Hi, can you help me solving problems below and also providing detailed solution and explanation step by step? Thank you

1. Amalgamated Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, you have observed that weekly popcorn sales are well-described by the demand equation: Q = 1,200 - 800P + 2.0A, where A denotes advertising weekly spending (in dollars). You are currently charging $1.50 per bag of popcorn (for which the marginal cost is $.75) and spending $500 per week on advertising. a) Compute the store's price elasticity and advertising elasticity. b) Check whether your current $1.50 price is profit maximizing. If not, determine the store's optimal quantity and price. c) Should the store consider increasing its advertising spending? Why or why not.

2. Recently, the major firms in the United States cigarette industry joined with the government in a settlement of liability claims. Under the tentative agreement, the industry would curb advertising and pay the equivalent of about $15 billion per year (for smoking-related state Medicaid expenses) in exchange for protection against smoker lawsuits. a) Before the settlement, a leading cigarette manufacturer estimated its marginal cost at $1.00 per pack and its elasticity of demand at -2. What is its optimal price? The firm's share of the industry payment (based on its historic market share) will raise its average total cost per pack by $.60. What effect will this have on its optimal price? b) A marketing manager suggests that the firm should offer price discounts to the company's longterm, older, most-loyal (addicted?) customers. Do you agree? Explain carefully. c) In the past, anti-smoking information campaigns have had some limited success in reducing smoking. What price reaction (if any) would the cigarette companies have to such programs? Explain carefully.

3. There are two competing Internet-based providers of medical information suitable for patients. ProPatient currently charges $150 per year to subscribers of its service, which helps patients learn more about their medical conditions. Its competitor, AskUs Health, currently charges $125 for a similar service. The current level of advertising by ProPatient is $2,500,000. ProPatient has tracked its volume of subscribers as a function of its price, the price of AskUs services, and of its own marketing expenditures designed to promote the service. The marketing department at ProPatient estimated its demand relationship based on these data. Here is the result: QP = 120,000 - 900PP + 400PA +.02M where QP = quantity of subscribers to ProPatient PP = price charged by ProPatient PA = price charged by AskUs Health M P = Marketing expenditures by ProPatient (all values of the independent variables are in dollars) ProPatient's fixed cost to establish and maintain the business is $10,000,000 plus marketing expenses per year. In addition, there is an incremental expense of $5 for each subscriber. a) What is the current quantity of subscriptions for ProPatient? b) Measure the cross price elasticity of demand for ProPatient subscriptions with respect to the price of AskUs service under the current conditions. c) What is the price elasticity of demand for ProPatient under the current conditions? d) What is marginal revenue for ProPatient under the current conditions? e) What is the current level of profits for the company? f) Given the values of the other variables, is ProPatient charging the optimal price? If not, what is the optimal price?

4. Intercontact INC. is a young and successful Southern California-based company. It manufactures highly sophisticated components that are used in both fixed line and cellular telephony. The relevant basic data on costs and market conditions for its ICX switch in the U.S. are the following (these data refer to a batch consisting of 10,000 units of the ICX): i) Incremental (or marginal) costs of producing, shipping and selling an additional batch is equal to $75,000. ii) Fixed annual costs (production, marketing, administrative and so on): $30,000,000. iii) Past experience has shown that the U.S. market for this type of switch is quite sensitive to price changes. After seriously researching the issue, the company's marketing department has concluded that if the price increases (decreases) by 1%, sales will decline (increase) by 2%. Detailed and careful statistical and technical analyses have confirmed that in the U.S. the company faces a price elasticity of demand equal to -2. In the U.S. the company charges $120,000 per batch, and last year total sales amounted to 4,000 batches. Last year total revenues were $480 million and total costs were $330 million. a) Review the pricing model(s) being used in the US. What can you find out - is the firm setting the optimal price and output level? b) What additional type of information would you like to have in order to undertake a more complete analysis?