3. Assume that Robertss 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. a. 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.b. Draw the demand curve for good X when PY = 35 and M = 1000.c. 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.d. Assume PX falls from 25 to 20, all other things equal. Using the demand functions, calculate Roberts new optimal consumption bundle and the utility it provides.e. Using the expenditure function calculate the compensation variation and the equivalent variation of the price decrease of good X from 25 to 20. f. Calculate the substitution and income effects of this price decrease. g. 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.
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