from the profit function for a particular type of tool is described by the follo

Question

from the profit function

for a particular type of tool is described by the following demand (2)Suppose the market for a particular type of curve (P) and a total cost function (C): P = 132-8Q 2 3 C (Q) = 128 + 690-14Q + Q (a)Form the profit function and then find the level o (b)What price would (c)Determine the tot output. e firm's profi the total profit the firm could earn by producing the profit maximizing level ine (d)Find the price elasticity of demand at equilibrium and briefly explain how the r be helpful to a revenue maximizing firm in shaping the firm's pricing policy. esult co (3)A cost minimizing firm has the following production function a-Af(L, K) = 96L + 6L -L

Explanation / Answer

a.

P = 132 – 8Q

PQ = 132Q – 8Q^2 = Total revenue

Profit function is as below:

Profit = Total revenue – Total cost

          = 132Q – 8Q^2 – (128 + 69Q – 14Q^2 + Q^3)

          = 132Q – 8Q^2 – 128 – 69Q + 14Q^2 – Q^3

          = 63Q + 6Q^2 – Q^3 – 128

Derivative of total revenue = Marginal revenue (MR) = 132 – 16Q

Derivative of total cost = Marginal cost (MC) = 69 – 28Q + 3Q^2

Profit maximization condition, MR = MC

                                    132 – 16Q = 69 – 28Q + 3Q^2

                                    Q^2 – 4Q – 21 = 0

                                    (Q – 7) (Q + 3) = 0

                                    Either Q = 7 or Q = -3

Q can’t be negative. Therefore, Q = 7 (Answer)

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