Question

The market demand function for corn is

              Q^d = 28 - 2P The market supply function is

                Q^s = 5P -4

both measured in billions of bushels per year. What would be the welfare effects of a policy that put a cap of $4.00 per bushel on the price farmers can charge for corn? (Assume that corn is purchased by the consumers who place the highest value on it.)

Instructions: Round quantities to one decimal place. Round prices and surpluses to two decimal places.

	Amount ($)
New level of consumer surplus	billion
New level of producer surplus	billion
New level of aggregate surplus	billion
Deadweight loss	billion

Answer 1

Qd= 28-2P

X intercept ( keeping P=0)= 28

Y intercept ( keeping Q=0) = 14

Qs= 5P-4

X intercept (keeping P=0) = -4

Y intercept (Keeping Q=0)= 4/5

At initial Equilibrium Qd= Qs

28-2P=5P-4

32= 7P

P*= 32/7

Q*= 28-2P= 132/7

In the diagram we have derived the value of point F as follow: At P=4 the Qs= 5P-4= 16 , Quantity=16

And at quantity=16 , Qd= 28-2P

16= 28-2P so, P= 6

1)Consumer surplus= Green region

Consumer surplus= Area of triangle ABF + Area of rectangle FBDK

•Area of triangle ABF= (1/2)*base*height

base= 16

height= 14-6= 8

Area of triangle ABF=(1/2)*16*8= 64

•Area of rectangle FBDK= Length*breadth

Length= 16

Breadth= 6-4= 2

Area of rectangle FBDK= 16*2= 32

• Consumer surplus= 64+32= 96

2) Producer surplus= Yellow region

Producer surplus= Area of triangle KDE

Producer surplus= (1/2)*base*height

Base= 16

Height= [4-(4/5) ] = 16/5

•Producer surplus= (1/2) *16* (16/5) = 128/5

3) Aggregate surplus= Consumer surplus+ Producer surplus

Aggregate surplus= 96+(128/5) = 121.6

4) Dead weight loss= Blue region

Dead weight loss= Area of triangle BCD

Dead weight loss= (1/2)*base*height

base= 6-4= 2

Height= [ (132/7)-16 ] = 2.85

Dead weight loss= (1/2)* 2* 2.85 = 2.85