preferably the mathematical equations should be proper, as I find it difficult to understand if done normally by a keyboard.
1209 PM Tue 29 Sep ?1100%- B doc-OO-cOappsviewergoogleusercontentcom Question 1 (4 points) Consider Logan, a consumer who has preferences represented by the utility function, U = [1% + J i, where H represents the number of healthy meals Logan consumes per week and J represents the number of unhealthy (junk) meals that Logan consumes per week. Logan has an income of Rs.42 per week. The price of healthy meals and unhealthy meals are each Rs.2 per meal. a. (2 points) Find Logan's utilitymaximizing consumption bundle. b. (1 point) What proportion of the meals that Logan consumes are healthy? c. (1 point) Now suppose that Logan's parents offer to pay for 50% of Logan's healthy meals, thereby lowering the price of a healthy meal to Re.1. Find Logan's new utilitymaximizing consumption bundle. Now what proportion of the meals that Logan consumes are healthy? Question 2 (8 points) Anusha has preferences over wheat and cars given by the utility function u(I1, 222) = 10\\/:_1+ .732 where 3:1 denotes how much of wheat she consumes and I2 denotes how many cars she has. The budget constraint of Anusha can be expressed as 101121 + 102352 = m, where p1 and 192 are the prices of wheat and cars. a. (2 points) Write an expression for Anusha's demand for wheat. Show your steps. b. (2 points) Write an expression for Anusha's demand for cars. Also, derive an expression for the income range, keeping prices xed, at which Anusha will demand zero number of cars. Please show your steps. (Note that this expression will take the form in E [0, f (191, 102)] where f (pl, 192) is function of two prices.) c. (2 points) Derive the demand for wheat and cars if (101, p2,m) = (1,2,9). Briey explain your answer. (1. (2 points) Given prices (101,392) 2 (l, 2), what is the minimum amount of income at which Anusha will demand positive amount of both the commodities? 1209 PM Tue 29 Sep ?1100%- B doc-OO-cOappsviewergoogleusercontentcom Question 3 (4 points) Suppose Avinash consumes tea and coffee. His demand for tea is given by gt = m20pt+20pc, where m is the income, pt is the price of tea, pC is the price of coffee and qt is his consumption of tea. Avinash's income is Rs. 1000 and the price of coffee is Rs. 10. a. (1 point)Write the inverse demand function for tea and plot it on a graph. b. (1 point) Suppose the prices of coffee and tea are both equal to Rs.10 and income is m. Write down an expression for the engel curve and draw it on a graph. G. (2 points) Is coffee a substitute for tea or a complement? Explain your answer. Question 4 (4 points) There are three commodities available for consumption. In week 1, the prices of these com- modities are (p1,p2, p3) = (4, 2, 2) and you observe Antwan consume quantities (q1, (12, (13) = (6, 3, 2). In week 2, the prices of the commodities are (101,102,173) = (3, 4, 1) and you observe Antwan consume quantities(q1,q2, q3) = (2, 4, 6). In week 3, the prices of the commodities are (131,102,123) = (1,5,2) and you observe Antwan consume quantities (q1,q2,q3) = (4, 2, 8). You may assume that Antwan has monotonic and convex preferences. a. (2 points) Show that Antwan's choices satisfy the Weak Axiom of Revealed Preference (WARP). b. (2 points) D0 Antwan's choices satisfy the Strong Axiom of Revealed Preference (SARP)? Explain
