000 - 46g 50 2 CH4d JI, =TT,- L1833:33X 2083·33 2 25 = 1649306 う g - 2000 – Y2, 25 > MG = 9 P:10fit is monimiscd ohu MC-MR - 2000 Hene , maikt price= 1893 33 a firm ()Prefit fer ecch farm - 1 649306 so 2000 X50 46 2 ラ % 50 46 X25 each 2083 33 %3D 25 > q + 24 : 2000 , q > シ Gu'ves ス0C0x 25 = 1851.85 -> 2173-91 - 0• 43592 フー 3.
Question 1: Consider a production function with two inputs, capital (k) and labor (1), given by f(k,1) = kP + Lº where p < 1,p # 0. Price per unit of each input is given by r for capital and w for labor. a. Compute the total cost function C(r,w,q) b. Now suppose p = Rewrite the total cost function C(r,w, q) for this case. Suppose inverse demand for output is given by p = 2000 -; 25 Consider the following different industry structures, but each firm in the industry has the same cost curve as in part (b) above. c. Suppose there is only one firm in the industry (monopoly). Find the profit-maximizing output, price, and profit. d. Suppose there are two firms in the industry (duopoly) competing as Cournot oligopolists. Find the profit-maximizing output, price, and profit for each firm. e. Suppose there are four firms in the industry competing as Cournot oligopolists. Find the profit-maximizing output, price, and profit for each firm. f. Compare industry price and total industry profit in each of the above three cases. Only PART C Mono 2000 - 1851-85 ろ onc %3D 2 Symmunir cot stuucturi 25 1 Propit is monimized when MC- MR P= 1425·92 2 Sinu (niwg) and firm's nerpers is : 2173- 91 - 0•04359, Prefit =pg-CC) =(1925 •926 X185)-85 1851· w ²+ n² Corng 9, =% in equation o /851852 6. MC= day Given p= 2000- 2カ。 Pard D > 2173.91 3 - 0•043591 9 Finm's pefit maseimization i T,=Pq, - c(q) 1004 3501 217391 ニ Total revenie > Pq =2000-9" 2000- 25 ス5 25 = 2173.91 2 MR TR - 2000 ー29 JT= 20009,2-4% 2. /•0435 25 25 ス5 2 20 83 · 333 At Equilibrium MC =MR 2000g, 234-4,9z 50 2000 - 29 25 25 P= 2000 (2083.39 + 2083.33 FOC: d7 - o Ą 2+ W2 25 For numvrical Answer , Lets cansidor W=r= ) Lets ccangidor W= r=1 ノ pa 1833:33 2083 -3 > 2000 - 46g 50 2 CH4d JI, =TT,- L1833:33X 2083·33 2 25 = 1649306 う g - 2000 – Y2, 25 > MG = 9 P:10fit is monimiscd ohu MC-MR - 2000 Hene , maikt price= 1893 33 a firm ()Prefit fer ecch farm - 1 649306 so 2000 X50 46 2 ラ % 50 46 X25 each 2083 33 %3D 25 > q + 24 : 2000 , q > シ Gu'ves ス0C0x 25 = 1851.85 -> 2173-91 - 0• 43592 フー 3.
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I need your help with the question attached. I am also adding solutions of Part C and D, which indicate the values for one firm, two firms. What I need is the values for 4 firms. Please consider the solutions and provide the answers of part E and F.
Transcribed Image Text:Question 1:
Consider a production function with two inputs, capital (k) and labor (1), given by
f(k,1) = kP + Lº
where p < 1,p # 0. Price per unit of each input is given by r for capital and w for labor.
a. Compute the total cost function C(r,w,q)
b. Now suppose p = Rewrite the total cost function C(r,w, q) for this case.
Suppose inverse demand for output is given by p = 2000 -;
25
Consider the following different industry structures, but each firm in the industry has the same
cost curve as in part (b) above.
c. Suppose there is only one firm in the industry (monopoly). Find the profit-maximizing
output, price, and profit.
d. Suppose there are two firms in the industry (duopoly) competing as Cournot
oligopolists. Find the profit-maximizing output, price, and profit for each firm.
e. Suppose there are four firms in the industry competing as Cournot oligopolists. Find the
profit-maximizing output, price, and profit for each firm.
f. Compare industry price and total industry profit in each of the above three cases.
Transcribed Image Text:Only
PART C
Mono
2000
- 1851-85
ろ
onc
%3D
2
Symmunir cot
stuucturi
25
1
Propit is monimized when MC- MR
P= 1425·92
2
Sinu (niwg)
and firm's nerpers is : 2173- 91 - 0•04359,
Prefit =pg-CC) =(1925 •926 X185)-85
1851·
w ²+ n²
Corng 9, =% in equation o
/851852
6.
MC=
day
Given p= 2000-
2カ。
Pard D
> 2173.91 3 - 0•043591
9
Finm's pefit maseimization i T,=Pq, - c(q)
1004 3501
217391
ニ
Total revenie > Pq =2000-9"
2000-
25
ス5
25
= 2173.91
2
MR
TR - 2000 ー29
JT= 20009,2-4%
2.
/•0435
25
25
ス5
2
20 83 · 333
At Equilibrium MC =MR
2000g,
234-4,9z
50
2000 - 29
25
25
P= 2000
(2083.39 + 2083.33
FOC: d7 - o
Ą 2+ W2
25
For numvrical Answer , Lets cansidor W=r= )
Lets ccangidor W= r=1
ノ
pa 1833:33
2083 -3
> 2000 - 46g
50
2
CH4d JI, =TT,- L1833:33X 2083·33
2
25
= 1649306
う g
- 2000 – Y2,
25
> MG = 9
P:10fit is monimiscd ohu MC-MR
- 2000
Hene , maikt price= 1893 33
a firm
()Prefit fer ecch farm - 1 649306
so
2000 X50
46
2
ラ %
50
46 X25
each
2083 33
%3D
25
> q + 24 : 2000 , q >
シ
Gu'ves
ス0C0x 25
= 1851.85
->
2173-91 - 0• 43592
フー
3.
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