Question

In: Economics

Murphy was consuming 100 units of X and 50 units of Y . Theprice of...

Murphy was consuming 100 units of X and 50 units of Y . The price of X rose from $2 to $3. The price of Y remained at $4.

(a) How much would Murphyís income have to rise so that he can still exactly a§ord 100 units of X and 50 units of Y ? Assume that Murphy spends all of his income on X and Y .

(b) Now say that Murphyís income falls to $300. If the price of Y is $4, what does the price of X have to fall to in order for Murphy to be able to a§ord 100 units of X and 50 units of Y ?

(c) Now say that Murphyís income falls to $100. If the price of Y is $4, what does the price of X have to fall to in order for Murphy to be able to a§ord 100 units of X and 50 units of Y ?

Solutions

Expert Solution

a) The budget line is given by:

x*Px + y*PY = M

Before price change,

100*2 + 50*4 = M

M = $400

After price change,

100*3+50*4 = M'

300+200=M'

M' = $500

So, income has to rise by M'-M = $500-$400 = $100

b) M = $300

100*Px+50*4 = 300

100*Px =100

Px = 1

The new price is $1. So, the price changes by $1-$2 = -$1

The price should fall by $1 for Murphy to be able to afford 100 units of X and 50 units of Y

c) M = $100

If he consumes 50 units of Y, then expenditure on good Y = $4 * 50 = $200

He is doing more expenditure that what his income is even if he tries to consume only 50 units of good Y.

Therefore, no matter how much the price falls, he cannot afford to consume 100 units of X and 50 units of Y given that his income is $100. This bundle is outside his budget set.

Rahul Sunny answered 2 years ago
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