[Please, you can ignore A, B and C, I only need Part D and E. Thank you]

Consider the labour pooling model. The individual worker is risk averse and their utility function is given by: () = where M is the income they earn from their job. The worker can choose to work for a firm in an isolated location or in a cluster. If the individual works in a firm in an isolated location, their income is 196. Assume initially that the switching cost in the cluster is zero and the probability of the worker losing their job in the isolated location is 50%.

(a) PLEASE IGNORE: Suppose the switching cost for the isolated site is initially 52. What income would firms in the cluster have to offer to attract employees from the isolated site (i.e. what is the certainty equivalent of the isolated job)?

(b)PLEASE IGNORE: Suppose the switching cost for the isolated site increases to 96. Calculate the new certainty equivalent value.

(c) PLEASE IGNORE: Suppose the probability of losing you job in the isolated location is now lower, at 30%. Calculate the new certainty equivalent value. Assume the switching cost is still 52.

(d) Suppose the switching cost in the cluster is now 20. How would your answer in a) change?

(e) Based on your answers above, what can you conclude about the advantages of larger cities (with more firms) in terms of labour pooling? How are these affected by differences in switching costs and in the probability of losing one's job in the isolated location?