The consumer's problem is max u(C1, C2) s.t. C1 +5 < y1 C2 < y2 +...
2. Consumption-Savings Decision: The Household's decision problem is: 1- 1- max - C1,C2,8 1-7."1-7 s.t. Ci+s=(<)yi C2 = (*)(1+r)s + y2 where ci and c2 are consumption in periods 1 and 2 respectively; yi and Y2 are income in periods 1 and 2 respectively; s is savings; r is the interest rate on savings.y is a parameter controlling the concavity of the utility function, and will determine intertemporal substitution of consumption.4 We assume that y> 1; so utility is increasing...
5.4.([1] 5.6) The joint density function for Y1 and Y2 is f(y1,92) = {o 0 < y1 = 1,0 < y2 = 1 else a) what is P[Y1-Y2>0.5]? b) what is P[Y|Y2<0.5]?
Consider the following 2-period model U(C1,C2) = min{4C1,5C2} Ci + S = Y1-T C2 = Y2 - T2 + (1+r)S Where C: first period consumption C2: second period consumption S: first period saving Y] = 20 : first period income Ti = 5 : first period lump-sum tax Y2 = 50 : second period income T2 = 10 : second period lump-sum tax r= 0.05 : real interest rate Find the optimal saving, S*
2. Consider the following linear model where C1 has not yet been defined. Max s.t. z = C1x1 + x2 X1 + x2 = 6 X1 + 2.5x2 < 10 X1 > 0, x2 > 0 Use the graphical approach that we covered to find the optimal solution, x*=(x1, xỉ) for all values of -00 < ci so. Hint: First draw the feasible region and notice that there are only a few corner points that can be the optimal solution....
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
5.3.([1] 5.5) The joint density of Y and Y2 is given by 0 < y2 < y1 <1 else f(y1.92) = {3 a) Find F (33) = P[Y; <z, Y s. b) Find P[Y2 = ").
C2 Done session.masteringengine AA <HW10 - Attempt 1 Problem 10.2 < 5 of 7 > Review Consider the beam shown in. Assume the 9k 9k 2 k/1 15 Ft 15 ft --5ft -- 5ft--ft- supports at A and D are fixed and B and Care rollers. El is constant. Part A > C2 Done session.masteringengine AA <HW10 - Attempt 1 Problem 10.2 < 5 of 7 > Part A Determine the internal end moment MAB acting on span AB at...
5-1. Let U - Uniform(0,1) and X = - In(1-U). Show that the CDF of X is Fx(x) = 1 -e*, 0<x<0 In other word, X is exponentially distributed with 1 = 1.
Show that if 0 < μ < 2-r has a unique relative extreme (max) value for x in (0,1)