Question 3 [20 marks). Irene spends all of her income M on soda and chips The price diode is 2 per unit. Irene's ulity function is Huge) = 5111(1 + s) +ln(1 +o). Hint: throughout the question. you can assume M 2 50 and pa 5 8 (these assumptions just rule out the possibility of corner solutions but do not affect the way we solve the problem). (a) Derive Irene's demand function for chips (as a function of her income and the price ofchips). (5 marks) (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect? (5 marks) (c) Obtain Irene's inverse demand function for chips when her income is M = 50. Show that this function is decreasing and content. (5 marks) (d) Is Irene's Engel curve (as defined in our Lecture 5) upward sloping or downward sloping? Explain in detail. (5 marks) Question 2 {20 marks}. Georgina consumes only pasta (good :17} and wine (good 3;). Her utility function is given by U(:r:, y} = 31111: +lny. (a) Consider only bundles with both 12 1\" l} and y '.> 0. Are Georgina's preferences monotone? Are they strictly monotone? Does this utility function satisfy diminishing MR5? (5 marks) (b) Find the expenditure-minimising bundle (1:, y} as a function of the prices p1 and pH, and the target utility E. (5 marks) (c)(c.1) Find the expenditure necessary to attain the utility 5 as a function of the prices p: and py, and the target utility E itself. If the prices are P: = 1, P1: = I, obtain the expenditure necessary to attain the utility E = 11116. (3 marks} (Q2) What is Georgina's utility-maximising bundle if her income is M = 16 and prices are p: = 3 and Pi: = 1? What utility does she attain? (2 marks) (d) The owner of the store where Georgina buys her grooeries has a special offer: any customer that buys more than 2 units of pasta is charged only p; = l per unit for any quantity in excess of 2 units (but for the first two units of :1: customers still have to pay p: = 3 per unit}. Recall that Georginals income is M = 16 and p3,, = 1 (d1) What is (are) the equation(s) describing Georgina's budget line under this special offer? (2 marks} (d2) What is Georgina's optimal consumption with this special offer? (3 marks}