Assume that Adam’s utility from consuming good X and good Y is given by
the following function:
U = 4X
0.8Y
0.2
Where X is the quantity of good X while Y is the quantity of good Y.
Assume the price of X (PX) is £45, the price of Y (PY) is £15, and he has a
budget of £2250 to spend on the two goods.
a. Using the Lagrange multiplier, calculate Adam’s optimal
consumption bundle (You must clearly show all working and explain
the economic intuition to receive the marks for this question).
b. Calculate Adam’s utility at his optimal consumption bundle (You
must clearly show all working and explain the economic intuition to
receive the marks for this question).
c. Calculate  at Adam’s optimal consumption bundle and provide an
economic interpretation of its value (You must clearly show all
working and explain the economic intuition to receive the marks for
this question).
d. Illustrate your answers to all the previous parts to this question on a
clearly drawn and labelled indifference curve diagram. In particular,
illustrate and explain:
- The intercepts and slope of the budget constraint
- The optimum consumption combination.
- The optimal quantity of both goods.
- The level of utility at the optimum consumption bundle