Q1. Louis has $50 to decide on consuming Coffee (C, with price P_c) and Tea (T, with price P_t). He has utility function u(C, T) = 12C C²+ T.

a. Holding Louis' income I = $50, P_t= $1 but P_c= P as a variable, what is Louis' Demand Function on Coffee (use C_L^Das Louis' Quantity Demanded on Coffee)? Hint: You may not need to use the Budget Constraint here.

b. There is another person, George, also a Coffee lover. George has his (inverse) Demand on Coffee as: P = 63C_G^D. Assume there are only Louis and George in the market of Coffee, what is the Total Market Demand of Coffee (denoted by C_M^D)?

c. Plot Louis', George's and the Total Market's Demand of Coffee clearly in the same graph. Make sure you indicate the coordination of the kink point (if there is any) on the Total Market Demand Curve.

d. When PC = 4, what is the Total Market's Quantity Demanded and the Price Elasticity of Total Market's Demand at this point? Does the Coffee Supplier have the incentive to increase the price of Coffee?

IF YOU CAN ANSWER THESE 2 QUESTIONS, PLEASE DO SO

E. Suppose the inverse Market Supply is given as P = C_M^S. Plot it on the same graph in Q1c. What is the Equilibrium price and quantity? Can you do the analysis in Q1d.?

F. Given PC = 3, PT = 1 and keep Income I as a variable, derive the Louis' Income-Consumption Curve.