In an unregulated, competitive market we could calculate consumer surplus if we knew the equations representing supply and demand. For this problem assume that supply and demand are as follows: Supply P = 4 + 0.116Q Demand P = 25 - 0
10Q, where P represents unit price in dollars and Q represents number of units sold each year. Calculate the annual value of aggregate consumer surplus.
We must calculate the area above the equilibrium price and below the demand curve. The equilibrium price is:
4 + 0.116Q = 25 - 0.10Q
0.216Q = 21
Q = 97.22 units per year.
The area below the demand curve can be calculated after we know the height of demand at Q = 0 and Q = 97.22.
At Q = 0, P = 25.
At Q = 97.22, P = 25 - 0.10(97.22 ) = 15.28.
Since demand is linear, we can use the difference of 25 and 15.28 or 9.72 as the height of the space under demand.
Area = 1/2 b ? h = (1/2 )(97.22 )(9.72 ) = $472.49
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