Question

In: Economics

1. U( x 1 , x 2 ) = min { x 1, x 2 }...

1. U( x 1 , x 2 ) = min { x 1, x 2 }

If the price of good 1 is $8/unit, the price of good 2 is $2/unit, and income is $51...

What is this person's optimal consumption level for good 2?

2. U( x 1, x 2 ) = min { x1 /2 , x 2}

If the price of good 1 is $4/unit, the price of good 2 is $8/unit, and income is $93...

What is this person's optimal consumption level for good 2?

Solutions

Expert Solution

1)

here the utility function is u(x1,x2)= Min (x1,x2)

For utility to be maximum, x1=x2 -------Relation 1

Now we find the budget constrain: His total income is $93 and the price for good 1 and good 2 is $8 and $2 per unit ,respectively.

So, the budget constrain is, 51=8*x1 + 2*x2 ------Relation 2

putting x1=x2 (from relation 1 ) in relation 2

we get, 51=8*x2 + 2*x2 i.e 51=10x2 i.e x2= 51/10 i.e 5.1 units

So , x1=x2=5.1

Finally his utility function is = min(5.1 , 5.1) i.e 5.1

So , he will consume 5.1 units of good 2

2)

here the utility function is u(x1,x2)= Min (x1/2,x2)

For utility to be maximum, x1/2=x2 and so x1=2(x2) -------Relation 1

Now we find the budget constrain: His total income is $93 and the price for good 1 and good 2 is $4 and $8 per unit ,respectively.

So, the budget constrain is, 93=4*(x1) + 8*x2 ------Relation 2

putting x1=2(x2) (from relation 1 ) in relation 2

we get, 93=4*2(x2) + 2*x2 i.e 93=8(x2)+4(x2) i.e93=12x2 i.e x2= 93/12 i.e 7.75 units

So , x1=2x2=2*7.75 unit = 15.5

Finally his utility function is = min(15.5 , 7.75) i.e 7.75

So , he will consume 7.75 units of good 2


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