Question

In: Economics

1. U ( x 1 , x 2 ) = 2 x1 + 3 x 2...

1. U ( x 1 , x 2 ) = 2 x₁ + 3 x ₂

If the price of good 1 is $4/unit, the price of good 2 is $5/unit , and income is $20...

What is this person's optimal consumption level for good 1?

2. U( x 1 , x 2 ) = 5 x₁ + 3 x₂

If the price of good 1 is $2/unit, the price of good 2 is $1/unit , and income is $10...

What is this person's optimal consumption level for good 1?

Expert Solution

Ans.1

I = PxX + PyY or 20 = 4X + 5Y or in slope intercept form Y = 4– (1/4)X

To find the consumption bundle that maximizes utility is where the slope of the indifference curve (MUx/MUy) is equal to the slope of the budget line (Px/Py) in absolute value terms.

MUx = Y and MUy = X, so MUx/MUy = Y/X.

Px/Py = 4/5 So, Y/X = 5/4 or X = 4Y/5

Substitute this into the budget line to get Y = 4 – (1/4)(4Y/5) or Y = 2.5. If Y = 2.5, then X = 2

Therefore, The consumption bundle that maximizes utility is thus (x,y) = (2, 2.5).

Ans. 2
I = PxX + PyY or 10 = 2X + 1Y or in slope intercept form Y = 10– (1/2)X

To find the consumption bundle that maximizes utility is where the slope of the indifference curve.

(MUx/MUy) =(Px/Py)

MUx = Y and MUy = X, so MUx/MUy = Y/X.

Px/Py = 2/1 So, Y/X = 1/2 or X = 2Y

Substitute this into the budget line to get Y = 10 – (1/2)(2Y) or Y = 2.5. If Y = 2.5, then X = 5

Therefore, The consumption bundle that maximizes utility is thus (x,y) = (5, 2.5).

Rahul Sunny answered 2 years ago

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