Math/Physic/Economic/Statistic Problems

You have to submit your answers to the questions on this guide study sheet as part of the assessment for this module. All diagrams must be hand drawn and scanned into the answers. I will not mark any diagrams cut and paste from a website.

Questions

  • Explain the limitations of using changes in consumer surplus as a monetary measure of the welfare impact of a price rise or fall.
  • Provide a clear and intuitive written explanation of both the compensating and equivalent variation of a price change. Assume the person reading your explanation has never studied economics before.
  • Assume that Roberts’s utility from consuming good X and good Y is given by the following function:

U = X0.3Y0.7 

Where X is the quantity of good X while Y is the quantity of good Y.

Assume the price of X (PX) is £25, the price of Y (PY) is £35 and he has a budget of £1000 to spend on the two goods. 

  • What is his demand function for X and his demand function for Y? Comment on the relationship between X and Y in consumption making reference to the cross price elasticity of demand in your answer.
  • Draw the demand curve for good X when PY = 35 and M = 1000.
  • Using the demand functions, calculate the quantities of X and Y Robert should purchase to maximise his utility. Calculate the utility this optimal consumption bundle provides.
  • Assume PX falls from £25 to £20, all other things equal. Using the demand functions, calculate Robert’s new optimal consumption bundle and the utility it provides. 
  • Using the expenditure function calculate the compensation variation and the equivalent variation of the price decrease of good X from £25 to £20.
  • Calculate the substitution and income effects of this price decrease.
  • Using your results from all of your answers to the previous questions illustrate the impact of the price decrease of good X from £25 to £20 on an indifference curve/budget constraint diagram. In particular, clearly explain and label (i) the intercepts of the budget constraints (ii) the slope of the budget constraints (iii) the optimum consumption bundles (iv) the compensating/equivalent variation of the price decrease and (v) the substitution and income effects of the price decrease.
  • Using an indifference curve/budget constraint diagram, illustrate the compensating and equivalent variation of a price decrease of an inferior good. Using this diagram:
  • Derive a Marshallian demand curve.
  • Derive a compensated demand curve holding utility constant at its original level i.e. before the price decrease (compensating variation).
  • Derive a compensated demand curve holding utility constant at its new level i.e. after the price decrease (equivalent variation). 
  • Compare and contrast the three monetary measures of welfare for a price decrease of an inferior good i.e. EV, CV and CS. Compare the relative magnitude of EV and CV with your answers to question 3. 
  • Using an example with two goods (X and Y), explain the key characteristics of a quasi-linear utility function e.g. the MRS, the demand functions for good X/good Y, the shape/slope of the indifference curves and the size of the income effect for a change in the price of X.
  • Under what circumstances would the three different measures of welfare (CV, EV and the CS) provide similar monetary values? Explain your answer making reference to the Slutsky equation.

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