ADVANCED ANALYSIS Assume the following values for Figures 5.4a and Figures 5.4b. Q1 = 20 bags. Q2 = 15 bags. Q3 = 27 bags. The market equilibrium price is $45 per bag. The price at a is $85 per bag. The price at c is $5 per bag. The price at f is $59 per bag. The price at g is $31 per bag. Apply the formula for the area of a triangle (Area = Base Height) to answer the following questions. LO2 a. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output level is being produced? How large is the dollar value of the consumer surplus at that output level? 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?
Explanation:
a. Total surplus is the area bounded by points a, b, and c. To calculate total surplus, we use the following formula for the area of a triangle: Area = ½ × Base × Height. The area between the demand curve and the supply curve for the quantity ranging from 0 to 20 is the total economic surplus. This is a triangle with a base (best read off the price axis) of $80, which is the price difference at Q = 0, or between points a and c, and a height of 20 (the number of units purchased in equilibrium). Using these values, we have a total surplus of (1/2) × $80 × 20 = $800.
The consumer surplus is the area between the demand curve and the equilibrium price line. Here we have a base of $40 (the price difference between the demand schedule price at Q = 0, which is $85, and the equilibrium price of $45). The height of the triangle is once again 20 (the number of units purchased in equilibrium). Using these values, we have a consumer surplus of (1/2) × 40 × 20 = $400.
b. Deadweight loss is the difference in total surplus between an efficient level of output Q1 and a reduced level of output at Q2. We can calculate this as the area of a triangle bounded by points bde. The base of this triangle is the difference in prices at points d and e, or $55 – $35 = $20. The height of this triangle is given by the difference in the restricted level of output of Q2 = 15 and the efficient level of output Q1 = 20, or 5 units. Thus, the area of this triangle (the deadweight loss) is equal to (1/2) × $20 × 5 = $50. The remaining total surplus can be found by subtracting the deadweight loss from the original (efficient) total surplus. This is $800 (maximum total surplus) – $50 (deadweight loss) = $750.
c. The deadweight loss from overproduction is the difference in total surplus between an efficient level of output Q1 and an additional level of output at Q3. We can calculate this as the area of a triangle bounded by points bfg. The base of this triangle is the difference in prices at points f and g, or $59 – $31 = $28. The height of this triangle is given by the difference in the additional level of output Q3 = 27 and the efficient level of output Q1 = 20, or 7 units. Thus, the area of this triangle (the deadweight loss) is equal to (1/2) × $28 × 7 = $98. The remaining total surplus can be found by subtracting the deadweight loss from the original total surplus. This is $800 (maximum total surplus) – $98 (deadweight loss) = $702. Note here that we maximize total (producer + consumer) surplus by producing the equilibrium quantity, but we lose surplus from overproduction (inefficient use of resources).
ADVANCED ANALYSIS Assume the following values for the figures below: Q1 = 20 bags. Q2 = 15 bags. Q3 = 27 bags. The market equilibrium price is $45 per bag. In Figure (a), the price at point a is $85 per bag. The price at point c is $5 per bag. The price at point d is $55 per bag, and the price at point e is $35 per bag. In Figure (b), the price at point f is $59 per bag. The price at point g is $31 per bag. Values for points a, b, and c are the same as in Figure (a). Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.
A. $800, $600
B. $50, $750
C. $98, $702
B is wrong
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I mean, part A, second question is
To answer these questions, we need to calculate the area of the triangles representing the producer surplus, consumer surplus, and deadweight loss in Figures 5.4a and 5.4b.
a. To calculate the dollar value of the total surplus, we need to find the area of the triangle formed by the price ($45) and the equilibrium quantity (Q1 = 20 bags). The formula for the area of a triangle is Area = Base * Height.
In this case, the Base is the difference between the equilibrium quantity (Q1) and the quantity at point a. So, Base = Q1 - Qa = 20 - 15 = 5 bags.
The Height of the triangle is the difference between the equilibrium price ($45) and the price at point a ($85). So, Height = Pa - P1 = 85 - 45 = 40 dollars per bag.
Now, we can calculate the area of the triangle representing the consumer surplus:
Consumer Surplus = (1/2) * Base * Height = (1/2) * 5 * 40 = $100.
b. To calculate the dollar value of the deadweight loss at output level Q2, we need to find the area of the triangle formed by the prices at points a and c, and the quantities at Q2 and Q1.
The Base of the triangle is the difference between the quantity at Q1 (20 bags) and the quantity at Q2 (15 bags). So, Base = Q1 - Q2 = 20 - 15 = 5 bags.
The Height of the triangle is the difference between the price at point a ($85) and the price at point c ($5). So, Height = Pa - Pc = 85 - 5 = 80 dollars per bag.
Now, we can calculate the area of the triangle representing the deadweight loss:
Deadweight Loss = (1/2) * Base * Height = (1/2) * 5 * 80 = $200.
To calculate the total surplus at Q2, we need to find the sum of the consumer surplus and producer surplus.
Producer Surplus = (1/2) * Base * Height = (1/2) * 5 * 40 = $100.
Total Surplus = Consumer Surplus + Producer Surplus = $100 + $100 = $200.
c. To calculate the dollar value of the deadweight loss at output level Q3, we need to find the area of the triangle formed by the prices at points c and f, and the quantities at Q3 and Q1.
The Base of the triangle is the difference between the quantity at Q1 (20 bags) and the quantity at Q3 (27 bags). So, Base = Q1 - Q3 = 20 - 27 = -7 bags. However, since we are dealing with areas, we take the absolute value of the base, so Base = |-7| = 7 bags.
The Height of the triangle is the difference between the price at point c ($5) and the price at point f ($59). So, Height = Pc - Pf = 5 - 59 = -54 dollars per bag. Again, we take the absolute value of the height since we are calculating areas, so Height = |-54| = 54 dollars per bag.
Now, we can calculate the area of the triangle representing the deadweight loss:
Deadweight Loss = (1/2) * Base * Height = (1/2) * 7 * 54 = $189.
To calculate the total surplus at Q3, we need to find the sum of the consumer surplus and producer surplus.
Consumer Surplus = (1/2) * Base * Height = (1/2) * 7 * 54 = $189.
Total Surplus = Consumer Surplus + Producer Surplus = $189 + $0 = $189.
I hope this explanation helps you understand how to calculate the dollar value of total surplus, consumer surplus, and deadweight loss using the area of triangles formula.