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Peter decides to only consumes two goods in a week: those two good are steak and tea. Let x represent the amount of tea (per pint) and y represent the amount of steak (per ounce) that Peter consumes each week. Peter's two goods that he prefers are represented by the Cobb-Douglas utility function ux, y) = x 2y. Peter's goal is to reach weekly utility level U* consuming his favorite goods at the minimal expenditure level. The price of one pint of tea is px, and the price of one ounce of steak is px (a) Carefully write down Peter's expenditure minimization problem and find the compensated demand functions for steak and tea using the Lagrange method. (b) What is Peter's compensated demand for each of the goods at px = $1, py = $4, and Up = 64? What is the minimal income, I, that Peter needs in order to achieve utility level U= = 64 if px = $1, py = $4? (c) Acquire Peter's expenditure function and indirect utility function. (d) Acquire Peter's Marshallian demand functions by using the duality between utility maximization and expenditure minimization problems