Exercises of Managerial Economic

Question

Komalavalli · Accepted Answer

a)
Profit maximising condition MR = MC
TR = P*Q
TR = 55Q – 2Q2
TR
MR = ∂TR/∂Q
MR = 55-4Q 
TC = 100 -5Q+Q2
MC = 2Q – 5
MR =MC
55-4Q = 2Q -5
6Q =60
Q = 60/6 =10
Q = 10
P = 55-20
P = 35
Profit = TR –TC
Profit = 350 -150 = 200
Profit = $200
Consumer surplus = ½( 55-35)*10 = 100
Consumer surplus is $100
b)
perfect competition
MC =P
MC = 2Q – 5
P = 55-2Q
55-2Q = 2Q -5
4Q = 60
Q = 15
P = 55 -30
P = 25
Profit = 25*15 – 100+5*15-152
 	= 375 – 100 + 75 - 225
Profit = 125
Consumer surplus = ½*(27.5-25)*15
Consumer surplus = $19
Dead weight loss = ½(35-25)*(10-15)
Dead weight loss = ½(10)*(5)
Dead weight loss = 25
c)
price ceiling P = 27
27 = 55 -2Q
2Q = 28
Q = 14
Consumer surplus =1/2(55-27)*14
Consumer surplus = 196
Dead weight loss = ½(35-27)*(14-10)
Dead weight loss = ½(8)*(4)
Dead weight loss = 16
Price ceiling increase the social welfare , because it increases the consumer surplus from 100 to 196
	
a)
MC = 4
Market A
QA = 40 – 2PA
2PA = 40 –Q
PA = 20 -0.5Q
TR = 20Q – 0.5Q2
MR = ∂TR/∂Q = 20 – Q
MR =MC
20 – Q = 14
QA = 6
PA = 20 -3
PA = 17
Market B
QB =90– 3PB
PB = 30 -0.3 QB
TRB = 30Q – 0.3Q2
MR = 30 -0.6Q
MR = MC
30 -0.6Q = 14
0.6Q = 30-14
0.6Q = 16
Q = 16/0.6
QB = 27 appx.
PB = 30-0.3*27
PB  =22
Price elasticity calculation for Market A
If PA increases from 17 to 18
QA = 40 – 2PA
QA = 40 – 2*18
QA =4
Percentage Change in quantity demand in market A = 6-4/6 =0.33*100 =33%
Percentage Change in price in market A = 17-18/17 =0.05*100 =5%
Price elasticity demand in market A = -33/5 =-6.6%
Inelastic demand for product in Market A
Price elasticity calculation for Market B
If PB increases from 22 to 23
QB =90– 3PB
QB =90– 3*23
QB = 21
QB =21
Percentage Change in quantity demand in market A = 27-21/27 =0.22*100 =22
Percentage Change in price in market A = 22-23/22 =0.04*100 =-4
Price elasticity demand in market A = -22/4 =-5.5%
Inelastic demand for product in Market B
Profit in Market A = 6*17 -14*6 = 18
Profit in Market B = 27*22 – 14*27 = 216
Total profit = 18+216 = 234
b)
Q = QA+QB
Q = 130 – 5P
5P = 130-Q
P = 26 – 0.2Q
TR = 26Q -0.2Q2
MR = 26 -0.4Q
MR = MC
26 – 0.4Q =14
26-14 = 0.4Q
12 = 0.4Q
Q = 12/0.4
Q = 30
P = 26 – 0.2Q
P = 26 – 0.

Exercises of Managerial Economic

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