Question

# Imran consumes two goods, X1 and X2. his utility function takes the form: u(X1, X2)= 4(X1)^3+3(X2)^5....

Imran consumes two goods, X1 and X2. his utility function takes the form: u(X1, X2)= 4(X1)^3+3(X2)^5. The price of X1 is Rs. 2 and the price of X2 is Rs. 4. Imran has allocated Rs. 1000 for the consumption of these two goods.

(a) Fine the optimal bundle of these two goods that Imran would consume if he wants to maximize his utility. Note: write bundles in integers instead of decimals.

(b) What is Imran's expenditure on X1? On X2?

(c) Do you find more than one bundle satisfying the first order conditions? Why?

Looking at the utility function, we need to determine what kind of utility function it is, for that you need to calculate MRS or Marginal rate of subsitution, in this question, MRS is of the form x/y which indicates the utility function isn't of convex form. As for convex or Max utility, always corner solutions are considered optimal.

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