In: Economics
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.
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.