Question: 4. Consider a consumer who has utility function u(x, y) = min{2x, 3y}

Question

Question: 4. Consider a consumer who has utility function u(x, y) = min{2x, 3y} where x, y are amounts of goods X, Y consumed respectively.

(a) If px = 1, py = 1, consumer has total budget w = 10. What’s the optimal consumption bundle of this consumer? Explain in detail, using either graph or algebra to justify your answer.

(b) If there is an inflation which doubled the prices px, py as well as the wealth w. Consumer preference is still the same as before. What will be the consumer’s optimal consumption bundle in this case? Explain your answer clearly.

Explanation / Answer

u = min{2x, 3y}

Budget line: w = x.px + y.py

(a) Budget line: 10 = x + y

The utility function is a fixed-proportion consumption function and consumption is optimal when

2x = 3y

x = 3y / 2

Substituting in budget line,

10 = x + y = (3y / 2) + y

10 = 5y / 2

5y = 20

y = 4

x = 3y / 2 = 3 x 4 / 2 = 6

(b) New px = 2, py = 2, w = 20

New budget line: 20 = 2x + 2y

10 = x + y

So, budget line is unchanged, therefore optimal consumption is same as before, i.e.

x = 6, y = 4

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