Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

The threshold level of asset is determined from . Substituting the numerical values yields or equivalently .

An ICC is determined from the perspective of a lender who is to approve or reject a loan. An entrepreneur can invest the loan and earn income that exceeds the cost of the loan. The loan application of a worker will be automatically rejected.

c) Calculate the threshold wage that leaves a credit-constrained individual indifferent between becoming a worker and a self-employed.

The wage that leaves a credit-constrained individual indifferent between becoming a worker and a self-employed is the solution of , which is .

d) Calculate the threshold wage that leaves a non-credit-constrained individual indifferent between becoming a worker and an entrepreneur.

The wage that leaves a non-credit-constrained individual indifferent between becoming a worker and an entrepreneur is the solution of the equation , which is .

e) Briefly describe the implications on technology use if the entrepreneur’s participation constraint is violated.

No individual would like to become an entrepreneur as they could earn a higher income by choosing a different occupation.

The entrepreneurial technology requires one entrepreneur and one worker. In the absence of entrepreneurs, all individuals will become self-employed.

f) Briefly explain why and and the critical wages for determining labour demand and labour supply.

These are the wages, for which individuals have an incentive to switch their occupation. This indirectly affects the size of labour demand and labour supply.

g) Briefly explain why the asset distribution does not affect your answer in part f). Hint: Compare your answer to the other asset distribution (70 % have and 30 % have ) we went over in the lecture notes.

The asset holdings and the return do not change if one chooses a different occupation.

h) Briefly explain you must analyze labour demand and labour supply at, below and above each of the wages and .

These are the only two wages at which quantity the labour demanded (share of entrepreneurs each of which demanding one worker) and/or the quantity labour supplied (share of individuals willing to become workers) change.

i) Determine the labour demand and the labour supply for each of the relevant wage ranges noted in part h). Justify your answer with the concept of an opportunity cost as well as the relationship between and .

1)

If , all non-credit constrained individuals want to become entrepreneurs () but no one wants to become a worker (). All credit constrained individuals want to become self-employed. A wage cannot be sustained as an equilibrium since .

2)

If , all non-credit-constrained workers want to become entrepreneurs and all credit-constrained workers are indifferent between becoming self-employed and becoming workers. This implies that . That is, a wage can be sustained as an equilibrium since there is a potential intersection between and .

For this to be an equilibrium, each entrepreneur must be matched with one worker, that is , due the production requirements of the entrepreneurial technology. In addition, no individual has an incentive to switch their occupation.

3)

If , all non-credit constrained individuals want to become entrepreneurs () and all credit constrained individuals want to become workers (). No one has an incentive to become self-employed. A wage cannot be sustained as an equilibrium since .

4)

If , all credit-constrained individuals want to become workers and all non-credit-constrained workers are indifferent between becoming entrepreneurs and becoming workers. No individual has an incentive to become self-employed. This implies that and . That is, a wage cannot be sustained as an equilibrium since there is no overlap between and .

5)

If , everyone wants to be a worker () but no one wants to be an entrepreneur () or self-employed. A wage cannot be sustained as an equilibrium since .

j) Draw a carefully labelled graph depicting the labour demand and supply curves as well as the labour market equilibrium.

k) Calculate the occupational distribution and the corresponding income distribution.

The labour market equilibrium results in:

· occupational distribution (shares individuals who become entrepreneurs, workers and self-employed), i.e., and .2,

· labour market outcomes in the entrepreneurial sector, i.e., employment and wage ,

· Income distribution: there is income inequality since ,

l) Verify that the modern technology is superior to the self-employment technology. Justify your answer.

Any pair of individuals operating the entrepreneurial technology as entrepreneur and worker generates more income than these same two individuals becoming self-employed.

m) Briefly explain why is the critical mass of credit constrained individuals that gives rise to a poverty trap for an economy.

The fixed proportions labour requirement of the modern technology ensures that there is a unique equilibrium, where 1/2 become entrepreneurs and 1/2 become workers. Since for this equilibrium, i.e., an individual is indifferent between becoming an entrepreneur and a worker, some individuals switch occupations until there is no exceed demand for workers or excess supply of workers.

n) Briefly explain why this critical mass depends on the technological requirement of the entrepreneurial technology.

For the entire population to use the entrepreneurial technology, each entrepreneur must be matched with one worker. For this to happen, at least one half of the population must be non-credit constrained.

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