Kate has $75 to decide on consuming Coffee (C, with price PC) and Tea (T, with price PT ). She has utility function u(C; T) = 18C 3C2 + 2T.

a. Holding Kate' income I = $75, PT = $1 but PC = P as a variable, what is Kate' Demand Function on Coffee (use CD

K as Kate' 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 = 12 2CD

G . Assume there are only Kate and George in the market of Coffee, what is the Total Market Demand of Coffee (denoted by CDM )?

c. Plot Kate', 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 = 11, 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?

e. Suppose the inverse Market Supply is given as P = 1:5CSM . 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 Kate' Income-Consumption Curve.