A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility function given by Ux,y=x+y-0.05x2-0.05y2 subject to

2x+5y=128

Where $128 is the consumer’s budget and the prices of the two goods are, respectively, 2 and 5. Assuming marginal utilities Ux, Uy > 0,

a. Find the quantity x and y that maximize the utility function.

b. Using bordered Hessian, check utility for a maximum.

c. What is the maximum utility of the consumer?

Expert Solution

Rahul Sunny answered 1 year ago

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility function given by Ux,y=x+y-0.05x2-0.05y2 subject to 2x+5y=128 Where $128 is the consumer’s budget and the prices of the two goods are, respectively, 2 and 5. Assuming marginal utilities Ux, Uy > 0, a. Find the quantity x and y that maximize the utility function. b. Using bordered Hessian, check utility for a maximum. c. What is the maximum utility of the consumer?

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility function given by Ux,y=x+y-0.05x2-0.05y2 subject to 2x+5y=128 Where $128 is the consumer’s budget and the prices of the two goods are, respectively, 2 and 5. Assuming marginal utilities Ux, Uy > 0, a. Find the quantity x and y that maximize the utility function. b. Using bordered Hessian, check utility for a maximum. c. What is the maximum utility of the consumer?

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility function given by Ux,y=x+y-0.05x2-0.05y2 subject to 2x+5y=128 Where $128 is the consumer’s budget and the prices of the two goods are, respectively, 2 and 5. Assuming marginal utilities Ux, Uy > 0, a. Find the quantity x and y that maximize the utility function. b. Using bordered Hessian, check utility for a maximum. c. What is the maximum utility of the consumer?

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A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

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