Question

commodities x and y are perfect complements and the utility function is given by u =min(x,3y) price of x is 2 price of y is 1 income =140 find equilibrium level of consumption

Answer 1

Although we could solve this by means of the lagrangean - in this case you're given everything you'll need to make this a simple multivariate within the question.

Since we know that the goods are perfect complements and the Utility function is given by U=min(x,3y) we can infer that regardless of income - in the end your consumption bundle will be x=3y (meaning you take 3 units of good x for each unit of y)

So x=3y.

At the same time, we know that the budget constraint can be defined as 2x+y=140.

Simple substitution yields this :

2(3y)+y=140
7y=140
y=20
x=3y
x=60

Nice and simple, eh?

Answer 2

i also thought the same but it was supposed to be a tough question and i thought answer could not be a simple linear equation. yeah but it makes perfect sense so thanks man.