Question

Lin spends her income on green goods (G) and born goods (B).  Her utility function is

Her marginal utility for green goods is

Her marginal utility for brown goods is

Find Lin's demand for brown goods expressed in terms of exogenous parameters

Answer 1

Lin spends income on green goods and Brown goods. As it is mentioned in the question the Marginal Utility derived from both the goods is the same. It is only possible in case of a substitute good where we take U = X + Y

MUx = 1 and MUy = 1

At equilibrium MUX /MUY = Px/Py

putting the values we get Px = Py.

If Px equals Py, then the consumer distributes it's income between two goods.

However if Px > Py, as these are substitute goods, consumer entirely spends his income on Y and( X = 0) Similarly if Px < Py, Consumer spends all his income on X and ( Y = 0)

We have our budget equation M= Px.X + Py.y

We put X = 0 to get the demand curve of Y which is M/Py = Y

And if we have Y = 0, to get the demand curve of X we have X = M/Px

For further info, i am attaching my hand written note.