Question

I. U=(x y)=x^(1/3)y^(2/3) that subjected to budget constant 6x+3y=720 then find
1. MUx,
2. MUy,
3. MRSx,y
4.write equilibrium optimum condition.
II. Assume u function of a consumers is u=x^(2) + y^(2) then, Required.
1. MRSy,x
III. a consumers u function give as u=x^(4). y^(-2)
1. MUx,
2. MUy,
3. MRSx,y

Answer 1

Answer on question #72034, Economics / Microeconomics

I. U=(x y)=x^(1/3)y^(2/3) that subjected to budget constant 6x+3y=720 then find

1. Mux

$$\mathrm {M u x} = \mathrm {U} ^ {\prime} = (\mathrm {x y}) = (1 \backslash 3) \mathrm {x} ^ {\wedge} (- 2 / 3) \mathrm {y} ^ {\wedge} (2 / 3)$$

2. MUy

$$\mathrm {M u y} = \mathrm {U} ^ {\prime} = (\mathrm {x y}) = (2 \backslash 3) \mathrm {x} ^ {\wedge} (1 / 3) \mathrm {y} ^ {\wedge} (- 1 / 3)$$

3. MRSx,y

$$M R S _ {x y} = M U _ {x} / M U _ {y}$$ $$\mathrm {M R S x , y} = (1 \backslash 3) \mathrm {x} ^ {\wedge} (- 2 / 3) \mathrm {y} ^ {\wedge} (2 / 3): (2 \backslash 3) \mathrm {x} ^ {\wedge} (1 / 3) \mathrm {y} ^ {\wedge} (- 1 / 3) = \mathrm {y} / 2 \mathrm {x}$$

4. write equilibrium optimum condition:

$$(1 \backslash 3) x ^ {\wedge} (- 2 / 3) y ^ {\wedge} (2 / 3) / 6 = (2 \backslash 3) x ^ {\wedge} (1 / 3) y ^ {\wedge} (- 1 / 3) / 3$$ $$6 x + 3 y = 7 2 0$$

II. Assume u function of a consumers is $\mathrm{u} = \mathrm{x}^{\wedge}(2) + \mathrm{y}^{\wedge}(2)$ then, Required.

1. MRSy,x

$$\mathrm {M u x} = 2 \mathrm {x}$$ $$\mathrm {M u y} = 2 \mathrm {y}$$ $$\mathrm {M R S y , x} = \mathrm {M u y / M u x} = 2 \mathrm {y / 2 x} = \mathrm {y / x}$$

III. a consumers u function give as $\mathrm{u} = \mathrm{x}^{\wedge}(4) \mathrm{y}^{\wedge}(-2)$

1. Mux = 4x^(3) y^(-2)

2. MUy = -2 x^(4) y^(-3)

3. MRSx,y = 4x^(3) y^(-2) : (-2) x^(4) y^(-3) = -2y/x

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