Joan’s gross monthly income is 3000 kwacha. She consumes two goods only, food and clothing. Her utility function is given by . The price of clothing has been at k50 per unit, and the price of food has been at k100 per unit.
(a) Derive Joan’s demand functions for food and clothing
(b) Mathematically derive and graphically present Joan’s budget line.
(c) Derive and graphically present Joan’s optimal choice of clothing and food, as well as her optimal level of utility.