1. Ps = .02 Q s => Q s = Ps/.02 Pd = 3 - .01 Q d => Q d = (3-Pd)/.01 At equilibrium,
Q s = Q d
P*/.02 = (3-P*)/.01
P*
= 2.00
Putting P s & Pd as $2.20, Q s = 110 million & Q d = 80 million That means consumer will buy 80 million and the rest 30 million will be purchased by Govt @ $2.20. Hence, cost to Govt = $ (30 * 2.20) million million = $ 66 million.
(A)
Now Govt will not buy anything, i.e. Q d = 110 million
Pd = $ 1.90
Hence subsidy / bushel = $ (2.20 – 1.90 ) = $ 0.30 Hence cost cost to Govt = $ ( 110 * 0.30) million = $ 33 million (B) And consumers will buy 110 million @ $ 1.90
(B)
The 1st policy is more expensive for Govt.
(C )
2. Xd = 5Py – 2Px +1400 x = K.L0.5 => L = x2 / K2 => L = x2 / 25
( as K = no. of sewing machines = 5)
Cost function => C = r.K + w.L w.L + FC + m.x = 20 + 125. (x2 / 25) + 300 + (15+4+1).x = 5.x2 + 20.x + 320 At profit max. condition, P = MC = dc/dx = 10.x + 20 => x = (P-20)/10 (P -20)/10 Hence, Xs = N.x = 100. { (P-20)/10 } => Xs = 10.P – 200 At equilibrium,
Xs = Xd
10.P – 200 = 5.88 – 2.Px +1400 Px = 170
Hence the profit max o/p = x = (170-20)/10 = 15
(Py = 88, given) (A) (B)
From the eqn. of cost function , TVC = 5.x 2 + 20.x Hence ,
AVC = 5.x + 20 = 5.15+20 = 95
(C )
C = 5.x2 + 20.x + 320 AC = 5.x +20 + 320 / x = 116.33
(D)
Profit in short run / day = (P * - AC ) * x = ( 170 – 116 1/3 ) * 15 = 810 – 5 = 805 L = x2 / 25 = 225 /25 = 9
(E ) (F)
At long term equilibrium, P = AC min. For AC min. ,
d(AC)/ dx = 0
d ( 5.x + 20 + 320/x ) /dx = 0
5 – 320/x2 x
=0 =8
P = AC min. = (5*8 + 20 + 320/8) = 100 Xd = 5*88 – 2*100 + 1400 = 1640 Xd =N. x => N = 1640 / 8 = 205 Before coming to new equilibrium, 105 firms will join.
(G)
Long term equilibrium o/p of the industry = 1640
(H)
[Contribution /unit]Cappers = c = ( P – AVC ) = 100 – (5.x+20) = 100 – 60 = 40
3. New cost func.
C = 5.x2 + 20.x + 320 + 5.x
At long term equilibrium, P = AC min.
(i)
( as sales tax imposed on each cap)
For AC min. ,
d(AC)/ dx = 0
d ( 5.x + 25 + 320/x ) /dx = 0 5 – 320/x2 =0
x
=8
P = AC min. = (5*8 + 25 + 320/8) = 105 Xd = 5*82 – 2*105 + 1400 = 1600
( As Py is reduced by 6 )
Xd =N. x => N = 1600 / 8 = 200 Before coming to new equilibrium, 5 firms will exit.
(A)
o/p / firm at long term equilibrium = x = 8
(B)
4. Xd = 2Py – 2Px +18200 x = 5.L0.5 => L = x2 / 25 Cost function => C = r.K + w.L + FC + m.x = 0 + 125. (x2 / 25) + (5400/30) + (9+8+3).x = 5.x2 + 20.x + 180 At profit max. condition, P = MC = dc/dx = 10.x + 20 => x = (P-20)/10
(A)
Hence, Xs = N.x = 1000. { (P-20)/10 } => X s = 100.P – 2000
(B)
At equilibrium,
Xs = Xd
100.P – 2000 = 2.100 – 2.Px +18200 Px = 200
(Py = 100, given) (C )
Hence the profit max o/p = x = (200-20)/10 = 18 From the eqn. of cost function , TVC = 5.x 2 + 20.x Hence ,
AVC = 5.x + 20 = 5.18+20 = 110 C = 5.x2 + 20.x + 180 AC = 5.x +20 + 180 / x = 120
Profit in short run = (P * - AC ) = ( 200 – 120 ) = 80
(D)
The market price will not be unchanged.
(E )
As there is profit, more firm will be interested to enter and as soon as more firms will enter, the equilibrium will be changed resulting change in the price as well as profit margin.
(F)
At long term equilibrium, P = AC min. For AC min. ,
d(AC)/ dx = 0
d ( 5.x + 20 + 180/x ) /dx = 0
5 – 180/x2
=0
x
=6
P = AC min. = (5*6 + 20 + 180/6) = 80 Xd = 2*100 – 2*80 + 18200 = 18240 Xd =N. x => N = 18240 / 6 = 3040
5. At equilibrium,
(G)
Xs = Xd
3040 {(Px – 20)/10} = 2.159 – 2.Px +19000
306 Px
= 25398
Px
= 83
(Py = 159, given) (A)
Δ x = ( x 1 – x0 ) / x0
= [ (83-20)10 – (80-20)/10 ] / [ (80-20)/10 ] * 100 %
(as x = (P-20)/10)
= 5 % increase
(B)
Cost function => C = r.K + w.L + FC + m.x + Sales Tax. x = 0 + 125. (x2 / 25) + (5400/30) + (9+8+3).x + 2.x = 5.x2 + 22.x + 180 At profit max. condition, P = MC = dc/dx = 10.x + 22 => x = (P-22)/10 At equilibrium,
Xs = Xd
3040 {(Px – 22)/10} = 2.159 – 2.Px +19000
(Py = 159, given)
306 Px
= 26006
Px
= 84.98
(C )
So, the firms will get price as (84.98-2) i.e. 82.98
(D)
