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. x= 100 and Y=80 - I know.

(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!????? I dont know...

(c) If his budget goes down to 80 and prices remain the same, how many apples and berries will he consume? X=100 but Y= 4? Is that correct?

(d) At the optimum consumption point under (c) above, what is the value of the marginal rate of substitution?MRS=-dy/dx but how?

(e) Explain why the value of the marginal rate of substitution that you found in (d) above is not equal to the ratio of prices??? why not?

Thanks!