Fred won a lottery that pays him $1000 a month. While that's not a lot of cash, that's fine - Fred only consumes garlic and anchovies. While his breath may be rough, these two goods give him utility according to the function, U(g,a)=g.25a.75, where ‘g' represents the amount of garlic he consumes and ‘a' represents the amount of anchovies he consumes. The price of garlic is $1 and the price of anchovies is $2. Fred doesn't make any money other than his lottery check of $1000/month.

a) Find Fred's Marshalian demands (uncompensated demands) for anchovies and garlic.

b) Calculate the value of utility at the optimum and the value of the expenditure function for Fred.

c) Fred's generous grandmother decides to give him an allowance. She likes fish too and is willing to reimburse 75 percent of Fred's anchovy expenditures. How does this allowance affect Fred's budget constraint? How many anchovies does Fred consume? What is the utility level with the allowance? What is the total subsidy that Fred's grandmother pays him?

d) Fred's grandmother realizes that Fred is eating way too many anchovies and decides to stop paying the allowance. Fred disagrees, and wants to be as well off as he was with the allowance.

How much income (in addition to his lottery earnings) would Fred need to go out and find to be as well off as he was with the allowance?