Question

In: Economics

Suppose that for ABC Company we have the following functions:     Inverse Demand Function:   P =...

Suppose that for ABC Company we have the following functions:

    Inverse Demand Function:   P = 360 - 0.8Q

    Cost Function: 120 + 200Q

    Marginal Revenue Function (MR) = 360 – 1.6Q

    Marginal Cost (MC) = 200

Determine quantity (Q) and price (P) that maximizes profit for ABC Company. Show your calculations.

Solutions

Expert Solution

So we have been provided with all the data now we can calculate the value of quantity (Q) and price (P) that can maximize the profit for ABC Company, as we know  In a perfectly competitive market price is equal to marginal cost

we have the following given data

P = 360 - 0.8Q

Marginal Cost (MC) = 200

Marginal Revenue Function (MR) = 360 – 1.6Q

price = marginal cost ..............................(1)

on putting value in the above equation from the given question

360 - 0.8Q = 200

by simple transposition on the above equation

360 - 200 = 0.8 Q

0.8 Q = 160

Q = 160 / 0.8 = 200 .......................(2)

THUS THE TOTAL NUMBER OF THE QUANTITY THAT CAN BE MANUFACTURED IN THE COMPETITIVE MARKET IS 200 UNIT

now on putting this value of Q in demand function equation we can get the price per unit (P)

P = 360 - 0.8 * 200

P = 360 - 160 = $ 200 .........................(3)

Thus the price (P) that maximizes profit for ABC Company is $ 200.


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