Question Nora consumes only two goods (food and clothing) and her preferences for these goods can be represented by the following utility function where is the quantity of food consumed and is the amount of clothing consumed respectively. Suppose Nora's allocated monthly income on the two goods is $and the prices of the two goods (food and clothing) she prefers are for food and for clothing.

(a)Using the above information write Nora's utility maximization problem stating clearly the objective function, the budget constraint and the nonnegativity condition. (Hint: Food is on the horizontal axis and clothing on the vertical axis. You do not need to use the Lagrange multiplier to answer this question. Use the simple equilibrium condition of the consumer to solve this.)

(b) From the utility maximization problem obtained in (a) derive the ordinary or uncompensated (Marshallian) demand for each of the two goods.

(c)If Nora's allocated monthly income on the two goods is $3,000, a unit of food costs $100 and a unit of clothing is $50, use your answer in (b) to obtain her optimal amount of food and clothing consumed.

(d) Now suppose Nora's allocated monthly income on the two goods is again $, a unit of food costs $100 and a unit of clothing is $50, obtain an expression for the Engel curves of the two goods. (Hint: Substitute for the prices into the ordinary demand functions obtained in (b) and solve.)