question 4 parts 1-5

Question 4 (1) A project produces profit of x dollars per year at the end of each year. Interest is r per year. The project life is infinite and there is no production cost. Derive a simple expression for the present value V of the project. Partner Itr I Kol (2) Assume the project in the previous question has a project life of 20 years. Write an expression for the present value of the project, using the answer to the previous question to simplify the expression 20 ki (1+rk (3) Assume that there is an innovation that will yield an annual demand = 100 - P for infinite many years. This demand will be the same always. The invention requires startup costs of $30,000. The marginal cost equals zero and the interest rate is 5%. Should the government develop the innovation? (sketch a figure to illustrate your answer.) (4) The government can authorize a firm that with certainty has the capability to develop the innovation at a cost of $40,000. The incentive that the government can give to the firm is an infinite patent life. Is this incentive enough for the firm? (Sketch a figure.) (5) Say patent life is 20 years, not infinity. Will the firm develop the innovation? Question 4 (1) A project produces profit of x dollars per year at the end of each year. Interest is r per year. The project life is infinite and there is no production cost. Derive a simple expression for the present value V of the project. Partner Itr I Kol (2) Assume the project in the previous question has a project life of 20 years. Write an expression for the present value of the project, using the answer to the previous question to simplify the expression 20 ki (1+rk (3) Assume that there is an innovation that will yield an annual demand = 100 - P for infinite many years. This demand will be the same always. The invention requires startup costs of $30,000. The marginal cost equals zero and the interest rate is 5%. Should the government develop the innovation? (sketch a figure to illustrate your answer.) (4) The government can authorize a firm that with certainty has the capability to develop the innovation at a cost of $40,000. The incentive that the government can give to the firm is an infinite patent life. Is this incentive enough for the firm? (Sketch a figure.) (5) Say patent life is 20 years, not infinity. Will the firm develop the innovation