Alex consumes only two goods. The consumption bundle is written as (, ). Alex's preference is represented by a utility function (, ) = 2. The price of good 1 is 2, the price of good 2 is 3, and Alex's income is 60. (a) What is the general expression for Alex's marginal rate of substitution (MRS)? What is the MRS when Alex is consuming the bundle (2, 4)? Does Alex's indifference curves exhibit diminishing marginal rate of substitution? (b) Please write down Alex's budget equation. If Alex spends all the income on good 1, how many units of good 1 could Alex buy? How about Alex spends all the income on good 2? Please draw the budget line on -coordinate plane. (c) At Alex's optimal consumption bundle, the MRS must equal the slope of the budget line. Please find the mathematical expression of this condition. (d) Please find Alex's optimal consumption bundle. (e) Please draw the income consumption curve. What is the slope of the income consumption curve? (f) Please draw the Engel curves of both goods. What are the slopes of them?