Economics Elasticity of income and Demand Questions

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I’m working on a economics multi-part question and need support to help me learn.

 

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= 1. Edith’s preferences over donuts (x) and croissants (y) can be represented by u(x,y) = min[2x,y). a) Find Edith’s Marshallian demand functions for donuts and croissants. b) If Px = 2, Py = 3 and I = 80 then how many donuts and croissants does she buy? Illustrate your answer in a diagram. c) If income rises to 88, then what will be her new best bundle? Illustrate the new budget line and best bundle in your diagram. d) Calculate the income and the own price elasticity of Edith’s demand for donuts. Write your answer as functions of prices and income only P/x The book derives the equality 0.73 +0,, = 1 where 0,4 = is the share of income spent on the x 1 good and Yx is the income elasticity of the x good, donuts (similarly Oy and Ny are the share of income and the income elasticity of the y good, croissants. e) Use your income elasticities above to verify that this expression holds for Edith’s demands. де f) In general (not just for Edith’s demands) how does Ox vary when I changes (i.e. find -)? ai g) If nx< 1 then what is the sign of the derivative in part (f)? If nx = 1 then what is the sign of the derivative in part (f)? If a good is a necessity then as income rises does the share of income spent on that good rise or fall? h) Given the income elasticity that you found for donuts in part (d) what will be the derivative of Ox with respect to I for Edith’s demands? i) Write 0x as a function of only prices and income for Edith’s demand for donuts. Verify your answer to part h (ie calculate the derivative directly to show that it equals your answer). j) The income-consumption curve (icc) shows how Edith’s consumption of donuts and croissants increases as her income increases. Illustrate the ice in your diagram above. X 2. Lionel eats ham (x) and cheese (y). The utility function u(x, y) = 0.25x + 2y0.5 represents his preferences. a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) increased? b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer. d) Holding prices constant, what is the effect of an incre

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