ECON410 Practice Test _1

# ECON410 Practice Test _1 - Demand Curves: To solve...

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Demand Curves: To solve analytically for Demand Curves use the following steps: 1. Set up a constrained optimization problem using the specified utility function and a general budget line of the form I - p 1 x 1 - p 2 x 2 . Note I , p 1 , and p 2 are left as constants. 2. Solve the constrained optimization problem for the optimal x* 1 and x* 2 using one of the mathematical techniques we have established. Your results will be in terms of I , p 1 , and p 2 and are called your Demand Functions. 3. (Optional) To more easily plot your Good 1 Demand Curve, solve your optimal x 1 solution for p 1 . Plug in points for x 1 and plot the corresponding values of p 1 . To more easily plot your Good 2 Demand Curve, solve your optimal x 2 solution for p 2 . Plug in points for x 2 and plot the corresponding values of p 2 . Question 1: Assume an individual’s preferences can be represented by the Cobb-Douglas utility function: U(x1, x2) = x 1 1/2 x 2 1/2 Solve for her x 1 and x 2 demand functions then plot her Good 1 demand curve. Step 1: Set up a constrained optimization problem using the specified utility function and a general budget line of the form I - p1x1 - p2x2 . Note I , p1, and p2 are left as constants. Step 2: Solve the constrained optimization problem for the optimal x* 1 and x*2 using one of the mathematical techniques we have established.

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Step 3: Plot your Good 1 Demand Curve, solve your optimal x1 solution for p1. Plug in points for x1 and plot the corresponding values of p1. To more easily plot your Good 2 Demand Curve, solve your optimal x2 solution for p2. Plug in points for x2 and plot the corresponding values of p2. Law of Demand: demand curves should be downward sloping. In other words, if we are consuming our optimal constrained bundles, if the price of a good goes down we will purchase more of the good. We can directly check this by calculating the derivative of a good’s demand function and checking the sign of the derivative with respect to the price of the good. NOTE: The Law of Demand holds when the derivative is negative. If , the Law of Demand holds. Question 2: Assume we have determined that an individual’s demand functions are of the form: x 1 = Ip 2 / p 1 2 +p 2 and x 2 = Ip 1 / p 2 2 +p 1
Do both Goods 1 and 2 follow the Law of Demand? Step 1: Calculate the derivative for x 1 . Is the derivative negative? The Law of demand does / does not hold for Good 1. Step 2: Calculate the derivative for x 2 . Is the derivative negative? The Law of demand does / does not hold for Good 2. Elasticity: Elasticity A,B : Ɛ A,B “Elasticity of A with respect to B” “B Elasticity of A” The percent change in A that results from a percent change in B. Demand Elasticity

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## This note was uploaded on 01/05/2012 for the course ECON 410 taught by Professor Codrin during the Fall '07 term at UNC.

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ECON410 Practice Test _1 - Demand Curves: To solve...

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