Granting a pharmaceutical company a patent for a new medicine will lead to (i) a product that is priced higher than it would be without the exclusive rights. (ii) incentives for pharmaceutical companies to invest in research and development. (iii) higher quantities of output than without the patent.

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). however, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). what is the future value of a 13-year annuity of $2,800 per period where payments come at the beginning of each period? the interest rate is 9 percent. use appendix c for an approximate answer, but calculate your final answer using the formula and financial calculator methods. to find the future value of an annuity due when using the appendix tables, add 1 to n and subtract 1 from the tabular value. for example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to appendix c for n = 6 and i = 10 percent. look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716)

Ursus, inc., is considering a project that would have a five-year life and would require a $1,650,000 investment in equipment. at the end of five years, the project would terminate and the equipment would have no salvage value. the project would provide net operating income each year as follows (ignore income taxes.):

Suppose that electricity producers create a negative externality equal to $5 per unit. further suppose that the government imposes a $5 per-unit tax on the producers. what is the relationship between the after-tax equilibrium quantity and the socially optimal quantity of electricity to be produced?