6)Assume the graph below represents the market demand for a patented prescription drug together with the firm-level marginal cost and average cost functions for producing the drug. Assume these cost curves do not reflect R&D costs of developing this drug, but only reflect production costs of the drug once the formula for it is known. (Note: the diagram assumes that in the output range from 250-400 thousand MC =ATC = $20). Rising MC at Q>400,000 increases ATC.)
A) Draw the marginal revenue function for this firm.
B) What is the profit-maximizing price for this firm?
To draw the marginal revenue function for this firm, we need to first understand the relationship between marginal revenue (MR) and the demand curve.
The demand curve represents the market demand for the patented prescription drug, and it shows the quantity of the drug that consumers are willing to buy at different prices. We will assume that the demand curve is downward sloping, meaning that as the price increases, the quantity demanded decreases.
To determine the marginal revenue, we need to consider how a change in quantity sold affects total revenue. Marginal revenue is the additional revenue generated from selling one more unit of output.
Here's how you can draw the marginal revenue function for this firm:
1. Start with the demand curve: Plot the market demand curve on a graph with price (P) on the y-axis and quantity (Q) on the x-axis.
2. Find the total revenue (TR) function: Multiply the price (P) by the quantity (Q) sold at each price to get the total revenue. This will give you a function TR(P).
3. Calculate the marginal revenue (MR) function: The marginal revenue is the derivative of the total revenue function with respect to quantity (MR = dTR/dQ). To find the marginal revenue function, you need to differentiate the total revenue function with respect to quantity.
4. Plot the marginal revenue function: Once you have the marginal revenue function, plot it on the same graph as the demand curve.
To determine the profit-maximizing price for this firm, we need to consider the relationship between marginal cost (MC) and marginal revenue (MR). The profit-maximizing price occurs where the marginal cost equals marginal revenue.
1. Identify the marginal cost curve: The marginal cost curve represents the additional cost incurred from producing one more unit of the drug.
2. Find the intersection between the marginal cost curve and marginal revenue curve: Plot the marginal cost curve on the same graph as the marginal revenue curve. The profit-maximizing price is where these two curves intersect.
3. Read the price at the intersection: The price at the intersection point between the marginal cost and marginal revenue curves is the profit-maximizing price for the firm.
It's important to note that without access to the actual graph or equations, we can only provide a general explanation of how to draw the marginal revenue function and determine the profit-maximizing price. The actual values and details of the graph will affect the specific results.