The market demand for milk is Additionally,suppose that a dairy's variable costs are (where Q is the number of gallons of milk produced each day),its marginal cost is 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,what is the short run market supply function in terms of price?
A) 40P if price is greater than $20
B) P/4 if price is greater than $20
C) 2.5P if price is greater than $20
D) 300-10P

Question

The market demand for milk is  Additionally,suppose that a dairy's variable costs are  (where Q is the number of gallons of milk produced each day),its marginal cost is  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,what is the short run market supply function in terms of price?
A) 40P if price is greater than $20 
B) P/4 if price is greater than $20 
C) 2.5P if price is greater than $20 
D) 300-10P

Quizplus · Accepted Answer

Given, the market demand for milk is Q = 11ea8a01_e40e_15b4_8b44_8dd10ed24bc8_TB1639_11 Variable cost = 11ea8a01_e40e_3cc5_8b44_ff9e53173c42_TB1639_11 Marginal cost = 11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11 Avoidable fixed cost = $50 per day In the long run, there is free entry into the market. If the demand for milk doubles, in short run, the number of firms is fixed and their fixed costs are sunk. To find the short run market supply function in terms of price, we need to determine the short run market equilibrium output level. In the short run, each firm will produce where P = MC. Let us first find the market supply function for the given demand and cost functions. Total cost (TC) = Fixed Cost (FC) + Variable cost (VC) = 50 + 11ea8a01_e40e_3cc5_8b44_ff9e53173c42_TB1639_11Q Marginal cost (MC) = derivative of total cost with respect to Q = 11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11 In the short run, each firm will produce where P = MC. So, from the given demand function, we can find the short run market supply function as follows: Qs = (P - 11ea8a01_e40e_3cc5_8b44_ff9e53173c42_TB1639_11)/11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11 If the demand for milk doubles, the new demand function becomes Q = 22ea8a01_e40e_15b4_8b44_8dd10ed24bc8_TB1639_11. The new equilibrium price can be obtained by substituting this new demand into the existing market supply function: 22ea8a01_e40e_15b4_8b44_8dd10ed24bc8_TB1639_11 = (P - 11ea8a01_e40e_3cc5_8b44_ff9e53173c42_TB1639_11)/11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11 P = $55 Therefore, the short run market supply function in terms of price is given by: Qs = (P - 11ea8a01_e40e_3cc5_8b44_ff9e53173c42_TB1639_11)/11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11 Qs = (P - 50)/11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11, if P>55 Qs = 0, if P<=55 Putting P = $20 in the above equation, we get Qs = -2.73, which is not possible. Hence, the supply function is zero when P<=55. Thus, the short run market supply function in terms of price is: Qs = (P - 50)/11ea8a01_e40e_3cc6_8b44_cdac7d0197eb_TB1639_11, if P>55 Qs = 0, if P<=55 Simplifying the above equation, we get: Qs = 2.5P - 125, if P>55 Qs = 0, if P<=55 Therefore, the answer is C.

The Market Demand for Milk Is Additionally,suppose That a Dairy's