4. Solve the following: A. The demand function for a product is given by p = 0.0
ID: 2891540 • Letter: 4
Question
4. Solve the following:
A.
The demand function for a product is given by p = 0.03x^2 0.7x +10 where p is the unit
price in dollars and x is the weekly demand for the product each week, measured in thousands of units. Find the consumer’s surplus if the quantity demanded is 4 thousand units.
A. 21.4815
B. 6.67
C. 12.4928
D. 13.9049
E. None of the above.
B.
The supply function for a product is given by p=0.05x^2 + 0.02x +9 where p is the unit price in dollars and x is the number available for sale each week, measured in thousands of units. The demand function for the product is given by p=-0.02x^2 -0.4x +16, where x is the number of units demanded in thousands, and p is the unit price in dollars. Find the equilibrium quantity, equilibrium price, and producer's surplus.
A. 82.3375
B. 6.594
C. 12.4928
D. 13.9049
Explanation / Answer
4)
A)
for x =4
p = 0.03*42 0.7*4 +10
p = 6.72
consumer surplus =[0 to 4]( 0.03x2 0.7x +10 -6.72) dx
consumer surplus =[0 to 4]( 0.03x2 0.7x +3.28) dx
consumer surplus =[0 to 4]( 0.01x3 0.35x2 +3.28x)
consumer surplus =( 0.01*43 0.35*42 +3.28*4) -( 0.01*03 0.35*02 +3.28*0)
consumer surplus =( 6.88) -0
consumer surplus =6.88
E. None of the above.
=================================================
B)
supply function p=0.05x2 + 0.02x +9 ,demand function p=-0.02x2 -0.4x +16
for equilibrium , supply =demand
=>0.05x2 + 0.02x +9=-0.02x2 -0.4x +16
=>0.07x2 + 0.42x -7=0
=>x2 + 6x -100=0
=>x=7.44031
eqilibrium quantity =7.44031 thousand units
equilibrium price =11.9167 dollars
producer's surplus=[0 to 7.44031][11.9167-(0.05x2 + 0.02x +9 )]dx
producer's surplus=[0 to 7.44031][2.9167-0.05x2 - 0.02x]dx
producer's surplus=[0 to 7.44031][2.9167x-(0.05/3)x3 - 0.01x2]
producer's surplus=[2.9167*7.44031 -(0.05/3)7.440313 - 0.01*7.440312] -0
producer's surplus=14.2829
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.