Bunter derives utility from consuming two goods. Let xi denote the quantity if good i consumed.

His preferences over bundles (x1; x2) are represented by the following utility function:

U(x1; x2) = 3 ln x1 + ln x2

where ln stands for the natural logarithm.

The price per unit of good 1 is $5 and the price per unit of good 2 is $2 and Bunter's income is $100.

Hunter derives utility from consuming two goods. Let 1'.- denote the quantity if good i. consumed. His preferences over bundles {11,12} are represented by the following utility function: U{I],I:I = 3lnI1+ln12 where ln stands for the natural logarithm. The price per unit of good 1 is $5 and the price per unit ofgood 2 is $2 and Hunter's income is SIDE. 1. Is Hunter's utility function quasiconcaw? Horas.r do you llDW? [1 points] 2. The government implements an income tax. Let t be the fraction of income that the Gov ernment extracts. Write down Hunter's budget constraint. [1 points] 3. Assume t = DIED. Solve for the optimal demand of both goods and the amount collected in income tax. [2.5 points] Optimal quantity of good 1 purchased is: Optimal quantity of good '2 purchased is: Amount collected in income tax is: Justication: 4. A studyr from the University of Ruritania suggests that consumption of good 1 [which hap- pens to be Brando} is linked to poor cardiovascular health. To discourage consumption of good 11 the Govemment will impose a quantityr tax on good 1 only instead of an income tax. Good '2 is not subject to the quantity tax. The quantity tax will cost Hunter tr dollars per unit of good I that he purchases. The magnitude of v is set by the Government so as to raise the same amount of revenue collected in taxes as in part {c}. Using the same prices and income as before, nd this value of a and Eunter's new optimal demand for both goods. [2.5 points] Optimal quantity of good 1 purchased is: Optimal quantity of good '2 purchased is: The value of tr is: Justication: 5. lCompare the optimal utility levels attained in part {c} and [d]. Which tax scheme does Hunter prefer? [1 points] Maximum utility under income tax is: Maximum utility under quantity tax is: Hunter prefers: Justication