Questions   Assume that Jayden’s utility from consuming good X and good Y is given by the following Cobb Douglas utility function: U = X0

Questions  

1. Assume that Jayden’s utility from consuming good X and good Y is given by the following Cobb Douglas utility function:

U = X0.6Y0.4

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

Assume the price of X (P_X) is £25, the price of Y (P_Y) is £20 and he has a budget of £1000 to spend on the two goods. 

1. 1. Using the Cobb-Douglas demand functions, calculate the quantities of X and Y Jayden should purchase to maximise his utility. Calculate the utility this optimal consumption bundle provides. 
   2. Assume P_X increases from £25 to £50 while P_Y and M remain unchanged. Using the demand functions, calculate Jayden’s new optimal consumption bundle and the utility it provides.
   3. Using the expenditure function calculate the compensation variation and the equivalent variation of the price increase of good X from £25 to £50.
2. 4. Using the following expression for the Hicksian/compensated demand function: 

Calculate the substitution and income effects on good X of the increase in P_X from £25 to £50 using both compensating and equivalent variation.

1. 5. Using your results from all of your answers to the previous questions illustrate the impact of the price increase of good X from £25 to £50 on an indifference curve/budget constraint diagram. In particular, clearly explain and label:
      1. The intercepts and slope of the budget constraints.
      2. The optimum consumption bundles both before and after the price increase.
      3. The compensating and equivalent variation of the price increase. (NB Remember the units of good Y are on the Y axis, not a composite good.)
      4. The substitution and income effects of the price increase using both compensating and equivalent variation.
2. Using an indifference curve/budget constraint diagram, illustrate the compensating and equivalent variation of a price increase of an inferior good. Using this diagram:
3. 1. Derive a Marshallian demand curve.
   2. Derive a compensated demand curve holding utility constant at its original level i.e. before the price increase (compensating variation).
   3. Derive a compensated demand curve holding utility constant at its new level i.e. after the price increase (equivalent variation).  
   4. Compare and contrast the three monetary measures of welfare for a price increase of an inferior good i.e. EV, CV and ?CS. Compare the relative magnitude of EV and CV with your answers to question 1.
4. Under what circumstances would the three different measures of welfare (CV,

EV and the ?CS) provide similar monetary values? Make reference to the Slutsky equation in your answer. (Maximum 250 words, no diagrams required).