iv. Imagine that the government raises a per-unit tax on good 2, which equals to 50% of its initial price. Discuss how this would change his optimal consumption levels of these three goods v. Imagine that Pankaj gets a promotion and becomes as senior web developer, which increases his hourly wage by 50%. Dis cuss how this would change his optimal consumption levels of these three goods. Q7. Pankaj is a junior web developer working for a major company. He divides his income between the consumption of goods 3:1, 3:2, and 3:3 and paying his rent. He can afford to buy one unit of 9:1 by working for one hour, 1 unit of 3:2 by working for two hours, and one unit of 1:3 by working for three hours. His rent costs him 40% of his income. His utility function is given by: u=mif2+$2+$y2 Assuming that Pankaj works for 40 hours a week: i. Write down Pankaj's weekly budget constraint and briefly describe his maximisation problem; ii. Set up the Lagrangian and find how many of 1:1, :52, and 333 he would consume per week to maximise his well-being; iii. What is the interpretation of the Lagrange multiplier? What does it tell us in this particular example? Q4. A firm produces three goods (G1, G2, G3) and sells them in a perfectly competitive market. Table 1 shows the number of units (in thousands) sold of each good along with the total revenue (in 1,000$) the firm raised by these sales in each calendar month of 2019. Find the equilibrium prices of these goods using matrices. Table 1: Sales and revenue by calendar month Nb. units sold Total Month G1 G2 G3 revenue January 5 5 3 46 February 4 6 2 42 March 7 3 46 April 3 40 May 63 June 5 4 33 July 4 37 August GWNAWNO 4 6 44 September 39 October 6 JWNAO 37 November 43 NA December 40