Mypreferenceshavechanged Sothatidon Tlikesugarasmuchasididbefore Thismeansthati

  1. “Mypreferenceshavechanged,sothatIdon’tlikesugarasmuchasIdidbefore.ThismeansthatInowhaveasteeperbudgetline.”Canthisstatementbetrue,orisitfalse?Explainwhy.
  2. MypreferencesarerepresentedbytheutilityfunctionAx10.5+x2.Mymarginalutilityfromgoodoneisequaltothemarginalutilityfromgood2whenIhave4unitsofgood1.WhatdoyouthinkthenumberAis?Proveyouranswer.
  3. Drawtheindifferencecurvefortheutilityfunctionu=x10.5+x2forthefixedutilitylevelu=3.(identifythreepointsontheindifferencecurvewherex1=0,x1=1andx1=4).
  4. Is the utility function in question 3 above representing preferences that are (i) monotonic? (ii) convex? Where do you know?
  5. Drawtheindifferencecurvefortheutilityfunctionu=x12+x2forthefixedutilitylevelu=9.(identifyonthefigurefourpointsontheindifferencecurvewherex1=0,x1=1,x1=2andx1=3).
  6. Is the utility function in question 5 above representing preferences that are (i) monotonic? (ii) convex? Where do you know?
  7. Obtaintheexpression(formula)ofthemarginalrateofsubstitutionfortheutilityfunctionu(x1,x2)=ln(x1)+ln(x2).Forwhatquantitiesofx1andx2isthisconsumerwillingtogiveuponesmallunitofx1togetanadditionalsmallunitofx2?
  8. (i) Obtain the expression (formula) of the marginal rate of substitution for the utility function u(x1, x2) = x10.75 x20.25. (ii) Suppose the consumer has ten units of each good. How many small units of x2 should be given to take one small unit of x1 so that the consumer’s utility remains the same? (iii) Answer the same question when the consumer has 10 units of good 1 and 100 units of good 2. (iv) What common explanation or justification can you offer for the different rates of substitutions in cases (ii) and (iii)?
  9. Theutilityfunctionisu=min{x1,3×2}.(i)Drawthreeindifferencecurvesforthreedifferentutilitylevels,u=1,2and3.(ii)Onaseparatefigure,drawthebudgetlinewithm=40,p1=1andp2=1.Findandidentifyonthefiguretheoptimalchoice(x1*,x2*)oftheconsumerwithutilityfunctionu=min{x1,3×2}.(iii)Ifthepriceofgood1increasessothatp1=2,howmuchextra(additional)incomeshouldbegiventotheconsumersothathereachesthesameutilitylevel(indifferencecurve)asinpart(ii)?
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