6. Angus consumes agricultural goods and manufactured goods. There is a minimum subsistence level of agricultural goods, y, that is necessary for survival. Only after obtaining y of the agricultural goods will Angus consider manufactured goods. A simple way to represent these preferences is as follows. U(Ca, Cm) = (Ca - y)"Cm-a a. Solve for his optimal consumption of the two goods as a function of income and the goods prices. b. Can the relative Marshallian demand function be written as a declining function of the relative prices alone and is it a function of income? Show the algebraic reasoning behind your answer. C. Solve for the expenditure function for these preferences. Find the Hicksian demand function for both goods. d. Derive an equation for Angus's indifference curves and graph a few of these curves along with the budget constraints. What is the slope of the indifference curve at the optimal consumption bundle. f. How do the optimal consumption bundles change when income changes? Trace out the income expansion curve on a graph of indifference curves and budget constraints