1. Assume that Matt's utility from consuming good X and good Y is given by the following Cobb Douglas utility function: U = 2X^0.75 Y^0.25 Where X is the quantity of good X while Y is the quantity of good Y. Assume the price of X (PX) is 5, the price of Y (PY) is 2.50, and he has a budget (M) of 1600 to spend on the two goods.

a. Using the Marshallian demand functions, calculate the quantities of X and Y Matt should purchase to maximise his utility. Calculate the utility this optimal consumption bundle provides. (You must clearly show all working and explain the economic intuition to receive marks for this question).

b. Assume PX decreases from 5 to 3 while PY and M remain unchanged. Using the Marshallian demand functions, calculate Matt's new optimal consumption bundle and the utility it provides. (You must clearly show all working and explain the economic intuition to receive marks for this question).

c. Calculate the income and substitution effects of the decrease in price of good X from 5 to 3 on both good X and Y using: - The Slutsky decomposition. - The Hicksian decomposition. (You must clearly show all working and explain the economic intuition to receive marks for this question).

d. Using the expenditure function for this utility function, calculate the compensating variation and the equivalent variation of the price decrease of good X from 5 to 3. (You must clearly show all working and explain the economic intuition to receive marks for this question).

e. Using the Hicksian demand function for this utility function, calculate the income and substitution effects of the fall in the price of good X holding utility constant at its new level after the price change i.e. the equivalent variation. Calculate the income and substitution effects on both the demand for X and Y. (You must clearly show all working and explain the economic intuition to receive marks for this question).

f. Using the results from all your answers to the previous questions illustrate the impact of the price decrease of good X from 5 to 3 on an indifference curve/budget constraint diagram. In particular, clearly explain and label:

- The intercepts and slopes of all four budget constraints.

- The optimal consumption bundles both before and after the price increase.

- The utility Matt obtains at his optimum consumption bundles both before and after the price increase.

- The compensating and equivalent variation of the decrease in the price of good X.

(NB Remember the units of good Y on the Y axis are not a composite good.) - The substitution and income effects of the decrease in the price of good X on both the demand for good X and good Y. Illustrate these substitution and income effects holding utility constant (a) at its original level and (b) at its level after the price change. NB Do not illustrate the income and substitution effects using the Slutsky decomposition as this will make the diagram very difficult to draw and read.