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# econ300-final-review-answers - For the next two questions...

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ECON300 Final Review Page 1 of 7 For the next two questions, the consumer’s utility 22 (, ) 3 4  Uxy x y x y depends on the consumption of two goods x and y . Assume the consumer selects x and y to maximize utility subject to the budget constraint x + y = 4. 1. Using the substitution method, determine the utility function () Ux that internalizes the constraint by solving to remove the y variable. A. 2 4 2 4 8 x x B. 2 6 8 1 6 x x C. 6 x D. 2 8 2 4 1 6 x x E. None of the above 2. What are the optimum values of the variables x and y ? A. x = 3, y = 1 B. x = 2/3, y = 10/3 C. x = 3/2, y = 5/2 D. x = 2, y = 2 E. None of the above For the next three questions, we have the same consumer’s utility 3 4 x y x y but different constraint x + 2 y = 1. 3. What is the Lagrangian function for the constrained situation? A. 34 ( 2 1 )   xy x y B. ( 2 1 ) x y C. ( 2 1 ) x y D. 2  x yx y x y E. None of the above 4. The marginal utility of good y is A. 2 32 4 x B. 624 x C. 42 x y D. 2 x y E. None of the above

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ECON300 Final Review Page 2 of 7 5. What is the utility maximizing level of x and y ? A. x = 1/3, y = 2/3 B. x = 2/3, y = 1/3 C. x = 8/21, y = 5/21 D. x = 5/21, y = 8/21 E. None of the above 6. A company has a cost function 2 29 1 5  Cx x , where x is the quantity of the raw material. Because of the limited supply, the quantity of the raw material x cannot exceed 8 units. The company wants to determine the material supply level such that the cost can be minimized. What is the Lagrangian function in this constrained situation? A. 2 1 5 ( 8 )  xx x B. 2 1 5 ( 8 )  x C. 2 1 5 ( 8 ) x D. 2 1 5 ( 8 ) x E. None of the above For the next two questions, suppose you have \$18 to buy apples x and oranges y . The price of apple is \$1/lb and the price of orange is \$2/lb. Your utility is (, ) l n2 4 l n Uxy x y . You seek to maximize utility subject to your budget constraint that the total cost cannot exceed \$18.
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econ300-final-review-answers - For the next two questions...

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