Solved 5 Suppose That X1 X2 вђ Xnв јu 0 оё I I D Given оё And Chegg 1.a) suppose u(x1,x2)=x1a,x2(1−a). given m,p1 and p2 derive the demands for the two goods: solve for mu1,mu2 and the mrs. now use the tangency condition mrs=−p2p1 together with the budget line to solve for x1(m,p1,p2) and x2(m,p1,p2). (10 pts) b) now suppose a=21. further, suppose m=12,p1=2 and p2=2. 1.a) suppose u(x1,x2) = x1a, x2(1 a) . given m, p1, and p2 derive the demands for the two goods: solve for mu1, mu2 and the mrs. now use the tangency condition mrs = p1 p2 together with the budget li.
Solved Suppose X1 X2 вђ Xnв јu A B For Some Unknown A Chegg 1) x 2 s.t. p 1x 1 p 2x 2 = m with p 1 >0,p 2 >0,m>0. 1. write down the lagrangean function (1 point) 2. write down the first order conditions for this problem with respect to x 1, x 2,and λ.(1point) 3. what do the first order conditions tell you regarding the value of λ? (hint: use the first order condition with respect to x 2) does the. An agent consumes quantity (x1;x2) of goods 1 and 2. she has utility u(x1;x2) = x1x22 the prices of the goods are (p1;p2). (a) set up the expenditure minimisation problem. (b) derive the agent’s hicksian demands. (c) derive the agent’s expenditure function. solution (a) the agent minimises l = p1x1 p2x2 ‚[u¡x1x22] (b) the focs are: p1. Now use the tangency condition mrs= p1 p2together with the budget line to solve for x1 (m,p1,p2) and x2 (m, p1,p2). suppose u ( x 1 x 2 ) = x 1 ^ a , x 2 ^ ( 1 a ) given m , p 1 and p 2 derive the demands. Suppose u(x1;x2) = x1x2. the tangency condition yields: x2 x1 = p1 p2 (2.4) rearranging, p1x1 = p2x2. the constraint states that u = x1x2. substituting (2.4) into this yields, u = p1 p2 x2 1 solving for x1, the hicksian demand is given by h1(p1;p2;u) = µ p2 p1 u ¶1=2 (2.5) 6.
Solved Problem 1 Suppose X1 X2 Are I I D Uniform 0 1 Chegg Now use the tangency condition mrs= p1 p2together with the budget line to solve for x1 (m,p1,p2) and x2 (m, p1,p2). suppose u ( x 1 x 2 ) = x 1 ^ a , x 2 ^ ( 1 a ) given m , p 1 and p 2 derive the demands. Suppose u(x1;x2) = x1x2. the tangency condition yields: x2 x1 = p1 p2 (2.4) rearranging, p1x1 = p2x2. the constraint states that u = x1x2. substituting (2.4) into this yields, u = p1 p2 x2 1 solving for x1, the hicksian demand is given by h1(p1;p2;u) = µ p2 p1 u ¶1=2 (2.5) 6. A) suppose u(x1,x2) = x1 a, x2 (1 a) . given m, p1, and p2 derive the demands for the two goods: solve for mu1, mu2 and the mrs. now use the tangency condition mrs = p1 p2. together with the budget line to solve for x1 (m, p1, p2) and x2 (m,p1, p2). b) now suppose a = 1. further, suppose m 12, p1 = 2 and p2 = 2. 1;x 2) was optimal. we conclude that the solution to the maximization problem with goods that are perfect complements must satisfy: ax 1 = x 2. we can then solve the following sistem: ˆ ax 1 = x 2 p 1x 1 p 2x 2 = y hence, the marshallian demand functions are: x 1(p 1;p 2;y) = y p1 p2 x 2(p 1;p 2;y) = y p1 p2 an indi⁄erence curve is shown. Thus, an indifference curve is described by the following equation 3x21 x22 = u equivalently x2 = c x1 ( )1 where c = u3 2 to show that an indifference curve is decreasing we need 2 to compute its first derivative dx dx1 and show that it is negative. dx2 dx1 5 = − c <0 (x1 )2 since c > 0 and (x1 )2 > 0. U(x 1,x 2) = f(x 1) x 2 is linear in just x 2 and is called quasi linear. e.g.u(x. u(x 1,x 2) = 2x 1 1 2 x 2.
Solved 1 N N I 1 Suppose X1 X2 Xn 1 2 U 0 0 In Chegg A) suppose u(x1,x2) = x1 a, x2 (1 a) . given m, p1, and p2 derive the demands for the two goods: solve for mu1, mu2 and the mrs. now use the tangency condition mrs = p1 p2. together with the budget line to solve for x1 (m, p1, p2) and x2 (m,p1, p2). b) now suppose a = 1. further, suppose m 12, p1 = 2 and p2 = 2. 1;x 2) was optimal. we conclude that the solution to the maximization problem with goods that are perfect complements must satisfy: ax 1 = x 2. we can then solve the following sistem: ˆ ax 1 = x 2 p 1x 1 p 2x 2 = y hence, the marshallian demand functions are: x 1(p 1;p 2;y) = y p1 p2 x 2(p 1;p 2;y) = y p1 p2 an indi⁄erence curve is shown. Thus, an indifference curve is described by the following equation 3x21 x22 = u equivalently x2 = c x1 ( )1 where c = u3 2 to show that an indifference curve is decreasing we need 2 to compute its first derivative dx dx1 and show that it is negative. dx2 dx1 5 = − c <0 (x1 )2 since c > 0 and (x1 )2 > 0. U(x 1,x 2) = f(x 1) x 2 is linear in just x 2 and is called quasi linear. e.g.u(x. u(x 1,x 2) = 2x 1 1 2 x 2.
Solved Suppose That X1 X2 Xn I I De N U 1 1 1 Chegg Thus, an indifference curve is described by the following equation 3x21 x22 = u equivalently x2 = c x1 ( )1 where c = u3 2 to show that an indifference curve is decreasing we need 2 to compute its first derivative dx dx1 and show that it is negative. dx2 dx1 5 = − c <0 (x1 )2 since c > 0 and (x1 )2 > 0. U(x 1,x 2) = f(x 1) x 2 is linear in just x 2 and is called quasi linear. e.g.u(x. u(x 1,x 2) = 2x 1 1 2 x 2.