Hi can you help me with detailed solutions to problems below:

Problem # 1 Demand for a firm's product is: P = 140 - 6Q. The firm's cost equation is: C = 300 + 20Q.

a) Determine the firm's optimal quantity and price.

b) Suppose that demand changes to P = 80 - 6Q. Determine the new optimal quantity and price. Explain why the results differ from those in part a. Problem # 2 The University Eye Institute in upper New-York state is a state-of-the-art ophthalmology center that specializes in a sophisticated laser surgery to correct myopia. Current annual volume is 1000 operations. A major customer of the center is the United Health Insurance system. United currently sends the University Eye Institute 200 patients per year or 20% of the total. United pays $2,500 per operation as does every payor. The United Health Insurance Company is satisfied with the quality and service provided by the University Eye Institute and has proposed that they send the Center an additional 100 patients (operations) per year. United proposes that the fee be reduced to $2,000 for the additional 100 patients and for the prior 200 patients. Assume the fee paid by payors other than United Health remains the same.

a) What is the marginal revenue per patient if the proposal is accepted?

b) What is the marginal cost per patient if the proposal is accepted? Here are some cost data to help you answer part b. Volume 1000 per year 1100 per year Average Total Cost $2,125 $2,100

c) Would you recommend that the proposal be accepted or not? Why?

Problem # 3 Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by: C = $60,000 + .5Q. (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 120,000 rolls of tape per year. a) If Night Timers plans to sell 120,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000? b) The marketing manager forecasts demand for the tape to be: Q = 400,000 - 200,000P. Find the firm's profit-maximizing output and price.

c) If the demand forecast in part b is realized in the first year of production, should the company consider expanding capacity? Explain.

Problem # 4 Idea Inc. is a small publishing company operating in the college and textbook market, which is one of the most profitable segments for book publishers. Idea Inc. has a cost of producing, handling, and shipping of about $30 for each additional book. The publisher's overall marketing and promotion spending (set annually) accounts for an average cost of about $10 per book. Idea Inc.'s best-selling game theory text has a demand curve: P = 200 - Q, where Q denotes yearly sales (in thousands) of books. For this text Idea Inc. pays a $10 per book royalty to the author.

a) Determine the profit-maximizing output and price for the game theory text.

b) A rival publisher has raised the price of its best-selling game theory text by $20. One option is to exactly match this price hike and so exactly preserve your level of sales. Do you endorse this price increase? (Explain briefly why or why not.)

c) To save significantly on fixed costs, Idea Inc. plans to contract out the actual printing of its textbooks to outside vendors. When this happens, Idea Inc. expects to pay a somewhat higher printing cost per book (than in part a) from the outside vendor (who marks up price above its cost to make a profit). How would outsourcing affect the output and pricing decisions in part a?