. Answer all parts (a)-(e) of this question. The question deals with agglomeration

economies and the urban labour market.

(a) [10 marks] Consider the theoretical framework of labour pooling. Suppose the wage

(w) offered by an isolated firm is $64 and there is a 50 percent chance of being fired

(r=1/2). The switching cost (s) is $28 and the utility function is u(i)= (i)1/2 where i is

income, and i=w-s. What is the expected utility of a job at the isolated firm? What is

the certainty equivalent of a job in the isolated site? If the moving cost in a cluster is

zero, what is the wage in the cluster?

(b) [10 marks] Consider the standard matching theoretical framework in a spatial context.

Workers are uniformly distributed along a roadway. Each firm chooses an address

along the roadway of unit length and hires two workers. The cost of commuting is

incorporated in the market wage: wage = 50+60d where d is the distance from the

worker to the nearest firm. Calculate the wage in (i) a city with 4 workers and 2 firms

and (ii) a city with 6 workers and 3 firms.

(c) [10 marks] Consider the theoretical framework of the size of the cluster. Consider

manufacturing firms that use advertising firms to develop marketing campaigns. The

marketing cost per manufacturing firm is M=120/n and the labour cost per

manufacturing firm is L=30n where n is the number of manufacturing firms in a local

labour market. The total revenue of manufacturing firm is R=$300 and profit is π=R- M-L. What is the number of manufacturing firms in the location in the efficient

outcome? In equilibrium, what is the number for manufacturing firms in the location?

(d) [10 marks] Imagine a hypothetic scenario of West Ham football team playing games

in Colchester. A consultant writes a report on the economic effects. The consultant

estimates that this would increase total spending in the Colchester economy by 61.6

million pound per year, computed as Δspending=s x N x m= £40 x 700,000 x 2.2,

where s is spending per football fan, N is the number of fans attending the games and

m is the average spending multiplier for the Colchester economy. Discuss the report,

assuming that the trainings would take place in London, and the players and coach

would live there. Is the increase overstated? [Think of an outsider as a person who

lives outside Colchester and an insider as a person who lives in Colchester.]

(e) [10 marks] Consider the theoretical framework of the local labour market. In the city

of Growille, the equilibrium employment is 100,000 workers and the equilibrium

wage is $100 per day. The wage elasticity of demand for labour is -1.0 and the wage

elasticity of supply of labour is 5.0. Suppose the demand for labour increases by 18

percent. What are the effects on the equilibrium wage and total employment?