Absorbing markov chains are used in marketing to model the probability that a customer who is contacted by telephone will eventually buy a product. consider a prospective customer who has never been called about purchasing a product.

What is one counter argument to the premise that the wealth gap is a serious problem which needs to be addressed?

Your subscription to investing wisely weekly is about to expire. you plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $620, also payable immediately. assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

By 2020, automobile market analysts expect that the demand for electric autos will increase as buyers become more familiar with the technology. however, the costs of producing electric autos may increase because of higher costs for inputs (e.g., rare earth elements), or they may decrease as the manufacturers learn better assembly methods (i.e., learning by doing). what is the expected impact of these changes on the equilibrium price and quantity for electric autos?