Question

A shop sells two competing brands of socks, Levis and Gap. Each pair of socks is obtained at a cost of 6 dollars per pair. The manager estimates that if he sells the Levis socks for x dollars per pair and the Gap socks for y dollars per pair, then consumers will buy 46- 32x + y pairs of Levis socks and 1/5x- 3y pairs of Gap socks. How should the manager set the prices so that the profit will be maximized?

Answer 1

To determine the profit-maximizing quantity, calculate total revenue, marginal revenue, total cost, and marginal cost for each output level.

Plot the curves for total revenue, total cost, marginal revenue, and marginal cost. The profit maximizing quantity is where marginal revenue equals marginal cost.

Step-by-step explanation:

To determine the profit-maximizing quantity, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level.

Given that the dog coats sell for $72 each, the fixed costs of production are $100, and the total variable costs for each output level are provided, we can calculate the total revenue and total cost by multiplying the quantity by the price and adding the fixed costs and total variable costs, respectively.

Using this information, we can then calculate the marginal revenue as the change in total revenue divided by the change in quantity, and the marginal cost as the change in total cost divided by the change in quantity.

Plotting these values on separate diagrams, we can sketch the total revenue and total cost curves, as well as the marginal revenue and marginal cost curves. The profit maximizing quantity is where the marginal revenue equals the marginal cost.