Question

Suppose that we have a utility function involving two goods that is linear of the form U(x,y)- ax + by. MU MU Suppose>- Hint: It may be helpful to draw yourself a diagram. What is true about the slope of the indifference curves and the slope of the budget constraint? This means the slope of the indifference curves are income is spent on good than the slope of the budget constraint. This implies that all of the consumers Therefore, the demand function for x is x* - and the demand function for y is ls MU MU Suppose PsP Hint: It may be helpful to draw yourself a diagram. What is true about the slope of the indifference curves and the slope of the budget constraint? This means the slope of the indifference curves are income is spent on good than the slope of the budget constraint. This implies that all of the consumers ▼ . Therefore, the demand function for x is x* and the demand function for y is When--> , the expenditure function is E- . However, when--<-, the expenditure function is E- Px

Answer 1

Suppose MUx/ Px> MUy/ Py

This means the slope of the indifference curve is greater than the slope of the budget constraint because slope of indifference curve =MUx/MUy and slope of budget constraint= Px/Py. This implies that all of the consumers income is spent on good x.

Budget constraint= Px X + Py Y= I

Y=0 , X= I/Px

Therefore, the demand function for x is I/Px and the demand function for y is 0.

Suppose MUx/ Px < MUy/Py

This means the slope of the indifference curve is less than the slope of the budget constraint because slope of indifference curve =MUx/MUy and slope of budget constraint= Px/Py. This implies that all of the consumers income is spent on good y.

Budget constraint= Px X + Py Y= I

X=0 , Y= I/Py

Therefore, the demand function for x is 0 and the demand function for y is I/Py.

When MUx/Px > MUy/Py ,the expenditure function is E = Px X +Py Y = Px (I/Px) +0 = I i.e equal to income.

Howeve, when MUx/Px < MUy/Py , the expenditure function is E= PxX + Py Y = 0 +Py(I/Py) = I i.e equal to income.