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.Suppose the demand for milk doubles.If in the short run the number of firms is fixed and their fixed costs are sunk,how much does each of the active firms produce in the short run equilibrium?

Quizplus · Accepted Answer

In the short run, firms produce where marginal cost (MC) equals marginal revenue (MR), which is derived from the demand curve. When demand doubles, the new demand equation is $Q_d = 300 - 5P$. To find the quantity each firm produces, we need to equate MC to MR. Given MC = 4Q, we need to find MR, which is the derivative of total revenue (TR). TR is $P \times Q$, and from the demand equation, $P = 60 - 0.2Q$ when demand doubles. MR is the derivative of TR with respect to Q, which would be the slope of the demand curve, -0.2, but since we're looking for where MC equals MR and we don't have the explicit MR equation, we use the given MC = 4Q directly. Setting MC equal to the price from the demand equation or finding the equilibrium directly from the given conditions without the explicit MR equation involves solving for Q using the given MC = 4Q, which doesn't directly apply without further information on price or total quantity in the market. However, given the options and the need to match MC to a condition of equilibrium, we look for a scenario where the firm's production decision aligns with the simplified market conditions. Without the explicit intersection calculation, the correct answer involves understanding that the firm's production level is determined by equating MC to the price or MR in the market, which requires additional steps not fully detailed in the provided information. Thus, the answer is inferred based on the need for additional calculation steps or information not fully provided.

Suppose the Market Demand for Milk Is Qd = 150