Question

Construct a utility function for a car-tire scenario where by a consumer derives satisfaction for every...

Construct a utility function for a car-tire scenario where by a consumer derives satisfaction for every group of 1 car and 4 tires. Now suppose cars cost x and tires cost y each. If a consumer has income M, solve the utility maximization problem facing the consumer.

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Answer #1

Answer :-

As we know that, car and tyres are complementary goods because they are always use together in a fixed proportion.

Therefore, utility function for perfect complement can be written as,

U(C, T)= Min [C, (1/4) T], where,

C= Quantity of car

T= quantity of tyres

These are used in fixed proportion,therefore

C = (1/4)T

4C = T ———(1)

Budget line: Cx + Ty = M ———(2)

Using equation 2 in equation 1 in budget line: Cx+ 4Cy= M

C(x+4y)= M

C= M/(x+4y); Use this in equation 1,

Utility maximization

4 [M/(x+4y)] = T

The above equation is the Utility maximization quantity of Tyre.

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