(Advanced Analysis) Given the following diagrams : Q 1 = 16 bags. Q 2 = 11 bags.
ID: 1227407 • Letter: #
Question
(Advanced Analysis) Given the following diagrams: Q1 = 16 bags. Q2 = 11 bags. Q3 = 23 bags. The market equilibrium price point b is $37 per bag.
The price at point a is $85 and the price at point c is $5 per bag. The price at point d is $52 and the price at point e is $27 per bag. The price at point f is $51 and the price at point g is $16 per bag.
Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.
a. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output Q1 level is being produced?
$
How large is the dollar value of the consumer surplus at that output Q1 level?
Instructions: Round your answer to one decimal place.
$
b. What is the dollar value of the deadweight loss when output level Q2 is being produced?
Instructions: Round your answer to one decimal place.
$
What is the total surplus when output level Q2 is being produced?
Instructions: Round your answer to one decimal place.
$
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?
Explanation / Answer
(a) When output = Q1, Total surplus = Area of triangle abc = (1/2) x ac x Q1
= (1/2) x $(85 - 5) x 16 = (1/2) x $80 x 16
= $640.0
Consumer surplus (CS) = Area between demand curve & price
= (1/2) x $(85 - 37) x 16 = (1/2) x $48 x 16
= $384.0
(b) When output = Q2, Deadweight loss (DWL) = Area of triangle bde = (1/2) x de x Q2
= (1/2) x $(52 - 27) x 11 = (1/2) x $25 x 11
= $137.5
Total surplus at Q2 = CS + Producer surplus, PS (area between supply curve & price)
= [(1/2) x $(85 - 52) x 11] + [(1/2) x $(27 - 5) x 11] = [(1/2) x $33 x 11] + [(1/2) x $22 x 11]
= $(181.5 + 121)
= $302.5
(c) When output = Q3, DWL = Area of triangle bfg = (1/2) x fg x Q3
= (1/2) x $(51 - 16) x 23 = (1/2) x $35 x 23
= $402.5
Total surplus = CS + PS
= [(1/2) x $(85 - 16) x 23] + [(1/2) x $(51 - 5) x 23] = [(1/2) x $69 x 23] + [(1/2) x $46 x 23]
= $(793.5 + 529)
= $1,322.5
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