microeconomic theory

Granny lives in the Woods and consumes only bread and fruits. One week she falls ill and has to ask her niece, Red, to buy her weekly food. Red lives in the City, where the price of fruit is $2 per kilogram and the price of bread is also $2 per load. Red knows that Granny's utility function is given by U(f,b) = In(f) +2 In(b) and that Granny has allocated $60 of her income for food each week. 1. How much food should Red buy for Granny? (Granny will reimburse Red for the $60 she spends on food, of course). Denote the optimal quantities by fo, by.(numerical answer required, too!). 2. Heading to Granny's house in Woods with the food from question 1 in her basket, Red unexpectedly meets the infamous trader B. B. Wolf, which offers to buy or sell food at a price of $2 per kilogram of fruits, and $1 per loaf of bread. In a diagram measuring the quantity of bread on the horizontal axis, show Red's budget constraint while shopping in the City, and her budget line after meeting Wolf. Should Red trade with Wolf? 3. After trading with Wolf, how much fruit and bread is in Red's basket? Show these quantities on the same diagram as above. Denote them by fw, bw.(numerical answer required, too!) 4. What is the income and substitution effect of Red meeting Wolf? 5. What is the equivalent variation and compensated variation of the meeting? 6. Answer again questions 1 to 5, assuming now that Granny always eats 1 unit of bread with 3 units of fruits