Question

Suppose that the demand for broccoli is given by:

Q=1000-5P

where Q is quantity per year measured in hundreds of bushels and P is the price in dollars per hundred bushels. The long-run supply curve for broccoli is given by:

Q=4P=80

A. Show that the equilibrium quantity here is Q= 400. At this output, what is the equilibrium price? How much in total is spent on broccoli? What is consumer surplus at this equilibrium? What is producer surplus at this equilibrium?

B. How much in total consumer and producer surplus would be lost if Q= 300 instead of Q= 400?

C. Show how the allocation between suppliers and demanders of the loss of total consumer and producer surplus described in part (b) depends on the price at which broccoli is sold. How would the loss be shared if P= 140? How about if P= 95?

D. What would be the total loss of consumer and producer surplus if Q= 450 rather than Q= 400? Show that the size of this total loss also is independent of the price at which the broccoli is sold.

Answer 1

A) Set QD=QS

1000-5P=4P-80

1000+80=4P+5P

1080=9P

P=1080/9 = 120

Q=1000-5(120) = 1000-600=400

The Y intercepts for Demand and supply is :When QD=0, P will be 1000/5 = 200

When QS=0,P will be 80/4 = 20

CS=0.5*400*(200-120) = 16000

PS = 0.5*400*(120-20) = 20000

B) When Q=300

CS=0.5*300*(200-120) = 12000

CS decreases by 16000-12000 = 4000

PS=0.5*300*(200-20) = 15000

PS decreases by 20000-15000=5000

C) When P=140,

QD=1000-5(140) = 300

QS=4(140)-80 = 480

CS=0.5*300*(200-140) = 9000

CS decreases by 16000-9000 = 7000

PS = 0.5*480*(140-20) = 28800

PS increases by 28800-20000 = 8800

The increase in PS is greater than CS so total welfare will increase.

When P=95

QD=1000-5(95) = 525

QS=4(95)-80 = 300

CS=0.5*525*(200-95) = 27562.5

CS increase by 27562.5-16000 = 11562.5

PS=0.5*300*(95-20) = 11250

PS decrease by 20000-11250 = 8750

Total welfare will increase

D) When Q=450

CS=0.5*400*(200-120) = 18000

CS increases by 18000-16000=2000

PS=0.5*450*(120-20) = 22500

PS increases by 22500-20000 = 2500

So total welfare will increase as both CS and PS increases and it is independent of the prices.