1) A consumer has preferences for apples (A) and Oranges (Or) given by the utility function U(A,Or) = log(A) / 2 + log(Or) where log() is the natural logarithm function. The Marginal Utility for A is 1/2A and the marginal utility for Or is 1/Or. The price of A is $1 and the price of Or is $2 per unit, and this consumer will devote $10 of his income to both goods. What is the optimal consumption of Or?
2) What is the total effect of a reduction in the price of Or to $1?
3) Make a graph showing the total effect you found in the previous question.
4) Suppose prices are like in problem 2. What is the minimum income necessary to achieve a total utility of 1.98?
5) What is the income and substitution effect? (Essentially you have to do the same thing you did in problem 4 but achieving the utility obtained with the original prices). Make a graph showing both effects.
Could you show me each answer step by step?