Suppose the market demand for milk is Q^d = 150

Question

Suppose the market demand for milk is Q^d = 150 - 5P.Additionally,suppose that a dairy's variable costs are VC = 2Q² (where Q is the number of gallons of milk produced each day),its marginal cost is MC = 4Q and there is an avoidable fixed cost of $50 per day.In the long run there is free entry into the market.What is the market equilibrium quantity?

Quizplus · Accepted Answer

To find the market equilibrium quantity, we need to set the market demand equal to the market supply: 150 - 5P = QS + 2Q² + 50 - MC We can simplify this equation by substituting in the expressions for VC and MC: 150 - 5P = QS + 2Q² + 50 - 4Q Simplifying further, we get: QS = 105 - 3P - 2Q² Now we can solve for the equilibrium quantity by setting QS equal to zero: 0 = 105 - 3P - 2Q² 105 - 3P - 2(50) = 0 3P = 55 P = $18.33 Substituting P back into the market demand equation, we get: Q = 150 - 5($18.33) Q = 50 Therefore, the market equilibrium quantity is 50 gallons per day.

Suppose the Market Demand for Milk Is Qd = 150