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 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 answer how 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). 1(c) According to diagram in part 1(b), show the income and substitution effects arising, as a result of the change in price of good X. 1(d) (i) Based on analysis and referring to diagram, note whether you find that good X is a normal or an inferior good for Sarah. (ii) Explain clearly how can determine whether a good is a normal or an inferior good (e.g. when the price of good X increases), and justify your answer in part 1(e)(i) referring to your analysis and diagram 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) 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 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 answer YES or No?! Explain Why! Question 2 2(a) Consider the following multiple-choice question: The concept of diminishing marginal returns refers to the situation where: a. Additions of one variable input increase output at an increasing rate. b. Additions of all inputs to production by some proportion increase output by a smaller proportion. c. It is a long-run concept when all inputs can change. d. Additions of one variable input increase output at a decreasing rate. e. Marginal Product curve will decrease but it may be positive. f. Marginal Cost curve will be decreasing. Only two of the answer choices above (a-f) are correct! What are the two correct answers? 2(b) Explain briefly referring to each of the answer options (a)-(f) of this question. Explain in one or two sentences for each option (a)-(f), noting why each one is either correct, or false. 2(c) Draw a stylised Total Product (output) curve and a Marginal Product curve that show the output levels for a farm with fertiliser as its only variable input. Show the typical shape of the Total Product curve in relation to fertiliser, if diminishing marginal product exists. Mark on the diagram for both Marginal Product and Total Product curves, and explain, in one or two sentences, the values of fertiliser input which correspond with 'diminishing marginal returns'. Remember to label your axes