Question

The inverse demand for a local holiday card maker is p = 50-20, where p is the price per card. The card shop's marginal cost and average cost is constant at $2. Suppose the card shop can set three prices (depending on the quantity a consumer purchases). Calculate these prices.

Answer 1

To calculate the profit maximizing quantity for a local holiday card maker, you need to analyze the total revenue, marginal revenue, total cost, and marginal cost for each output level. The inverse demand equation p = 50 - 20q is used to determine the prices at different quantities sold, and then the two prices are calculated to be $30 per card and $10 per card.

Step-by-step explanation:

To calculate the profit maximizing quantity, we need to analyze the total revenue, marginal revenue, total cost, and marginal cost for each output level. We start by calculating the total revenue, which is equal to the price per unit multiplied by the quantity sold. In this case, the price per card is given by the inverse demand equation p = 50 - 20q, where q is the quantity sold.

For the first price, we set q = 1 and solve for p: p = 50 - 20(1) = 30. So the first price is $30 per card.

For the second price, we set q = 2 and solve for p: p = 50 - 20(2) = 10. So the second price is $10 per card. For the third price, we set q = 3 and solve for p: p = 50 - 20(3) = -10. Since a negative price is not meaningful, we cannot set a third price. Therefore, the two prices are $30 per card and $10 per card.