5SSPP217 Microeconomics Assignment Brief 2026 | King’s College London

5SSPP217 Assignment Brief

Write your candidate number in the name of your file and at the top of the first page of your answers.

If you answer a question by showing just the solution or provide inconsistent, unexplained or too sketchy workings, your answer may receive a mark of 0.

You may either handwrite your answers or type the text and equations, whichever you prefer. In both cases, all graphs must be hand-drawn: draw them yourself on paper, then scan or photograph them (use one of the many scan apps available to keep file sizes reasonable) and insert them at the appropriate point in your document. Computer-generated or typeset graphs will not receive credit. Write your candidate number legibly on each hand-drawn figure.

Submit your answers well before the deadline to avoid stress and technical problems. Late submissions will be penalised as per DPE regulations.

For this assignment, use of generative AI is only allowed at Level 1 (”Minimal”), such as spell checkers and grammar check. For more information, check the College’s student guidance. Contravening this is a form of Academic Misconduct.

This problem set tells the story of three friends: Alice and Bob, who are two students, and John, who is a politician. Alice and Bob enjoy leisure (mostly by spending time together) and consumption. Denote by H_i and C_i the leisure and consumption student i = A,B enjoys in a week. The price of each unit of consumption is p (you can think of this as the composite price of the basket of goods they typically buy in a week). Similarly, denote by M_i the weekly stipend each of these students receives from their parents. In addition, Alice and Bob can work a few hours as tour guides to make some additional money. The wage they receive per hour worked is w. Once they subtract the time they must devote to study, sleep and chores, Alice and Bob have 40 hours per week available for leisure and work. However, the current labour regulations impose that students can work at most 20 hours per week. Assume perfect competition in the labour market and that Alice and Bob are price-takers.

1. [12 points] Find the expression for Alice’s budget constraint as a function of M_A, p and w. Then represent it in a hand-drawn, clearly labelled diagram with consumption on the horizontal axis. Your diagram must show all details, e.g., the axes, intercepts, for the particular case M_A = 48, p = 2 and w = 6.

2. [14 points] Alice’s preferences over weekly leisure and consumption are represented by the utility function u_A(C_A,H_A) = H_A(C_A)³. Use the Lagrange method to obtain her consumption demand and labour supply (denoted as L_A) as a function of M_A, p and w. Calculate Alice’s labour supply for the particular case M_A = 48, p = 2 and w = 6. Support this particular case with a hand-drawn, clearly labelled diagram in consumption–leisure space showing her budget set, at least one indifference curve and her optimal bundle, and use the diagram to explain why her optimum occurs where it does.

3. [14 points] Bob is a very particular person. He likes to consume exactly three units of consumption per each hour of leisure he enjoys. Are his preferences transitive? And monotone? Write the utility function that represents Bob’s preferences over consumption and leisure. Find his demand for consumption and his labour supply (denoted as L_B) as a function of M_B, p and w. Calculate Bob’s labour supply for the case M_B = 48, p = 2 and w = 6. Support this particular case with a hand-drawn, clearly labelled diagram in consumption–leisure space showing at least one indifference curve, the ray along which Bob’s optimal bundles lie, his budget constraint and his optimal bundle.

4. [20 points] John is very concerned about the state of public services in the region Alice and Bob live. He is contemplating two tax policies to obtain additional revenues for increased public spending. One policy is to tax wealth (that is, the stipends the two students receive) at 50%. The other is to tax all labour income at 50%. Assume M_A = M_B = 48, p = 2 and w = 6. Calculate the tax revenue under each policy and determine which one John should adopt to maximize revenue.

5. [20 points] Enters Mr Laffer, a very well-known economic advisor. Mr Laffer tells John that he must be wary of raising taxes too much because that may backfire and reduce revenue because Alice and Bob will work less the higher the tax on labour income. John asks for your advice. Call t the labour income tax (expressed as a decimal, e.g. t = 0.3 for a 30% tax), and assume throughout that 0 ≤ t < Find the total revenue obtained from labour income tax as a function of t when M_A = M_B = 48, p = 2 and w = 6. What t maximises that revenue?

Illustrate your answer with a hand-drawn, clearly labelled sketch of total labour-income tax revenue as a function of t, marking the revenue-maximising rate and the revenue it raises.

6. [20 points] John is very worried that the press, mainly The Phonograph and The Daily Fail, will attack his tax policies. He is considering introducing a mere 5% labour income tax and allowing students to work up to 40 hours per week. Calculate the tax revenue under this third policy and compare it to the revenue from the best policy (in terms of revenue) you found in section (4). Which of the three policies produces more revenue?

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