4 6 Suppose that a consumers utility function for goods x, y and z is expressed according to the CobbDouglas utility function U(x, y, z) x 0 5y 0 5(1 z)0 5 Prices are given by px 1, py 4, and pz 8 Consumer income is given by I 8 a Determine the utility maximising quantity of good z consumed b c 4 7 a b c Explain why this quantity of good z is optimal Determine the minimum income required for the consumer to purchase product z

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Question: 4.6 Suppose that a consumers utility function for goods x, y and z is expressed according to the CobbDouglas utility function U(x, y, z) =

4.6 Suppose that a consumer’s utility function for goods x, y and z is expressed according to the Cobb–Douglas utility function U(x, y, z) = x 0.5y 0.5(1 + z)0.5.

Prices are given by px = 1, py = 4, and pz = 8.

Consumer income is given by I = 8.

Determine the utility maximising quantity of good z consumed.

4.7 a.

Explain why this quantity of good z is optimal?

Determine the minimum income required for the consumer to purchase product z.

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