1. Assume that Jayden's utility from consuming good X and good Y is given by the following Cobb Douglas utility function: U = X0-5Y0-4 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 (Pv) is 20 and he has a budget of 1 000 to spend on the two goods. a. 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. b. Assume Px increases from 25 to 50 while Pr and M remain unchanged. Using the demand functions, calculate Jayden's new optimal consumption bundle and the utility it provides. c. Using the expenditure function calculate the compensation variation and the equivalent variation of the price increase of good X from 25 to 50. d. Using the following expression for the Hicksianlcompensated demand function: X*=t7(%x::)'8 Calculate the substitution and income effects on good X of the increase in Px from 25 to 50 using both compensating and equivalent variation. e. 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 20 on an indifference curvelbudget constraint diagram. In particular, clearly explain and label: i. The intercepts and slope of the budget constraints. ii. The optimum consumption bundles both before and after the price increase. iii. 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.) iv. The substitution and income effects of the price increase using both compensating and equivalent variation