(c) Suppose px increases by 50%. What is Joe’s new optimal consumption bundle? Calculateboth the Income Effect and the Substitution Effect.

Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.(b) Now, suppose α = 6, β = 2, px = 2, py = 3 and I = 24. Evaluate Joe’s optimal choice.(c) Suppose px increases by 50%. What is Joe’s new optimal consumption bundle? Calculateboth the Income Effect and the Substitution Effect

Question 1Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.

U(x, y) = (3x + 2y)2 .The price of x is px = $10 per unit and his income is $200.(a) Obtain the equation of Johnathan’s indifference curve for the utility level U = 100. Drawthis indifference curve. (2 marks)(b) The price of y is py = $8 per unit. Obtain the marginal rate of substitution (MRS) and theequation of the budget line. Using a graph, find Johnathan’s optimal consumption bundle.In this graph, show the budget line, the optimal bundle, and the corresponding indifferencecurve. Make sure to label carefully all the curves. (3 marks)(c) Suppose that the price of y drops to py = $6 per unit (the price of x remains the same,at px = $10 per unit, and the income remains the same). Obtain the equation of the newbudget line. Using a new graph, find Johnathan’s optimal bundle with this new price. Inthis graph, show Johnathan’s new budget line, new optimal bundle, and the correspondingindifference curve. Make sure to label carefully all the curves. (3 marks)(d) Now suppose that the price of y is py = $8 per unit if Johnathan buys less than 10 units ofthis product, and py = $6 per unit if he buys 10 units of y or more (as an example, 20 unitsof y would cost $120). Assume that the price of x remains the same, at px = $10 per unit.Derive the equation of the budget line and draw it in a separate graph. (3 marks)(e) Using a new graph, find the optimal bundle(s) for the problem in part (d). In this new graph,show the budget line, the optimal bundle and corresponding indifference curve. Make sureto label carefully all the curves. (3 marks)

Consider a consumer buying perfect complements. If there is a decrease in the price of good 1, the total change in consumption of good 1 is due toGroup of answer choicesthe pure substitution effectthe income effectthe pure substitution effect minus the income effectit depends on whether the good is inferior or normalnone of the above

Now suppose in addition to the price change of good Y (px = py = 4$), Mike’s income is reduced to $160.(j). How much X does Mike consume under new prices and new income?