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{"sheet":"Intro","index":0,"n_rows":46,"n_cols":1,"rows_kept":46,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["This file has a numerical example of a well-behaved utility function that exhibits Giffen behavior."]
[]
["Activity Title"]
["An Excel Spreadsheet Numerical Example of a Giffen Good"]
[]
["Author"]
["Humberto Barreto"]
["hbarreto@depauw.edu"]
["Please contact me if you run into problems or have questions."]
[]
["Summary"]
["This file enables a professor or student to use Excel to generate Giffen behavior. It provides a concrete example of a utility function "]
["that exhibits the paradoxical property that more of a good is purchased as its price rises, ceteris paribus. For every price increase,"]
["optimal consumption is tracked and it is obvious that an upward sloping demand curve is created."]
[]
["Goals"]
["This example provides an opportunity to review these basic concepts in microtheory:"]
["Utility maximization subject to a budget constraint (including the canonical indifference curve graph)"]
["The marginal condition for optimality: MRS = p1/p2"]
["Comparative statics: changing an exogenous variable (p1), holding everything else constant, and tracking the response of optimal values of endogenous variables (x1* and x2*)"]
["Giffen behavior: increasing x1* as p1 rises, ceteris paribus"]
["The behavior is true only for a range of values, Giffenness is a local phenomenon"]
[]
["Context for Use"]
["This simple example is ideally suited for an undergraduate Intermediate Microeconomics course. The professor can use computer "]
["projection to walk through the example or have students follow along in a computer lab. It can serve as a one-time example to give"]
["students a taste of Excel or as part of a course that uses Excel more frequently. The primary contribution is the utility function combined"]
["with Solver to easily find optimal solutions at different prices. The content is standard and surely covered by every Micro course."]
["The example could also be used in a lower level, Introductory Economics class as an advanced topic. Since there is an analytical solution"]
["(using the Lagrangean Method), the example would also be suitable for an Advanced Micro or Math Econ course. The math is worked"]
["out in the zip file available at www.depauw.edu/learn/microexcel."]
[]
["Original Source"]
["The Case of a \"Giffen Good\""]
["Author: Uriel Spiegel"]
["The Journal of Economic Education, Vol. 25, No. 2 (Spring, 1994), pp. 137-147"]
["www.jstor.org"]
[]
["Additional Information"]
["Other utility functions, extensive bibliographic references, and clearly solved reduced form expressions for the optimal solutions are available here:"]
["Intermediate Microeconomics with Microsoft Excel"]
["Humberto Barreto"]
["Cambridge University Press (2009)"]
["www.depauw.edu/learn/microexcel"]
["The chapter text and accompanying Excel workbook is available as a zip file:"]
["http://www.depauw.edu/learn/microexcel/MicroBook/MicroExcel/1.ConsumerBehavior/4.CompStatics/5.GiffenGoods/1.4.5.GiffenGoods.zip"]

{"sheet":"InstructorNotes","index":1,"n_rows":61,"n_cols":5,"rows_kept":61,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["This sheet provides step-by-step instructions for using this file."]
["The Intro and Quotes sheets can be deleted or modified as desired. I suggest using the quotes to spice up a lecture."]
["This sheet should be deleted or hidden."]
[]
["Preparation"]
["1) Open the file so the Example sheet is displayed."]
["2) Review utility maximization (tangency of the highest attainable indifference curve to the budget constraint) with the graph above."]
["3) Point out that the marginal condition for optimality, MRS = p1/p2, is met."]
["4) Remind students that a demand curve is derived by changing p1, ceteris paribus, and tracking the response of x1*."]
[null,"It is a good idea to present the indifference curves and budget constraint graph and derive a typical downward sloping demand curve."]
{"$rows_empty":10}
["To use this file to demonstrate Giffen behavior:"]
["1) Change p1 (in cell B16 of the Example sheet) to 1.05"]
["2) Run Excel's Solver (in the Data tab in Excel 2007 or greater, in the Tools menu in previous versions -- use Help if needed)."]
[null,"All of the information is provided -- simply click Solver to find the new optimal solution."]
["3) Fill in the second row in the Demand curve table (starting in cell L15): enter 1.1 in cell L18 and the new optimal x1* in cell M18."]
[null,"There's no doubt about it --- that's a Giffen good! The price went up from p1=1 to 1.1 and x1* INCREASED."]
[null,"Notice also that x2* dropped by a huge amount."]
[null,"At this point you can say, \"Well, this explains the complicated function -- it's going to be weird if it gives us a Giffen good!\""]
["4) Repeat steps 1, 2, and 3 for p1=1.1."]
[null,"It happened again!"]
["5) Draw an XYScatter chart of the data to show the upward sloping demand curve."]
["Here is what your completed table and chart should look like (the one on the left is x1*=f(p1) and the one on the right is the inverse demand curve):"]
[]
[null,null,"Demand Curve for x1"]
[null,null,"p1","x1*"]
[null,null,1,44]
[null,null,1.05,45.9,45.90529272623392]
[null,null,1.1,48.6,48.60759489186996]
[]
[]
["Emphasizing Giffenness"]
["1) Reset p1=1 and run Solver to return to the initial solution."]
["2) Change p1 (in cell B16 of the Example sheet) to 0.9 -- a p1 decrease"]
["2) Run Excel's Solver"]
[null,"Giffenness again! A p1 decrease leads to an x1* DECREASE"]
[]
[]
["Advanced, Optional Material"]
["Use the data to compute price elasticities of x1* and x2*"]
["Use the example to show that the function does not always exhibit Giffenness"]
[null,"1) Set p1=0.5 and run Solver."]
[null,"2) Change p1 to 0.6 and run Solver."]
[null,"x1 is no longer Giffen -- p1 rose and x1* fell, just as expected. "]
[null,"Lesson: Giffenness is a local phenomenon."]
["Drive p1 so high you get a corner solution."]
[null,"Set p1=1.2 and run Solver."]
[null,"The consumer buys no x2."]
["Trigger a disastrous result with Solver. This is rather complicated. Download the zip file if interested:"]
["The chapter text and accompanying Excel workbook is available as a zip file:"]
["http://www.depauw.edu/learn/microexcel/MicroBook/MicroExcel/1.ConsumerBehavior/4.CompStatics/5.GiffenGoods/1.4.5.GiffenGoods.zip"]
["Here is a quick summary of the idea: a utitliy function that exhibits Giffenness is used, but it's indifference curves have a local maximum that can confuse Solver:"]

{"sheet":"Example","index":2,"n_rows":28,"n_cols":38,"rows_kept":28,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["This sheet uses a well-behaved utility function that yields a Giffen x1 (over a certain price range)"]
[]
[]
[]
[]
["Goal",{"$nulls":21},"U",2535.5,"fixed level of utility"]
["max Utility",2535.5,{"$nulls":20},"step",2,"amount of the change in x1",{"$nulls":4},"change U",0]
[{"$nulls":22},"solve quadratic 0=(d/2)x2^2 + cx2 - (U-ax1 + (b/2)x1^2)"]
[{"$nulls":23},"(-b +/- sqrt(b^2 - 4ac))/2a"]
["Endogenous Variables",{"$nulls":33},"Not Used"]
["x1",44,{"$nulls":21},"U = 2535.5",{"$nulls":6},"U = 2535.5",{"$nulls":4},"U = 2535.5"]
["x2",11,{"$nulls":21},2535.5,null,null,null,"initial","new",null,2535.5,{"$nulls":4},2535.5]
[{"$nulls":22},"x1","x2","Dx2/Dx1","dx2/dx1","x1 budget constraint","x2 budget constraint",null,"x1","x2","Dx2/Dx1","dx2/dx1",null,"x1","x2","Dx2/Dx1","dx2/dx1"]
[{"$nulls":22},36,20.540659228538015,null,1,0,55,55,36,20.540659228538015,null,null,null,36,70.43055555555556,null,-1.9564043209876543]
["Exogenous Variables",{"$nulls":10},"Demand Curve for x1",{"$nulls":10},38,17.973665961010276,-1.2834966337638694,1,5.5,49.5,49.5,38,17.973665961010276,-1.2834966337638694,null,null,38,66.72368421052632,-1.853435672514621,-1.7558864265927978]
["p1",1,"price of x1",{"$nulls":8},"p1","x1*",{"$nulls":9},40,15.492422502470642,-1.240621729269817,1,11,44,44,40,15.492422502470642,-1.240621729269817,null,null,40,63.3875,-1.668092105263156,-1.5846875]
["p2",1,"price of x2",{"$nulls":8},1,44,{"$nulls":9},42,13.142135623730951,-1.1751434393698457,1,16.5,38.5,38.5,42,13.142135623730951,-1.1751434393698457,null,null,42,60.36904761904762,-1.5092261904761912,-1.437358276643991]
["m",55,"income",{"$nulls":19},44,11,-1.0710678118654755,1,22,33,33,44,11,-1.0710678118654755,null,null,44,57.625,-1.3720238095238102,-1.3096590909090908]
["a",100,"coefficient for x1",{"$nulls":19},46,9.198039027185569,-0.9009804864072155,1,27.5,27.5,27.5,46,9.198039027185569,-0.9009804864072155,null,null,46,55.119565217391305,-1.2527173913043477,-1.1982514177693762]
["b",2,"coefficient for x1",{"$nulls":19},48,7.944271909999159,-0.6268835585932049,1,33,22,22,48,7.944271909999159,-0.6268835585932049,null,null,48,52.822916666666664,-1.1483242753623202,-1.1004774305555556]
["c",1,"coefficient for x2",{"$nulls":19},50,{"$error":"#N/A"},{"$error":"#N/A"},1,38.5,16.5,16.5,50,{"$error":"#N/A"},{"$error":"#N/A"},null,null,50,50.71,-1.0564583333333317,-1.0142]
["d",1,"coefficient for x2",{"$nulls":19},52,{"$error":"#N/A"},{"$error":"#N/A"},0,44,11,11,52,{"$error":"#N/A"},{"$error":"#N/A"},null,null,52,48.75961538461539,-0.975192307692307,-0.9376849112426036]
[{"$nulls":25},1,49.5,5.5,5.5]
[{"$nulls":25},1,55,0,0]
[]
["Constraint",0,"income left over"]
[{"$nulls":6},"-p1/p2","MRS at x1, x2"]
[{"$nulls":6},-1,-1]

{"sheet":"Quotes","index":3,"n_rows":40,"n_cols":12,"rows_kept":40,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Giffen Goods Quotations"]
["Giffen Good, Giffen behavior, Giffenness:"]
[null,"Price and quantity demanded positively related, ceteris paribus"]
[null,"An upward sloping demand curve"]
[null,"A good so inferior that the income effect swamps the substitution effect"]
[null,"A perverse, paradoxical, counter-intuitive result"]
[]
[]
[]
[]
[]
[]
[{"$nulls":11},"George Stigler, \"Notes on the History of the Giffen Paradox\""]
{"$rows_empty":16}
["Dwyer and Lindsay, \"Robert Giffen and the Irish Potato\""]
{"$rows_empty":9}
[{"$nulls":8},"Sherwin Rosen, \"Potato Paradoxes\""]