Consider a perfectly competitive economy, that is, an economy in which all agents are price-takers and in which equilibrium prices are determined by the intersection of supply and demand at an equilibrium price pa. This economy is populated by two individuals, Alex and Bobby that consume only coffee and tea. Their preferences over the two goods can be represented by the following utility functions: 0;. )i (TN; UB = (cB (TB)? I 9 Both Alex and Bobby receive an endowment of one unit of tea and one unit of coee. $3 :23 || || 9".\" J'.' 0| 0| D: in | || _|- Budget constraints: Alex (as well as Bobby) can exchange these endow- ments for currency at market prices, which are exogenous to him, in a central marketplace. Consider Alex. (a) 5 points. If the price of coffee is 3 units of currency per unit of coffee, and the price of tea is 5 units of currency per unit of tea, show why Alex's income / month measured in currency is $8.00 . (b) 5 points. What is his income / month measured in units of coffee? In units of tea? (You may express your answer as a. simplied fraction, or as a decimal equivalent). (0) 5 points. What is the relative price of coffee? What are the units of this price? (d) 5 points. For these prices and endowments, write his budget con- straint in standard slope-intercept form with consumption of tea/moat. on the left-hand-side of the equality sign. (e) 5 points. With tea on the vertical axis and coffee on the horizontal, draw a schematic diagram of his budget constraint, making sure you identify all relevant features, i.e., slope, intercepts, and endowment point. (f) 5 points. What would happen to this schematic diagram if both PC and PT were to double? Triple? Be cut in half