Question

Assume the following values for the diagrams below: Q1 = 15 bags. Q2 = 10 bags. Q3 = 22 bags. The market equilibrium price is $25 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 $40 per bag. The price at point e is $20 per bag. The price at point f is $32 per bag. The price at point g is $4 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 + consumer surplus) when the allocatively efficient output level is produced?

What 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 produced?

What is the total surplus when output level Q2 is 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?

Answer 1

Step-by-step explanation:

a. $360

The total surplus of Q1 is found within triangle abc. The base is a ($70) to c ($10), and the height is the x value of b, or Q1 (12 bags). The total length of the base is 60 (70-10). Multiply that by the height of the triangle (12), and divide the total by 2. (60 x 12) / 2 = 360

a1. $144

The consumer surplus for Q1 is found within the triangle formed by point a, point b, and the y intercept of the equilibrium. The problem says equilibrium = 46, so the third is point (0, 46). The base is point a ($70) to the equilibrium intercept ($46). The height is Q1 (12). The total base is 24 (70-46). (24 x 12) / 2 = 144

b. $62.50

The deadweight loss for Q2 is found is found within triangle dbe. The base is d ($56) to e ($31). The height of the triangle is Q2 (7) to Q1 (12). The total base is 25 (56-31), and the total height is 5 (12-7). (25 x 5) / 2 = 62.5

b1. $297.50

The total surplus of Q2 is found by subtracting the deadweight loss from the total surplus. 360 - 62.5 = 297.5

c. $122.50

The deadweight loss for Q3 is found within triangle bfg. The base is f (67) to g (32). The height is Q1 (12) to Q3 (19). The total base is 35 (67-32) and the total height is 7 (19-12). (35 x 7) / 2 = 122.5

c1. $237.50

The total surplus for Q3 is found by subtracting the deadweight loss from the total surplus. 360 - 122.5 = 237.5

Answer 2

a. The dollar value of the total surplus at the allocatively efficient output level is $525. The consumer surplus at that output level is $375.

b. The dollar value of the deadweight loss when output level Q2 is produced is $150. The total surplus at Q2 is $225.

c. The dollar value of the deadweight loss when output level Q3 is produced is $275. The total surplus at Q3 is $275.

Step-by-step explanation:

a. To find the total surplus at the allocatively efficient output level, we need to calculate the area of the triangle formed by the points where the market price equals the marginal cost. The consumer surplus is the area between the demand curve and the price at the allocatively efficient output level. Using the formula for the area of a triangle,
`\( \text{Consumer Surplus} = (1)/(2) * (\text{Quantity at equilibrium} - \text{Quantity at efficient level}) * (\text{Price at equilibrium} - \text{Price at efficient level}) \),`we find it to be $375. The total surplus is the sum of the consumer and producer surpluses, resulting in a value of $525.

b. The deadweight loss at output level Q2 is the area of the triangle formed by the difference between the quantity at equilibrium and the quantity at Q2. Using the formula
`\( \text{Deadweight Loss} = (1)/(2) * (\text{Quantity at equilibrium} - \text{Quantity at Q2}) * (\text{Price at equilibrium} - \text{Price at Q2}) \),` we calculate it to be $150. The total surplus at Q2 is the area of the consumer surplus triangle, which is $225.

c. Similar to part b, the deadweight loss at output level Q3 is the area of the triangle formed by the difference between the quantity at equilibrium and the quantity at Q3. Using the formula, the deadweight loss is $275, and the total surplus at Q3 is also $275.