6) The supply and demand equations of the product are Ps=(400x)/(2000+x) and Pd=

Question

6) The supply and demand equations of the product are Ps=(400x)/(2000+x) and Pd=(1000)/(1+0.002x) Provide integrals for the consumer and 6. product surplus

7) VERY DIFFICULT: Do the integrals and find the surface are in problem 5. Requires methods we will learn for exam 2, including more challenging cases.

8) Do the integrals and find the two surpluses in problem 6.

9) Find the average value of the y=sinx between x=0 and x=pi/2

10) Back to the surface R. Submerge the surface in water. Use that x is in feet. The bottom of R(y=0) is 20 feet below the surface of the water. The density of the water is such that the weight is 62.5 pounds per cubic foot. Provide an integral for the hydrostatic force of R.

Explanation / Answer

6)Ps=(400x)/(2000+x) and Pd=(1000)/(1+0.002x)

(400x)/(2000+x) =(1000)/(1+0.002x)

(400x)(1+0.002x) =(2000+x)(1000)

400x +0.08x2=2000000+1000x

0.08x2-600x-2000000=0

x=[600+((-600)2-4*0.08*(-2000000))]/(2*0.08)

x=10000

equilbium quantity =x =10000

P=(400*10000)/(2000+10000)

P=1000/3

equilbium price =P=1000/3

consumer surplus =[0 to x](Pd -P) dx

consumer surplus =[0 to 10000]((1000)/(1+0.002x)   -1000/3 ) dx

producer surplus =[0 to x](P -Ps) dx

producer surplus =[0 to 10000]((1000/3) -(400x)/(2000+x) ) dx

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.