Jane and Duncan separate their incomes, mJ and mD (respectively), between pints of Cider, C, and pints of rum, R. The price of one pint of cider is PC; the price of one pint of rum is PR. Jane's preferences are shown by the utility function, UB(C, R) = 2C + 5R. Duncan's demand for Cider is Cl = 3mL/4pC .

(a) Jane has C > 5 pints of cider and R pints of rum. If she gives up 5 pints of cider, how many pints of rum must she gain to remain indifferent?

(b) Solve for Jane's demands of Cider and Rum.

(ci) Suppose a 1 tax is levied on cider. Explain why Jane might have the same utility before and after the tax.

(ii) Holding all else constant, can Duncan ever be indifferent to a 1 tax on Cider? Explain why.

d) Prices are PC = PR = 2. Draw Duncan's Engel curve for rum and label the slope. Put mL on the horizontal axis and R on the vertical axis.

(e)Duncan's income is mL = 16. The price of Rum increases to 4. For Duncan : Compute the total effect of the price change on consumption of rum and decompose the total effect into income and Slutsky substitution effects.