Assume the following values for the diagrams below: Q1 = 12 bags. Q2 = 7 bags. Q3 = 19 bags. The market equilibrium price is $34 per bag. The price at point a is $70 per bag. The price at point c is $10 per bag. The price at point d is $49 per bag. The price at point e is $24 per bag. The price at point f is $53 per bag. The price at point g is $18 per bag. Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.

Instructions: Round your answers to two decimal places
the dollar value of the total surplus (= producer surplus + consumer surplus) when the allocatively efficient output level is produced($ 360)
the dollar value of the consumer surplus at that output level($ 216)
the dollar value of the deadweight loss when output level Q2 is produced($ 62.5)
the dollar value of the deadweight loss when output level Q3 is produced($ 122.5)

a.
What is the total surplus when output level Q2 is produced?
$
b.
What is the dollar value of the total surplus when output level Q3 is produced?
$

Question

04-02-2024
Mathematics

contestada

Assume the following values for the diagrams below: Q1 = 12 bags. Q2 = 7 bags. Q3 = 19 bags. The market equilibrium price is $34 per bag. The price at point a is $70 per bag. The price at point c is $10 per bag. The price at point d is $49 per bag. The price at point e is $24 per bag. The price at point f is $53 per bag. The price at point g is $18 per bag. Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.

Instructions: Round your answers to two decimal places
the dollar value of the total surplus (= producer surplus + consumer surplus) when the allocatively efficient output level is produced($ 360)
the dollar value of the consumer surplus at that output level($ 216)
the dollar value of the deadweight loss when output level Q2 is produced($ 62.5)
the dollar value of the deadweight loss when output level Q3 is produced($ 122.5)

a.
What is the total surplus when output level Q2 is produced?
$
b.
What is the dollar value of the total surplus when output level Q3 is produced?
$

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Answer:

a. The total surplus when output level Q2 is produced can be calculated by finding the area of the triangle formed by points b, c, and Q2.

Base = Q2 - Q1 = 7 - 12 = -5 (Note: Since Q2 is smaller than Q1, the base is negative)

Height = Price at point c - Price at point e = $10 - $24 = -$14 (Note: Again, since the price at point c is smaller than the price at point e, the height is negative)

Area = 0.5 * Base * Height

= 0.5 * (-5) * (-14)

= 0.5 * 5 * 14

= 35

Therefore, the total surplus when output level Q2 is produced is $35.

b. The dollar value of the total surplus when output level Q3 is produced can be calculated by finding the area of the triangle formed by points b, a, and Q3.

Base = Q3 - Q1 = 19 - 12 = 7

Height = Price at point a - Price at point e = $70 - $24 = $46

Area = 0.5 * Base * Height

= 0.5 * 7 * 46

= 161

Therefore, the dollar value of the total surplus when output level Q3 is produced is $161.