Question 1: Sarah has a monthly income of $1,800 to spend on goods X and Y, where good Y is the composite good (therefore priced at $1 per "unit"). Good X is a type of food. The price of X is initially $5 per unit, then this price increases to $7 per unit. Sarah's MRS, measured at any point along her indifference curve, is given by the formula: Y/3X. In one diagram (for parts 1(a)-1(d)), show: 1(a) The budget constraints for Sarah, both before and after the price change for good X. Note: Remember to label the axes, and show on your diagram, the numerical values where the budget constraint meets the vertical and the horizontal axes, and the slope value of the budget constraint, and show in your answer how you have derived them. 1(b) The optimal consumption bundles for Sarah, both before and after the price change for good X (include the indifference curves). (2 marks) 1(c) According to your diagram in part 1(b), show the income and substitution effects arising, as a result of the change in price of good X. (3 marks) 1(d) (i) Based on your analysis and referring to your diagram, note whether you find that good X is a normal or an inferior good for Sarah. (2 marks) (ii) Explain clearly how you can determine whether a good is a normal or an inferior good leg, when the price of good X increases), and justify your answer in part 1(e)(j) referring to your analysis and diagram. (Word limit = 100 words). 1(e) For the two price levels for X given in this question ($5 and $7), and based on your analysis in parts 1(a) to 1(b), draw a new diagram of the demand curve for Sarah for good X, and derive the equation of the demand curve. Remember to label the axes! (Note: In deriving the equation of the demand curve's slope (and for deriving the P axis intercept value) you can use fractions, or decimal points up to 3 digits and round your result for the Y axis intercept)). 1 (f) (i) Following from question 1(b), show the formula, and derive the value of the MRS of Y for X for Sarah at the optimum consumption bundle point, when the per unit price of X is $5 (at optimum point A) and when the price of X increases to $7 (at optimum Point B). (ii) Do you agree with the statement that for normal goods: 'As the price of X increases, the new optimum consumption bundle's numerical value of the MRS of Y for X is expected to increase in absolute terms."? Is your answer YES or No?! Explain (in one or two sentences) Why