Refer to section 11.6 in Chapter 11 pp427-434. Consider a competitive industry and a price-taking firm that produces a certain product in that industry. The market price for that product is $5 per unit. The manager estimates the average variable cost function to be AVC = 5 – 0.0032Q + 0.0000008Q^2 Q^2 denotes Q squared 1. Average variable cost (AVC) reaches its minimum value at how many units of output? Hint: take the first derivative of the AVC function, make it equal 0, and solve for Q. 2. What is the minimum value of average variable cost (AVC)? Hint: plug the answer from question 1 back into the AVC function and solve for AVC. 3. Should the manager produce or shut down? Why? Hint: compare market price with the minimum value of AVC you get from question 2. 4. What is the marginal cost (MC) function? Hint: get the Total Variable Cost (TVC) function based on the AVC function, then take the first derivative of the TVC function. 5. What is the optimal level of production for the firm? Hint: MR=MC, solve for quantity Q. Here MR (marginal revenue) equals the market price. Show your work. You are required to ask questions, answer questions, or post hints, suggestions, or comments at least once.
