1. Assume that Matts utility from consuming good X and good Y is given by the following Cobb Douglas utility 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 (M) of 1000 to spend on the two goods. a. Using the Cobb-Douglas 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. Show all working and explain your answers. b. Assume PX decreases from 25 to 20 while PY and M remain unchanged. Using the Cobb-Douglas Marshallian demand functions, calculate Matts new optimal consumption bundle and the utility it provides. Show all working and explain your answers. c. Calculate the income and substitution effects of the decrease in price of good X from 25 to 20 on both X and Y using i. The Slutsky decomposition ii. The Hicksian decomposition Show all working and explain the method and answers. d. Using the expenditure function for these preferences calculate the compensation variation and the equivalent variation of the price decrease of good X from 25 to 20. Show all working and explain the economic interpretation of your answers. e. Using the Hicksian demand function for Cobb-Douglas preferences, 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. Show all working and explain your answers. f. Using your results from all 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 and slopes of all four budget constraints. ii. The optimum consumption bundles both before and after the price increase. iii. The compensating and equivalent variation of the decrease in the price of good X. (NB Remember the units of good Y are on the Y axis, are not a composite good.) iv. 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. 2. Using an indifference curve diagram, illustrate and explain the deadweight welfare loss of a per unit tax. Use both compensating and equivalent variation in your answer.