Question

Suppose that the demand curve for wheat is

and the supply curve is
The government provides producers with a specific subsidy of s=$2 per unit.
How do the equilibrium price and quantity change?
The equilibrium price
decimal places)
by $ and the equilibrium quantity
aº-200-10p
Q³ = 10p
by $units. (Enter numeric responses using real numbers rounded to beco

Answer 1

Answer: Derive equilibrium before subsidy:

At equilibrium: Qd = Qs

100 – 10P = 10P

100 = 10P + 10P

100 = 20P

P = 5

Equilibrium price = 5

Substitute in the demand function to derive equilibrium quantity:

Q = 100 – 10P

Q = 100 – 10(5) = 100 – 50 = 50

Q = 50

Equilibrium quantity = 50

Consumer surplus = ½ x 50 x (10 – 5) = 125

Producer surplus = ½ x 50 x (50 – 0) = 125

Derive new equilibrium after subsidy:

First calculate the new Qs function:

Qs = 10P

Qs = 10 (P + 1)

Qs = 10P + 1

Set: Qd = Qs

100 – 10P = 10P + 1

100 – 1 = 10P + 10P

99 = 20P

P = 4.95

New equilibrium price = 4.95

Substitute in either the demand or supply function to derive the equilibrium quantity:

Qs = 10P + 1

Qs = 10(4.95) + 1

Q = 49.5 + 1 = 50.5

New equilibrium quantity = 50.5

The effects of the subsidy are as follows:

Consumer surplus gain = ½

×

× (5 – 4.95)

×

× (50.5 – 50) + 50

×

× (5 – 4.95) = 0.025 + 2.5 = 2.525

Producer surplus gain = ½

×

× (5.95 – 5)

×

× (50.5 – 50) + 50

×

× (5.95 – 5) = 0.2375 + 47.5 = 47.7375

Government subsidy cost = 50.5

×

× 1 = 50.5

Welfare = Total Benefit – Total Cost

Total benefit = CS + PS = 2.525 + 47.7375 = 50.265

Total Cost = 50.5

Welfare = 50.265 – 50.5 = -0.2375

Deadweight Loss = -0.2375

i know it makes no sense but this is what i got.