Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

Expert Solution

Ans. Utility function, U = 2x + 3y

The utility function shows that the two goods are perfect substitutes, so, the consumer will only consume the good which is cheaper. So, consumer will consume x with all the income. Thus, consumption of x = 40 units and y = 0 units

For utility function, U = Min{x, 2y}

This utility function shows that the two goods are perfect complements, so, they must be consumed where,

x = 2y

Substituting this in the budget constraint, x + 2y = 40,

=> 2y + 2y = 40

=> y = 10 units and x = 20 units

Thus, the consumer will consume the bundle, (x,y) = (20,10)

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Rahul Sunny answered 2 years ago

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