- I Question 1 25 Marks A Man Has 24 Hours Everyday To Spend And Faces A Wage Rate Of W Pounds Per Hour By Choosing To 1 (91.15 KiB) Viewed 47 times
I Question 1 [25 marks] A man has 24 hours everyday to spend and faces a wage rate of w pounds per hour. By choosing to work for t hours, he earns an income of wt pounds which will be used for consuming two goods, denoted by 1 and 2. He gets utility from leisure (the time not spent for work) and from consumption of the goods, and his utility function takes the form of a{z}l}, where x; is the consumption of good i 1, 2, and l is the amount of leisure enjoyed. Let P1 £2 be the price of good 1, P2 £3 the price of good 2, and w = £14 the wage rate. (a) Derive his optimal consumption-leisure choice and indirect utility function. [18 marks] (b) Prove that his Marshallian demand function is homogeneous of degree zero in P1, P2, and w. [7 marks]