Consider an individual who considers x1 and x2 to be perfect substitutes at a rate of 2:1 i.e. he gets the same utility from consuming 2 units of x1 as he gets from consuming 1 unit of x2. Let his utility function be given as: U=x1+2x

Furthermore, let the price of x1 be $1 and the price of x2 be $4, while his income is fixed at $20.
a) Graph the budget line with x1 on the x axis and x2 on the y-axis. (1 Marks)
b) On the same sketch above, graph two indifference curves. (Be careful about the rate of
substitution between both x1 and x2 and hence the slopes of the indifference curves). (2 Marks)
c) What is the optimal bundle chosen by the consumer? What is her utility at this level? (2 Marks)
d) Does the utility maximizing condition, i.e. MRS= MRT hold in this case? Why or why not? (2
e) How would your answer in part (c) change if the price of x1 increases and becomes $2? (3 Marks)