Consider two young twin brothers named Lucas and Joshua. They allocate their income, coming from birthday gifts and weekly allocations, towards games and candies. Lucas and Joshua spend all their money on games and candies and decide jointly on money allocation. Their budget constraint is therefore:

m = pG^G + pC^C Note here that G denotes money spent on games, and C denotes money spent on candies.

In this example:

U(G,C)=200[G^0.5 +C^0.5]^-4 +500

m = 600 pG = 30 pC = 15

(a) Calculate the MRS and interpret. Use G on x axis. (b) Calculate the optimal bundle for G and C (use MRS = SBC) (c) Draw the budget curve line with numbers (slope and number on x and y axis). Put G on x axis. (d) Use the Lagrangian to solve for the optimal bundle for G and C (instead of MRS = SBC)