Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd = 139 - 2Q and the supply of frozen meals is given by Ps = 5 + Q. What is the value of Total Surplus?
Question
Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd = 139 - 2Q and the supply of frozen meals is given by Ps = 5 + Q. What is the value of Total Surplus?
Solution
To find the total surplus, we first need to find the equilibrium price and quantity where the demand equals the supply.
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Set the demand equal to the supply: 139 - 2Q = 5 + Q. Solving this equation gives Q = 45.
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Substitute Q = 45 into either the demand or supply equation to find the equilibrium price: P = 139 - 2*45 = 49.
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The consumer surplus is the area of the triangle formed by the demand curve, the price line, and the vertical axis. It is given by (1/2) * (P_max - P_eq) * Q_eq, where P_max is the maximum price consumers are willing to pay (where Q = 0), P_eq is the equilibrium price, and Q_eq is the equilibrium quantity. Substituting the given values gives consumer surplus = (1/2) * (139 - 49) * 45 = 2025.
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The producer surplus is the area of the triangle formed by the supply curve, the price line, and the vertical axis. It is given by (1/2) * (P_eq - P_min) * Q_eq, where P_min is the minimum price producers are willing to accept (where Q = 0). Substituting the given values gives producer surplus = (1/2) * (49 - 5) * 45 = 990.
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The total surplus is the sum of the consumer surplus and the producer surplus: 2025 + 990 = 3015.
So, the total surplus is 3015.
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