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2nd year microeconomic question please help explain.

Suppose that there are two goods (X and Y

). The price of X is $2 per unit, and the price of Y is $1 per unit.

There are two consumers (A and B). The utility functions for the consumers are

UA(x,y) = min{x,y}

UB(x,y) = min{2x,2y}

UC(x,y) = 2x+ 3y

UD(x,y) = 4x+ 6y

UE(x,y) = min{ax,ay},a>0

UF(x,y) =f(2x+ 3y), f(.) is a strictly increasing function

Consumer A has an income of $1000, and Consumer B has an income of $3000.

(a)Draw each consumer's utility curve (for consumers E and F explain in general how there utility would look like)

(b)solve the constrained utility-maximization problems for Consumer A and Consumer B

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