Suppose that a consumer has utility given by ?(?,?)=?0.5?0.5 ?and income of $100 ?to spend on goods ? ?and ?, ?for which the prices are $1. ?Suppose that the price of ? ?increases to $5 ?per unit. The two Budget constraints (before and after price change) ?has been shown on the graph. a. ?Derive an original optimal choice bundle of goods under the initial price scheme, (?0,?0). ?Show on the graph. (Hint: you need to show indifference) ?b. ?Derive a new optimal choice bundle of goods under the new price scheme, (??,??). ?Show on the graph. (Hint: you need to show indifference curve) ?c. ?Find total effects for good ?.(Difference between original consumption bundle (??,??) ?and consumption bundle with new prices (??,??)). ?d. ?Show the hypothetical bundle (??,??) ?on the graph. (Hint: you do not need to show the specific number of (??,??), ?just find the tangent point to the initial utility level by shifting the budget constraint under new price scheme.) ?e. ?Identify the substitution effect, the income effect as well as the total effects for good X on the graph.

1. (35 pts) Suppose that a consumer has utility given by U(X, Y) = xo.5yo.5 and income of $100 to spend on goods X and Y, for which the prices are $1. Suppose that the price of X increases to $5 per unit. The two Budget constraints (before and after price change) has been shown on the graph. a. Derive an original optimal choice bundle of goods under the initial price scheme, (X., Y.). Show on the graph. (Hint: you need to show indifference) b. Derive a new optimal choice bundle of goods under the new price scheme, (Xn, Yn). Show on the graph. (Hint: you need to show indifference curve) c. Find total effects for good X. (Difference between original consumption bundle (X., Y.) and consumption bundle with new prices (Xn, Yn)). d. Show the hypothetical bundle (Xh, Yn) on the graph. (Hint: you do not need to show the specific number of (Xn, Yn), just find the tangent point to the initial utility level by shifting the budget constraint under new price scheme.) e. Identify the substitution effect, the income effect as well as the total effects for good X on the graph