Part A:

We have discussed several examples of constrained utility maximisation in lectures and in classes. For example, we have learned how to find the optimal bundle of goods consumed by an individual trying to maximise the utility they get from consuming goods under a specific budget constraint. With this exercise, we want to apply the same logic and the same method to a slightly different case of utility maximisation.

Let us assume that John's main passion in life is preparing delicious food. Every day, he must decide how to share his time (24h) between cooking C and other leisure activities N, that he also enjoys such as spending time with his friends, reading and sleeping. Lucky John does not worry about money! We can assume that his utility function is U(N, C) = C*N^0.5.

1. In a two-dimensional graph, with C on the horizontal axis and N on the vertical one, illustrate John's maximisation problem. You will need to draw John's actual constraint and a stylised indifference curve (we assume U is well behaved).

2. Calculate the slope of the constraint and the slope of the indifference curve represented. What do they tell us?

3. What is John's optimal choice of C and N?

4. John's girlfriend offers him a sophisticated mixer which allows him to get the same amount and quality of cooking done in a third of the time. Assuming that his utility function is unchanged, how does it change his optimal choice of C and N?

Part B:

Linda has a Cobb-Douglas utility function u(x, y) = x^ay^1-a, where 0 ≤ a ≤ 1 and where x is chocolates and y is flowers. Suppose that Linda's income is ??, and that the prices for chocolates and flowers are p_x and p_y respectively.

1. Derive the demand functions for chocolates and flowers.

2. Are these goods inferior or normal? Ordinary or Giffen?

3. Are x and y substitutes?

Part C:

Ebony eats eggs on toast every morning for breakfast. She will always have two pieces of toast for every egg she eats, as she sees eggs and toast as complements. At current prices, she has 3 eggs and 6 pieces of toast every morning.

If the price of eggs double, she will only be able to have 2 eggs and 4 pieces of toast. So the total effect of the price change is a reduction in the number of eggs consumed from 3 to 2 and a reduction of the number of toasts from 6 to 4.

Is egg a normal good for Ebony? What about toast?

Part D: - No more than 500 words for this section.

The current Tory government is determined to increase the quantity of labour supplied by women, and women with children in particular. Currently, women account for less than 42% of the labour force in the UK, and they are more likely to working part-time or in low paid jobs than their male counter-part. What type of policy intervention could the government use to reach this objective?

They are currently considering three options:

1. Increasing the tax-free allowance (or "Personal Allowance") of women by £5,000 per child. [Note: in 2015/16, UK tax-payers can earn up to £10,600 tax free, this is their "personal allowance", then the next £31,785 are taxed at the basic rate of 20%, any amount above £42,385 is then tax at the higher rate of 40%. Above £150,000 the tax rate is 45%. See table below for a summary.]

2. Subsidising childcare to offer 20h of free childcare weekly per child under the age of 5 (pre-schoolers), and over 6-month old.

3. Funding a new soap opera on the BBC, giving a positive image of working women, and working mums in particular.

Using graphs, logic and economic intuitions, show how these policies will impact on individual labour supply (you may want to discuss the decision to participate in the labour force as well as the decision to increase or decrease one's working hours) and explain why these policies may increase the quantity of labour supplied by women.

What would you recommend the government to do and why?

Table 1: UK tax rate 2015-16