We are exploring Erik's preference for energy consumption in this question. Consider his utility equation is U = q0.8q20.2 (same mathematical notations as question 1). His monthly income (1) is $800. The prices of unit energy and composite goods are $4 (p) and $20 (P2). 000 (iv) (v) (vi) (vii) Calculate the marginal utility of energy and composite good for Erik. Describe the Erik's optimization problem and obtain his optimal consumption bundle of both goods. Graphically illustrate the optimal consumption bundle (i.e., budget constraint and corresponding indifference curve at optimal solution). Derive the energy demand function (i.e., demand as a function of energy price) for Erik. Obtain the price elasticity of energy demand for Erik. Obtain the indirect utility function for Erik. Demonstrate that you can compute demand function obtained in part (iv) by applying Roy's identity on the indirect utility function obtained in part (vi).