The citizens of country X consume only alcohol, x, and cigarettes, y. Each consu

Question

The citizens of country X consume only alcohol, x, and cigarettes, y. Each consumer has an income of I = 100, a utility function u(x, y) = min(x, y), and prices are initially px = 2, py = 3. The government, which is the sole purveyor of alcohol and cigarettes, wants to curb alcohol consumption by 20% and can choose either a per-unit tax or a lump sum tax to do so. If it chooses a per-unit tax on alcohol, determine the tax level that attains this reduction.

A. t = 1/2 B. t = 2/3 C. t = 0 D. t = 5/8. E. None of the above

Please show work.

Explanation / Answer

Let the initail equillibrium quantity of alcohol and cigarettes be 'X' and 'Y' respectively.

Then from the income constraint

2X + 3Y = 100 ------- (1)

Case 2, government wants to curb the alcohol consumption by 20% i.e reduce the alcohol consumtion by x/5

So it imposes a tax of 't' per unit of alcohol

Now from budget constraint equation,

(2 + t) (X - X/5) + 3Y = 100

(2 +t) 4X/5 + 3Y = 100 -------------(2)

Since equation (1) & (2) are equivalent, so equating its coefficients

(2+t)4/5 = 2

=> 2+t = 5/2

=> t = 5/2 - 2

=> t= 1/2

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