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PracticeFinal - ECON 321 Intermediate Microeconomics Spring...

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ECON 321 Intermediate Microeconomics, Spring 2011 Jason Murray Practice Final 1. (10 points) My utility function over apples, x A , and bananas, x B , is given by: u ( A, B ) = x 2 A x B If the price of apples is $5 and the price of bananas is $10 , what is my optimal con- sumption bundle when my income is $20 . What is my utility level at my optimal bundle? Plot and label my budget line, optimal bundle and the indifference curve at my optimal bundle. If the price of apples were to increase by $1 what would happen to his banana consumption? 2. (10 points) My cousin’s utility function over apples, x A , and bananas, x B , is given by: u ( A, B ) = x A + 5 x B If the price of apples is $1 and the price of bananas is $1 , what is my cousin’s optimal consumption bundle when my income is $10 . What is his utility level at his optimal bundle? Plot and label my budget line, optimal bundle and the indifference curve at my optimal bundle. If the price of apples were to increase by $1 what would happen to my banana consumption? 3. (10 points) Al’s preferences over apples, x A and bananas, x B are represented by the Cobb-Douglas utility function; u ( x A , x B ) = x 3 A x 2 B . Derive Al’s individual demand curves for ham and cheese as functions of the prices and income. (HINT: The deriva- tive of u with respect to x A is 3 x 2 A x 2 B and with respect to x B is 2 x 3 A x B ). 4. (10 points) John is risk averse and has expected utility over any two possible out- comes: u ( c 1 , c 2 , π 1 , π 2 ) = π 1 c 1 + π 2 c 2 . He owns a lottery ticket worth 10,000 1
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with probabilty, .1. Otherwise the ticket is worth nothing. If you want to buy the ticket from John, what is least you can pay him for him to be willing to sell? 5. (10 points) Bernice’s preferences over x and y are given by: u ( x, y ) = min { x, y } . The price of x is 4 and the price of y is 2. Her income is 24. How much would we have to pay Bernice for her to accept the increase from 4 to 6 in the price of x? Use a graph to demonstrate this variation and tell me which kind of variation it is. 6. (10 points) There are two people in the market for red wine. Bill has demand: D B ( p ) = 400 - 10 p . Dan has demand: D D ( p ) = 300 - 6 p . Plot the market de- mand curve below. Make sure to note the price at which the demand curve has a kink. Write down the formula(e) for the market demand noting the price ranges for
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