In: Economics
Dalahla Company Limited, focusing on producing tooth paste (in units) has a demand function 4? = 35 − 0.5? . If total fixed cost is GH¢80 and average variable cost function is 3? − 51 + 320 ? , where Q is number of tooth paste produced and P is the price per tooth paste (in GH¢). What is the total profit at the profit maximizing level of output, and what is the best pricing policy option?
Demand function: 4Q = 35 - 0.5P
or
Demand function: P = 70 - 8Q
Total Revenue = Price * Quantity = (70 - 8Q) * Q = 70Q - 8Q2
Marginal revenue (First derivative of total revenue with respect to Q) = 70 - 16Q
Total cost = Total Fixed cost + Total Variable cost
Total Fixed cost = 80
Average variable cost = 3Q - 51 + (320 / Q) where total variable cost = average variable cost * Q
Thus, total variable cost = 3Q2 - 51Q + 320
Total cost = 80 + 3Q2 - 51Q + 320
Total cost = 400 + 3Q2 - 51Q
Marginal cost (derivative of total cost with respect to Q) = 6Q - 51
Profit maximizing output occurs when Marginal Revenue = Marginal Cost
70 - 16Q = 6Q - 51
121 = 22Q
Q = 5.5
Price at this Q = 70 - 8 * 5.5 = 26 (By putting value of Q in demand equation)
Total revenue = 26 * 5.5 = 143
Total cost = 400 + 3 * (5.5)2 - 51 * 5.5 = 210.25
Profit = Total Revenue - Total Cost = 143 - 210.25 = -67.25
Average variable cost = 23.68
Firm can wait till the price is high and continue their production because price is greater than average variable cost which means that they are able cover some part of fixed cost plus variable cost of producing the product. If average variable cost further rises, firm should shut down.