A firm faces the total revenue schedule TR = 600q - 0.5q^2 (a) What is the marginal revenue when q is 100? (b) When is the total revenue at its maximum? (c) What price should the firm charge to achieve this maximum TR? For the non-linear demand schedule p = 750 - 0.1q^2, what output will maximize the sales revenue? A firm faces the demand schedule p = 200 - 2q and the total cost function TC = (2/3)q^3 - 14q^2 + 222q + 50. Derive expressions for the following functions and find out whether they have maximum or minimum points. If they do, say what value of q this occurs at and calculate the actual value of the function at this output. (a) Marginal cost (b) Average variable cost (c) Average fixed cost (d) Total revenue (e) Marginal revenue (f) Profit
Added by Rafael H.
Close
Step 1
So, MR = d(TR)/dq = 600 - q. When q is 100, MR = 600 - 100 = 500. (b) The total revenue is at its maximum when the marginal revenue is zero. So, setting MR = 0, we get 600 - q = 0, which gives q = 600. (c) Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Rashmi S.
Given the demand function: Q = 90 - 2P and the total cost function: TC = 50 + 20Q. a. Show that the total revenue function is given by the function TR = 45Q - 0.5Q^2. b. Determine the Marginal Revenue (MR) function, then calculate the marginal revenue value when the total output (Q) is equal to 10. c. Determine the profit function (π), then determine the level of output that will produce maximum profit. What is the maximum profit?
Charles M.
Use the following demand schedule to determine total revenue and marginal revenue for each possible level of sales: $$\begin{array}{|cccc|} \hline \begin{array}{c} \text { Product } \\ \text { Price } \end{array} & \begin{array}{c} \text { Quantity } \\ \text { Demanded } \end{array} & \begin{array}{c} \text { Total } \\ \text { Revenue } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { Revenue } \end{array} \\ \hline \$ 2 & 0 & \$ \text{_____} & \text{_____} \\ 2 & 1 & \text{_____} & \$ \text{_____} \\ 2 & 2 & \text{_____} & \text{_____} \\ 2 & 3 & \text{_____} & \text{_____} \\ 2 & 4 & \text{_____} & \text{_____} \\ 2 & 5 & \text{_____} & \text{_____} \\ \hline \end{array}$$ a. What can you conclude about the structure of the industry in which this firm is operating? Explain. b. Graph the demand, total-revenue, and marginal-revenue curves for this firm. c. Why do the demand and marginal-revenue curves coincide? d. "Marginal revenue is the change in total revenue associated with additional units of output." Explain verbally and graphically, using the data in the table.
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
Watch the video solution with this free unlock.
EMAIL
PASSWORD