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# Sample Paper - S ample Paper Attempt All Questions Q 1 A...

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Sample Paper Attempt All Questions: Q # 1: A company estimates that the demand for its product fluctuates with the price it char4ges. The demand function is: = , - q 280 000 400p where q equals the number of units demanded and p equals the price in dollars. The cost function is estimated as: = , + + . C 350 000 300q 0 0015q2 a) Determine how many units should be produced in order to maximize annual profit. b) What price should be charged? c) What is the annual profit expected to equal? Q # 2: An individual’s utility function is given by: = + . + . - . - . U 10x1 4 5x2 0 05x1x2 0 02x12 0 01x22 a) Determine the values of & MU1 MU2 when = . & = . x1 1 3 x2 5 Hence, estimate the change in utility if the x1 increases by one unit and x2 increases by 15 units. b) Does the law of Diminishing Marginal Utility hold for this function? Q # 3: Verify Euler’s theorem for the Cobb–Douglas production function: = Q AKαLβ NOTE: this is a homogeneous function of degree + . α β 1 | P a g e

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Q # 4: a) The owner of a grocery store purchases 50 glass items, used for decoration, to sell at \$15 each. The owner knows from the past experience that about 6% of
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Sample Paper - S ample Paper Attempt All Questions Q 1 A...

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