In: Economics
Eric has the utility function U(x, y) = x0.5y0.5, where x denotes the amount of food consumed and y the amount of clothing. Now suppose that he has an income of $80 per week and that the price of clothing is Py = $2 per unit. Suppose that the price of food is initially Px1 = $2 per unit and that the price subsequently increases to Px2 = $8 per unit.
Suppose the initial consumption basket, when the price of food is $2, is A. When the price of food is $8, Eric buys ? units of x. The price effect is ? units of food. At the initial basket A, Eric’s utility is ? . At the decomposition basket, B, Eric gets the utility equals the initial basket A. Basket B contains ? units of x. The substitution effect is, therefore, ? units of food, and the income effect is ? units of food. At the final basket, Eric’s utility is ?.
I have tried to answer. But, I think there is a problem with the qusetion since on solving the decomposition basket, the y and x values cannot be found as the quadratic equation is showing no real roots. I have explained how to approach this question further via appropriate formulae. I hope this helps. Please don't forget to upvote.