ans to problem set3 f06

# Intermediate Microeconomics: A Modern Approach, Seventh Edition

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p /p x y = 1 PCC y x u=x+y y x PCC u=min{x,y} Econ 301 – F06 PROBLEM SET 3 - ANSWERS Wissink 1. For changes in Px, diagrammatically show what the price offer/consumption curve (POC = PCC) looks like for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. y x POC/PCC u=xy

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ICC u=xy y x ICC u=min{x,y} y x 2. For changes in I, diagrammatically show what the income consumption/offer curve looks like for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. 3. For changes in Px, diagrammatically show the income and substitution effects ala’ Hicks for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. See next page. 2 y x indifference curves budget lines ICC Suppose "x" costs less than "y" u=x+y
y x u=xy E E E 0 1 H x y indifference curves budget lines u=x+y E E = E 0 H 1 suppose px<py y x u=min{x,y} E 0 H E = E 1 4. Derive the demand functions for x & y for the utility function: u(x,y) = y + bln(x). Assume values so that x>1. u(x,y) = y + bln(x) implies MRS = b/x. The ERS = Px/Py. At the optimal bundle it will be true that MRS = ERS which implies that b/x = Px/Py or, rearranging, that x* = b(Py/Px). Now substitute x* into the budget equation and solve for y*. From this you get: Px•b(Py/Px) + Py •y* = I y* = (I/Py) – b. 5. Initially a consumer with money income of \$100 chooses between goods x and y (there are no other goods) which have prices Px and Py both equal to \$2.00. The person is buying 30 units of x and 20 units of y. 3

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water \$aog E 1 E 0 IC IC 1 0 a. Graph the initial equilibrium. See diagram b. Now suppose that prices change so that Px = \$3.00 and Py = .50. What is the cost of the original bundle at the new set of prices? Is the original bundle affordable? \$100, yes c. Explain fully the consumer's final equilibrium position under the new set of prices and show it on your graph. New equilibrium must be on the bold section on the new budget line; e.g., E1. Consumer will buy less x and more y and end up on a higher indifference curve 6. Consider the following proposal to deal with the shortage of water in New York City this past summer.
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