a What is the dollar value of the total surplus producer sur

a. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output level Q₁ is being produced?

     How large is the dollar value of the consumer surplus at the output level Q₁?

b. What is the dollar value of the deadweight loss when output level Q₂ is being produced?

     What is the total surplus when output level Q₂ is being produced?

c. What is the dollar value of the deadweight loss when output level Q₃ is produced?

     What is the dollar value of the total surplus when output level Q₃ is produced?

Efficiency loss from underproduction Efficiency loss from overproduction , Q3 Quantity (bags) Quantity (bags)

Solution

Producer surplus (PS) = Area beteween supply curve & price

Consumer surplus (CS) = Area between demand curve & price

(a) Output Q1:

CS = (1/2) x $(70 - 25) x 15 = (1/2) x $45 x 15 = $337.5

PS = (1/2) x $(25 - 10) x 15 = (1/2) x $15 x 15 = 112.5

Total surplus = CS + PS = $(337.5 + 112.5) = $450

(b) Output Q2:

CS = (1/2) x $(70 - 40) x 10 = (1/2) x $30 x 10 = $150

PS = (1/2) x $(20 - 10) x 10 = (1/2) x $10 x 10 = $50

Total surplus = $(150 + 50) = $200

Deadweight loss, DWL = Reduction in total surplus = $(450 - 200) = $250

(c) Output Q3:

CS = (1/2) x $(70 - 4) x 22 = (1/2) x $66 x 22 = $726

PS = (1/2) x $(32 - 10) x 22 = (1/2) x $22 x 22 = $242

Total surplus = $(726 + 242) = $968

Deadweight loss (relative to case (a)) = $(968 - 450) = $518