# How to calculate income and substitution effect when equal marginal principle is violated

I am trying to calculate substitution and income effect for 2 goods, x and y.

Given that marginal utility x = 1, marginal utility y = -a (unknown number), price of x = 16, price of y = 20, how should I proceed? I am unable to use the equal marginal principle, since I cannot have a negative price. But without using the marginal principle, I am also unable to find the optimal basket.

I was also considering that the marginal rate of substitution of x will always be greater than that of y. Hence, the optimal basket would just be to spend all the income on x. Could that count as an optimal basket?

• Is there any information which says that a has to be positive? – erik Sep 10 '18 at 16:28
• Yes, it is given in the question that a > 0 – statsguy21 Sep 11 '18 at 1:35
• Then you should mention that in the post I think. Thanks. – erik Sep 11 '18 at 6:46
• This question might be helpful, although note that this is an example where both goods yield positive utility; economics.stackexchange.com/questions/25384/… – Ubiquitous Nov 10 '18 at 7:56