3. Assume that Roberts’s 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 Robert’s
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.