Mathematical Economics chapter 10

Q 4: Answer the following questions: i) Given the demand function P = 8.25e-0.20. (1) Determine the quantity and price at which total revenue will be maximized (2) and test the second order condition. ii) Given the demand function P = 12.50e-0.0050. (1) Determine the quantity and price at which total revenue will be maximized (2) and test the second order condition. iii) Land bought for speculation is increasing in value according to the formula V = 1000ev. The discount rate under continuous compounding is 0.09. How long should the land be held to maximize the present value? iv) The estimated value of a diamond bought for investment purposes is V = 250000(1.75) V . If the discount rate under continuous compounding is 7 percent, how long should the diamond be held? v) Cut glass currently worth $100 is appreciating in value according to the formula V = 100e Vr. How long should the cut glass be kept to maximize its present value if discount rate under continuous compounding is 12.7 percent