Profit Calculation for a Product
What are the quantity, price, and profit of the product based on the given information?
Given: Fixed cost: 300 MR = 64-4q MC = 4q P = 64-2q
Answer:
The quantity and the price of the product are q = 6 units and p = $51, respectively. The profit can be calculated as follows:
To find the quantity, we equate the marginal cost (MC) and marginal revenue (MR) equations:
q = (64 / 8) - (4 / 8)
q = 8 - 0.5Substitute the quantity in the demand equation to get the price:
p = 64 - 2(8 - 0.5q)
p = 64 - 16 + q
p = 48 + 0.5qNow, calculate the total revenue and total cost:
Total cost = Fixed cost + Variable cost
Total cost = 300 + 4q
Total cost = 300 + 4(6)
Total cost = $324Total revenue = Quantity x Price
Total revenue = 6 x 51
Total revenue = $306Finally, calculate the profit:
Profit = 306 - 324
Profit = -$18