Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd = 137 - 4Q and the supply of frozen meals is given by Ps = 8 + Q. What is the value of Consumer Surplus?
Question
Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd = 137 - 4Q and the supply of frozen meals is given by Ps = 8 + Q. What is the value of Consumer Surplus?
Solution
To find the consumer surplus, we first need to find the equilibrium price and quantity where the demand equals the supply.
Set Pd = Ps to find the equilibrium:
137 - 4Q = 8 + Q
Solving for Q gives Q = 23.
Substitute Q = 23 into either the demand or supply equation to find the equilibrium price P. Using the demand equation:
P = 137 - 4*23 = 137 - 92 = 45
The consumer surplus is the area of the triangle formed by the demand curve, the price axis, and the line P = 45. The base of the triangle is 45 (from P = 0 to P = 45), and the height is 23 (from Q = 0 to Q = 23).
So, the consumer surplus is (1/2) * base * height = (1/2) * 45 * 23 = 517.5.
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