Suppose that agent's preferences are represented by a quasi-linear utility function u(m, t) = -m + In(t), where t c R+ + is the amount of toilet paper (measured in rolls) that the agent consumes, m E R, is the amount of other goods she consumes and k > 0 is a parameter (a given value and not a good consumed by the agent). Note that t and m are perfectly divisible throughout the problem. Let the price of m be 1 and the price of toilet paper be p > 0. (a) [2pt] Write down the expenditure minimisation problem of this agent. (b) [7pt] Solve the expenditure minimisation problem in (a) for arbitrary price p. > 0, utility level u > 0 and parameter k > 0. Suppose in the remainder of the problem that the price of a roll of toilet paper has the following schedule: $0.4 ift 2. Recall that toilet paper rolls are perfectly divisible. (c) [7pt] Find the solution to the expenditure minimisation problem if u = 10 for k E (0, 4]. (d) [4pt] Find the solution to the expenditure minimisation problem if u = 10 and k = 4.001. Explain, but you do not need to provide any calculations with your explanation