Suppose Akirahas two sources of income Anticipated income, y 1 is spent on healthy food, represented by x 1 , and clothing, x 2 Unanticipated income, y 2 is spent on dessert items, x 3 Suppose the value function is given by so that marginal utility of good 1 is given by , marginal utility for good ...

The majority of this query does not require calculus but will require significant ability to manipul ...

Suppose Akirahas two sources of income. Anticipated income, y 1 is spent on healthy food, represented by

Question:

Suppose Akirahas two sources of income. Anticipated income, y₁ is spent on healthy food, represented by x₁, and clothing, x₂. Unanticipated income, y₂ is spent on dessert items, x₃. Suppose the value function is given by

so that marginal utility of good 1 is given by

marginal utility for good 2 is

and marginal utility of good 3 is given by

Suppose y₁= 8 and y₂= 2, and that the price of the goods is given by p₁ = 1, p₂ = 1, p₃ = 2. What is the consumption level observed given the budgets? To find this, set the marginal utility of consumption to be equal for all goods in the same budget, and impose that the cost of all goods in that budget be equal to the budget constraint. Suppose Akira receivesan extra $4 in anticipated income, y₁ = 12 and y₂ = 2; how does consumption change? Suppose alternatively that Akira receives the extra $4 as unanticipated income, y₁ = 8 and y₂ = 6; how does consumption change? What consumption bundle would maximize utility? Which budget is set too low?