Calculate the consumer surplus for the demand function P = 25/Q+2 when the market price P = 5.
We use the equilibrium price provided to solve for Q.
Therefore,
"5=\\frac{25}{Q+2}"
"Q=3" when we simplify the equation.
In order to calculate the Consumer Surplus, we need to integrate the demand function at Q=3 and Q=0 range. We would get 25−Q2dQ−(5)(3)
"25Q-\\frac{Q^3}{3}-15"
we substitute Q with 3 from the equation.
"(25\\times3)-\\frac{3^3}{3}-15"
51
Therefore Consumer Surplus will be $51
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