Solved Consider The Following Utility Functions I Chegg So, firstly we would calculate the marginal utility of both the goods. m u x = 1 3 x 1 3 − 1 × y 2 5 = 1 3 x − 2 3 × y 2 5 m u y = 2 5 y 2 5 − 1 × x 1 3 = 2 5 y − 3 5 × x 1 3 explanation:. U(x;y) = x y1 that is, that the cobb douglas is a special case of the ces function where ˆ = 0. hint: remember that limz!0 g(z) = elimz!0 lng(z). hint 2: you will need l’hôpital rule. solution: lim ˆ!0 u(x;y) = lim ˆ!0 ( x ˆ (1 )yˆ)1 = exp [lim ˆ!0 ln( xˆ (1 )yˆ) ˆ] = exp [lim ˆ!0 xˆ lnx (1 )yˆ lny xˆ (1 )yˆ] = exp [ lnx (1.
Solved 3 Suppose The Utility Function Is U X Y X1 3y2 5 Chegg A) utility function is given by u (x,y)=x^1 2*y^1 2; given bundle: x=16, y=9. for each of the following situations, i) find the marginal rate of substitution at the given bundle, and accurately draw the indifference curve that goes through that bundle. be sure to label your graph carefully and accurately. Utility maximization. (52 points) in this exercise, we consider a standard maximization problem with an unusual utility function. the utility function is. u(x, y) = √x √y. the price of good x is px and the price of good y is py. we denote income by m, as usual, with m > 0. this function is well defined for x > 0 and for y > 0. Starting with the first two equations, we see that x = y and λ drops out. from the third equation we can easily find that x = y = 50 and the constrained maximum value for z is. z = xy = 2500. a firm produces two goods, x and y. due to a government quota, the firm must produce subject to the constraint x y = 42. the firm’s cost functions is. Question: suppose the utility function is u = x^(1 3)y^(1 3) . price of x is $2 and price of y is $5. let the income be $50. please derive the optimal quantity of x and y demanded. (hint: ux=u 3x and uy=2u 3y ) now if price of x becomes $5. please derive the new optimal quantity of x and y demanded. what is the price effect on good x?.
Solved 4 Suppose The Utility Function For Goods X And Y Is Chegg Starting with the first two equations, we see that x = y and λ drops out. from the third equation we can easily find that x = y = 50 and the constrained maximum value for z is. z = xy = 2500. a firm produces two goods, x and y. due to a government quota, the firm must produce subject to the constraint x y = 42. the firm’s cost functions is. Question: suppose the utility function is u = x^(1 3)y^(1 3) . price of x is $2 and price of y is $5. let the income be $50. please derive the optimal quantity of x and y demanded. (hint: ux=u 3x and uy=2u 3y ) now if price of x becomes $5. please derive the new optimal quantity of x and y demanded. what is the price effect on good x?. Phil’s utility function is u=x1 3y2 3, where mu?? = 3x2 3 and mu?? = 3y1 3 . in los angeles, phil’s net income would equal $4500, and prices of good x and good y are $5 and $8, respectively. Any utility function of the form u(x 1,x 2) = x 1 a x 2 b with a > 0 and b > 0 is called a cobb dldouglas utilit f titility function. e.g. u(x 1,x 2) = x 1 1 2 x 2 1 2 (()a = b = 1 2) v(x 1,x 2) = x 1 x 2 3 (a = 1, b =3). Suppose h(p, u) minimizes the expenditure given (p, u). the corresponding expenditure func tion is e(p, u). use both graph and words to prove the following statement: h(p, u) also maximizes the utility given the expenditure level m = e(p, u) and price p. To analyze utility function u (x, y) = x 1 3 y 1 3, we determine whether goods x and y are net or gross substitutes compl suppose that the utility function is u (x,y)= x1 3 y1 3, then x and y are: (hint: in this particular example, the gross complementarity or substitution among goods has the symmetry property.).
Solved 5 Suppose The Utility Function For Goods X And Y Is Chegg Phil’s utility function is u=x1 3y2 3, where mu?? = 3x2 3 and mu?? = 3y1 3 . in los angeles, phil’s net income would equal $4500, and prices of good x and good y are $5 and $8, respectively. Any utility function of the form u(x 1,x 2) = x 1 a x 2 b with a > 0 and b > 0 is called a cobb dldouglas utilit f titility function. e.g. u(x 1,x 2) = x 1 1 2 x 2 1 2 (()a = b = 1 2) v(x 1,x 2) = x 1 x 2 3 (a = 1, b =3). Suppose h(p, u) minimizes the expenditure given (p, u). the corresponding expenditure func tion is e(p, u). use both graph and words to prove the following statement: h(p, u) also maximizes the utility given the expenditure level m = e(p, u) and price p. To analyze utility function u (x, y) = x 1 3 y 1 3, we determine whether goods x and y are net or gross substitutes compl suppose that the utility function is u (x,y)= x1 3 y1 3, then x and y are: (hint: in this particular example, the gross complementarity or substitution among goods has the symmetry property.).
Solved Consider The Utility Function U X Y X1 2y1 2 A Chegg Suppose h(p, u) minimizes the expenditure given (p, u). the corresponding expenditure func tion is e(p, u). use both graph and words to prove the following statement: h(p, u) also maximizes the utility given the expenditure level m = e(p, u) and price p. To analyze utility function u (x, y) = x 1 3 y 1 3, we determine whether goods x and y are net or gross substitutes compl suppose that the utility function is u (x,y)= x1 3 y1 3, then x and y are: (hint: in this particular example, the gross complementarity or substitution among goods has the symmetry property.).