Suppose that the preferences of a consumer regarding the consumption of goods q and q2 are represented by function: U(9, 92) In (91) + 921 = 1 Suppose also that the consumer is endowed with some disposable income Y> 0 and faces prices P and p2 respectively for goods q and q2. Finally, assume that the price of good q2 is equal to P = 1.1 a. Draw a diagram reporting the indifference curves representing the preferences of the consumer and the budget line. Also, derive and describe the demand functions of the consumer for goods q and q2. Draw the diagram for the (Marshallian) demand functions of the two goods. > [15 marks] > b. Consider an increase in price p. Drawing and describing the indifference curves and budget constraint, and referring to the concepts of substitution effect and income effect, report how the quantity demanded of q changes when p increases. Referring to the concepts of equivalent variation, compensating variation and consumer surplus, describe- how the consumer's welfare is affected by the change in price. [20 marks] c. Consider now the dual problem. Specifically, minimise the expenditure function subject to the consumer achieving a level of utility u > 0 and derive the Hicksian demands for goods 9 and 92. Report the expression of the minimised expenditure function... [15 marks]