Question 1

Consider two young twin brothers named Luca and Josh. They allocate their income, coming from birthday gifts and weekly allocations, towards games and candies. Luca and Josh spend all their money on games and candies and decide jointly on money allocation. Their budget constraint is therefore: m = pGG + pCC

Note here that G denotes money spent on games, and C denotes money spent on candies. In this example:

U(G, C) = 40[G 0.5 + C 0.5 ] 1 + 40

m = 300

pG = 25

pC = 5

(a) Calculate the MRS and interpret. Use G on x axis. (5 points)

(b) Calculate the demand function for G and C (use MRS = SBC) (10 points)

(c) Draw the budget curve line with numbers (slope and number on x and y axis). Put G on x axis. (5 points)

(d) Use the Lagrangian to solve for the demand function for G and C (instead of MRS = SBC) (10 points)