Course: ECO10002 Course: ECO10002 Instructor: Marian Melnyk Instructor: Marian Melnyk Problem Set 8 Problem 6 Due date: 11/14/2023 (11:59 PM) Use integration by parts to evaluate the following: Problem 1 (a) Suppose that the demand and supply curves for a commodity are P = f(Q) = 300-0.30 and P = g(Q) = 200+0.20, respectively. Find the equilibrium quantity and compute the consumer and producer surplus. Problem 7 (This problem is for practice and illustration only; it will not be graded and you can (b) Suppose that the demand and supply curves for a commodity are P = f(Q) = 10- VO and P = 8(0) = skip it) 20, respectively. Find the equilibrium quantity and compute the consumer and producer surplus. Use integration by parts to evaluate the following: Problem 2 (a ) Vilnidi (b ) [ (x - 2)e - 3 /2 dx Let K(t) denote the capital stock of an economy at time . Then net investment at time t, denoted (9 / 3-x3'dx by I(1), is given by the rate of increase K(1) of K(t). (a) If I(1) = 312 + 2t + 5 fort 2 0, what is the total increase in the capital stock during the interval from t = 0 to t = 5? (b) If K(to) = Ko, find an expression for the total increase in the capital stock from time t = to to 1 = T when the investment function /(t) is as in part (a). Problem 3 Suppose that the inverse demand and supply curves are, respectively, P = f(Q) = 200 - 0.20 and P = g(Q) = 20 + 0.1Q. Find the equilibrium price and quantity, then compute the consumer and producer surplus. Problem 4 Suppose the inverse demand and supply curves for a particular commodity are, respectively, P = f(Q) = 6000/(Q + 50) and P = 8(Q) = Q + 10. Find the equilibrium price and quantity, then compute the consumer and producer surplus. Problem 5 Use integration by parts to evaluate the following: (a) xedx ( b ) 3 xett dx