Question

Suppose your utility function is U(x,y) = 2ln(x)+4y

a) Solve for the individual demand for good x and the individual demand for good y.

b) Given Px = 1, Py = 2, and M = 5, find the income elasticity of demand for good x -- is good x normal or inferior (or neither)? Also find the income elasticity of demand for good y -- is good y normal or inferior (or neither)?

c) Given Px = 1, Py = 2, and M =5. Find the elasticity of demand (own-price elasticity) for good x -- is good x ordinary or Giffen?

Answer 1

• U= 2 lnx + 4y

• Budget line: M= Px.x+Py.y

At optimum MUx/Px= MUy/Py

MUx= ∆U/∆x

MUx= 2/x

MUy= ∆U/∆y

MUy= 4

2/Px.x= 4/Py

x= Py/2Px

Putting x=Py/2Px in budget line.

M= Px.[Py/2Px] + Py.y

2M= Py+2Py.y

y*=[ 2M-Py]÷2Py

x*= Py/2Px