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In: Economics

Think of the following linear attributes model. There are three goods, x, y and z, available...

Think of the following linear attributes model. There are three goods, x, y and z, available at prices px=3, py=2 and pz=4.A consumer cares about attributes a1 and a2 and one unit of good x has a1x=3 units of a1 and a2x=2 units of a2. For good y and z, suppose a1y=6, a2y=1 and a1z=4, a2z=3. Suppose the consumer has the initial wealth (income)w=12. We assume the consumer will spend all her wealth.

(a)If the consumer wants to consume (a1,a2)=(16,8), how many units of x,y and z should she purchase?

(b)Suppose the consumer has utility function u(a1,a2)=min{a1,a2}. How many units of goods x,y and z will the consumer choose to consume (at optimum)?

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