budget constraint problem - can Y be negative?

Hello,

Here is my question - 1) Ambrose consumes apples and berries only and his utility function is u = 4(x)^1/2 + y when x is his consumption of apples and y is his consumption of berries. Marginal utility of x and y are given by

(a) Suppose the price of apples is 1, the price of berries is 5 and his budget is 500. Find how many apples and berries he is going to consume.

(b) At the optimum consumption point in (a) above, if you offer him 40 apples in exchange for 9 berries, will he accept the offer? Explain why!

(c) If his budget goes down to 80 and prices remain the same, how many apples and berries will he consume?

(d) At the optimum consumption point under (c) above, what is the value of the marginal rate of substitution?

Here are my answers - a) X=100 and Y= 80
b) the answer is no becuz he will need 45 apples in exchange for 9 berries.
c) I still get X=100 and Y=-4... so this is my question. Is that even possible? plus since budget is 80 we can really buy 100 apples right?
and whats the answer to d)? Do these have anything to do with corner solutions?

Thanks!

the answer to your question "can Y be negative" is no. So you either have a corner solution or you made an alegraic mistake.


Depending on your level of study you may recognise the utility function as a quasilinear one...in which case you can more or less deduce the demand for each good by remembering what the engel curves look like for quasilinear utility.

Yes I agree on you. Y can't be negative in this table. Would you like to have the equation?