Please answer the question step by step and dealtaily. Thanks! Suppose the marke
ID: 1180304 • Letter: P
Question
Please answer the question step by step and dealtaily. Thanks!
Suppose the market for a particular type of tool is described by the following demand curve(P) and a total cost function (C): Form the profit function and then find the level of output that maximizes the firm's profit. What price would the firm charge for its product? Determine the total profit the firm could earn by producing the profit maximizing level of output. Find the price elasticity of demand at equilibrium and briefly explain how the result could be helpful to a revenue maximizing firm in shaping the firm's pricing policy.Explanation / Answer
Profit(P) = PQ - C
= 132Q - 8Q^2 - (128+69Q-14Q^2+Q^3)
for Profit max, dP/dQ = 0
132 - 16Q - 69 +28Q - 3Q^2 = 0
63+12Q-3Q^2 = 0
Q = 7
P = 132-8*7 = 76
Total Profit = 264
dQ/dP = -1/8 , P=76, Q=7
Price elasticity of demand = (change in Q/Q)/(change in P/P) = (dQ/dP)*P/Q
-1/8*76/7 = -19/14 = -1.35
as the elasticity is greater than 1, the product is elastic, and for a revenue maximizing firm, it would be aware that the increase in price could lead to a higher decrease in demand reducing the revenue and therefore will select the price accordingly
Revenue = PQ = 132Q-8Q^2
dR/dQ = 0, 132-16Q = 0 => Q = 8.25
P = 66