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handout 6 answers - MRS =(MU X/MU Y = Y/X 4 What does your...

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Microeconomics Handout 6 Microeconomics, Fall 2007, Dr. Laury A Mathematical Treatment of Demand Theory Let’s take our example with apple juice and sandwiches from the previous handout. So: Let Y =number of glasses of apple juice and X =number of sandwiches. Your utility function is of the form U(X,Y)= XY . You are told that the price of a glass of apple juice is $2 and the price of a sandwich is $5. Your income is $20 (and you spend all of your income on apple juice and sandwiches). 1. What is the marginal utility of X (i.e., MU X )? ( Hint: Take the derivative of the utility function with respect to X. ) MU X = Y 2. What is the marginal utility of Y (i.e., MU Y )? ( Hint: Take the derivative of the utility function with respect to Y. ) MU Y = X 3. What is the marginal rate of substitution of X for Y (i.e., the MRS)?
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Unformatted text preview: MRS = (MU X /MU Y ) = Y/X 4. What does your budget constraint look like? 20 = 5x + 2y 5. What is your optimal choice of glasses of apple juice ( Y ) and sandwiches ( X ) that you would consume? ( Hint: you will set MRS = P x /P y so that the slope of the indifference curve is equal to the slope of the budget constraint; this will give you the optimal ratio of the two goods. Next, you substitute this into your budget constraint to find the optimal quantity of each, given the prices and income you have.) MRS = (P x /P y ) (Y/X) = (5/2) 2Y = 5X Y = 2.5X Substitute this into the budget constraint: 20 = 5x + 2(2.5x) 20 = 5x + 5x 20 = 10x X = 2; y = 2.5X = 2.5(2) = 5...
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