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Econ 30041

Workshop 4

1. Poverty traps can also occur at a macro level for countries.  Consider the following table from Kraay and Mckenzie (Journal of Economic Perspectives, 2014).

(a) What can you deduce about the existence of poverty traps at the country level from the above table?

(b) Do you think that low average per capita GDP growth for countries in the second quintile implies the existence of a poverty trap?

2. Suppose an employer need 8000 units of work (in capacity units) to be performed, and they can hire all the labourers that you want.  Assume that all income earned by  the labourers is paid to them by the employer and that all income is spent on nutrition. The capacity curve for each labourer is described as follows: for all payments up to £100, capacity is zero and then begins to rise by 2 units for every additional pound. This happens until an income of £500 is paid out. Thereafter, an additional pound paid out increases capacity by only 1.1 units, until total income paid is £1000. At this point additional payments have no effect on work capacity.

If employer would like to get the work done in minimum cost

(i)  What would be the wage rate they should pay per unit of work?

(ii) Draw the labour supply curve.

(iii) If there are 100 employers in the society and 1200 workers, what would be the level of involuntary unemployment rate?

3. Consider the following utility function that individuals maximise

U = f α - p(1 - δθ)(B - c),         0 < α < 1, 0 < δ < 1, θ Œ [0,1],

subject to income

y = 2c + f,  where y = h(1 - θ) +P,  P Æ 0 .

f and c are respectively food and comfort goods, θ is the attention paid to home and  p is the probability of error happening at home. h is the human capital individuals are endowed with. Individuals decide on comfort goods and then on the level of θ .

[i] Find the optimal value of c.

[ii] Show that individuals with high h will always choose θ=0. Assume θ ∈{0,1}.

[iii] Find the optimal value of h, where anyone below it will choose θ=1.