Question at position 6 The graph above shows the demand and supply of vacuum cleaners. The demand for vacuum cleaners is given by: QD = 500 - 5 P. The inverse demand for vacuum cleaners is: P = 100 - 0.2QD. The supply of vacuum cleaners is given by: QS = 2.5P - 100. The inverse supply for vacuum cleaners is: P = 40 + 0.4QS. Calculate the dollar amount of Gains from Trade. (Do not include a "$" sign in your response. Round to the nearest two decimal places if necessary.) Hint: You will use the area of a triangle to calculate gains from trade in this case. Alternatively, recall that gains from trade are the sum of consumer surplus and producer surplus.Answer The graph above shows the demand and supply of vacuum cleaners. The demand for vacuum cleaners is given by: QD = 500 - 5 P. The inverse demand for vacuum cleaners is: P = 100 - 0.2QD. The supply of vacuum cleaners is given by: QS = 2.5P - 100. The inverse supply for vacuum cleaners is: P = 40 + 0.4QS. Calculate the dollar amount of Gains from Trade. (Do not include a "$" sign in your response. Round to the nearest two decimal places if necessary.) Hint: You will use the area of a triangle to calculate gains from trade in this case. Alternatively, recall that gains from trade are the sum of consumer surplus and producer surplus.[input]简答题
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Question

Question at position 6 The graph above shows the demand and supply of vacuum cleaners. The demand for vacuum cleaners is given by: QD = 500 - 5 P. The inverse demand for vacuum cleaners is: P = 100 - 0.2QD. The supply of vacuum cleaners is given by: QS = 2.5P - 100. The inverse supply for vacuum cleaners is: P = 40 + 0.4QS. Calculate the dollar amount of Gains from Trade. (Do not include a "$" sign in your response. Round to the nearest two decimal places if necessary.) Hint: You will use the area of a triangle to calculate gains from trade in this case. Alternatively, recall that gains from trade are the sum of consumer surplus and producer surplus.Answer The graph above shows the demand and supply of vacuum cleaners. The demand for vacuum cleaners is given by: QD = 500 - 5 P. The inverse demand for vacuum cleaners is: P = 100 - 0.2QD. The supply of vacuum cleaners is given by: QS = 2.5P - 100. The inverse supply for vacuum cleaners is: P = 40 + 0.4QS. Calculate the dollar amount of Gains from Trade. (Do not include a "$" sign in your response. Round to the nearest two decimal places if necessary.) Hint: You will use the area of a triangle to calculate gains from trade in this case. Alternatively, recall that gains from trade are the sum of consumer surplus and producer surplus.[input]简答题

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BlackTom AI · Accepted Answer

To tackle this problem, I start by restating the essential relationships and finding the equilibrium.
The demand function is QD = 500 - 5P, which gives the inverse demand P = 100 - 0.2QD. The supply function is QS = 2.5P - 100, giving the inverse supply P = 40 + 0.4QS.
First, determine the market equilibrium by setting QD = QS: 500 - 5P = 2.5P - 100. Solving yields 600 = 7.5P, so P* = 80. The corresponding quantity is Q* = 500 - 5(80) = 100 (also QS with P=80 gives 2.5(80) - 100 = 200 - 100 = 100).
Now, compute gains from trade as the sum of consumer surplus (CS) and producer surplus (PS).
- Consumer surplus: The choke price (where Q = 0) from the inverse demand P = 100 - 0.2Q is P = 100. The market price is P* = 80, and the equilibrium quantity is Q* = 100. CS is the area of a triangle: 0.5 × (choke price − market price) × Q*. That is 0.5 × (100 − 80) × 100 = 0.5 × 20 × 100 = 1000.
- Producer surplus: The intercept of the inverse supply at Q = 0 is P = 40. The market price is P* = 80, and Q* = 100. PS is also the area of a triangle: 0.5 × (market price − intercept price) × Q*. That is 0.5 × (80 − 40) × 100 = 0.5 × 40 × 100 = 2000.
Finally, Gains from Trade = CS + PS = 1000 + 2000 = 3000.
If you’re comparing to the visual triangles in a graph, the total shaded area representing gains from trade also sums to the same value, since the CS and PS triangles together fill the space between the demand and supply curves up to Q*. Note: all intermediate arithmetic steps align with the standard area formula for triangles in equilibrium analysis.