1) On ONE sketch, show the indiference cur ves through the points (1,1) and (2,4) for...
1) On ONE sketch, show the indifference curves through the points (1,1) and (2,4) for the following utility functions (a) ua(x, y)-x+y (b) ub(x,y)-+2y (c) ue(x, y) 3 y
2) On ONE sketch, show the indifference curves through the points (1,1) and (2, 4) for the following utility functions (a) ua (x, y)-y (b) ub(x, y) -zy (d) uy) 3,,3
3) On ONE sketch, show the indifference curves through the point (1,1) for the following utility functions (a) ua(x,y)-12y/2 (b) ub(z, y)=x1/2+91/2 (b) tle(x, y) = z1/4 + yi/4 (d) ud(x, y)--1/x - 1/y
) For each o the following utility functions derive direclly from the definition not using the formula(s) from class or the text- the MRS (marginal rate of substitution) of y for at the points (1, 1) and (2,4) a) a(x, y)+y (c) u(r,y)3ry
Find the equation for the plane through the points Po(-5, -2,4), Q.(-3,-1,1), and Ro(-1,4,1). The equation of the plane is (Type an equation.)
1:34 Find the parametric equations of the line in Rthat passes through the points (2,4, 1) and (-3, -2,-4). (A) x 25t y 6 6 (B) x 2-5t y 4 6t (C) x -3-5t y 4 6t (D) х--2-t y 6-6t y 6-6t (G) x 2 -5t y 4 6 Problem 45
4) For each of the following utility functions derive directly from the definition not using the formula(s) from class or the text - the MRS (marginal rate of substitution) of y for x at the points (1, 1) and (2,4 (a) ua(x, y)-y (b) us(x, y) x + 2y (c) uc (z, y) = 3x + y
(b) The graph of a parabola passes through the points (3/2,4/3) and (0, -6) and has a horizontal tangent line at (3/2,4/3). Find an equation for the parabola and sketch its graph. 1) (1 216+
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS] U (x, y) = min{2x + y, 2y + x}. (b) [6 PoINts] U (x,y) = max{2.x + y, 2y + x}. (c) 6 POINTS] U (x,y) = x + min {x, y}. (d) 7 POINTS] In which of these cases are preferences convex? 4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a)...
Solve the following problems. Show your work clearly. Q1. (10+10+5=25 points) a) Find the gradient of the function f(x, y) = 3x2 – 2xy + 2y and calculate it at (-1,1). b) Calculate the directional derivative of f(x,y) = 3x2 - 2xy + 2y at the point (-1,1) in the direction of the vector v =< -2,2> c) After solving part (a), if the vector in part (b) was given as v =< 1,0 > could you find the derivative...