Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd=100-2Q and the supply of frozen meals is given by Ps=10+Q. Which of the following statements is true at the market equilibrium? Group of answer choicesTotal surplus is equal to 450Consumer surplus is equal to 100Producer surplus is equal to 0Deadweight loss is equal to 0None of the other answers is correct
Question
Consider a perfectly competitive market for frozen meals. The demand for frozen meals is given by Pd=100-2Q and the supply of frozen meals is given by Ps=10+Q. Which of the following statements is true at the market equilibrium? Group of answer choicesTotal surplus is equal to 450Consumer surplus is equal to 100Producer surplus is equal to 0Deadweight loss is equal to 0None of the other answers is correct
Solution
To find the market equilibrium, we need to set the demand equal to the supply and solve for Q:
100 - 2Q = 10 + Q
Solving for Q gives Q = 30. Substituting Q = 30 into either the demand or supply equation will give us the equilibrium price (P). Let's use the demand equation:
P = 100 - 2*30 = 40
So, the equilibrium price (P) is 40 and the equilibrium quantity (Q) is 30.
Now, let's calculate the consumer surplus (CS), producer surplus (PS), and total surplus (TS).
Consumer surplus is the area above the price but below the demand curve. It's calculated as:
CS = 0.5 * (Pd - P) * Q = 0.5 * (100 - 40) * 30 = 900
Producer surplus is the area below the price but above the supply curve. It's calculated as:
PS = 0.5 * (P - Ps) * Q = 0.5 * (40 - 10) * 30 = 450
Total surplus is the sum of consumer surplus and producer surplus:
TS = CS + PS = 900 + 450 = 1350
So, the statement "Total surplus is equal to 450" is incorrect. The correct total surplus is 1350.
The statement "Consumer surplus is equal to 100" is also incorrect. The correct consumer surplus is 900.
The statement "Producer surplus is equal to 0" is incorrect. The correct producer surplus is 450.
The statement "Deadweight loss is equal to 0" is correct. In a perfectly competitive market at equilibrium, there is no deadweight loss because the market is efficient.
The statement "None of the other answers is correct" is incorrect because the statement about deadweight loss is correct.
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