Peter consumes no commodities other than Miller Lite and Bud Light. His annual budget for these two commodities is described by the equation 5x+30y = 300 where x is sixpacks of Miller Lite and y is cases of Bud Light. Peter considers 2 cases of Bud Light to be perfect substitutes for 6 sixpacks of Miller Lite. Which of the following is true?

(a) He will consume 60 sixpacks of Miller Lite per year.

(b) He will consume 10 cases of Bud Light per year.

(c) He will consume 14 cases of Bud Light per year.

(d) He will consume 12 sixpacks of Miller Lite per year.

(e) He is indi erent between anytwo bundles that use up his entire income.

Our answer is

Explanation: (a) He will consume 60 six packs of Miller Lite per year.

(a) He will consume 60 six packs of Miller Lite per year.

Explanation: Peter considers 2 cases of Bud Light to be perfect substitutes for 6 six packs of Miller Lite.

So, utility function is, U (x, y) = 2x + 6y

He will consume any one of the two goods because they are substitutes depending on the relationship between MRS and price ratio.

MRS = MUx/MUy = (dU/dx) / (dU/dy) = 1/6 = 1/3

5x+30y = 300

So, price of x, Px = 5 and price of y, Py = 30. Also, income (M) = 300

Price ratio = Px/Py = 5/30 = 1/6

So, MRS > Px/Py. Thus, only good x will be consumed because that will give him maximum utility at minimum cost.

So, x = M/Px = 300/5 = 60 and y = 0.

So, he will consume 60 six packs of Miller Lite per year.