There is Village A where the luxury axiom and the substitution axiom are satisfied (as discussed in Chapter 6). In this village, 200 households and 100 firms exist. Each household is composed of 4 household members: two adults and two children. One of the children is a teenage daughter and the other is a teenage son. The subsistence level of consumption for each individual is s = 2.5. One of the two adults in each household works on its private land and produces the value of agricultural output a = 3. The other adult earns a wage by working for a firm and decides whether to work at the firm with the two children. Regarding the labour input for firm’s production, one unit of child labour is equivalent to 0.5 units of adult labour. Accordingly, the child wage is half of the adult wage. Each firm produces output according to the following production function. Output = 16(Adult Equivalent Labour)^(1/2) We assume that the adults working on their private lands cannot work for firms. Wages, firms’ output, agricultural output, income, and consumption are measured in the same unit. Question 1) Find whether there is a unique equilibrium or multiple equilibria in Village A. Does child labour exist in equilibrium in this village? (For Question 1, you do not need to consider a case in which only one of the two children works.) (5 points) Question 2) Suppose that a drought shock hit Village A. The shock did not affect the firms, but all households experienced crop failure and produced zero agricultural output. Explain why the households in Village A suffer from hunger in this case. (3 points) Question 3) Corno et al. (2020) find that droughts increase the hazard ratio of child marriage in countries with bride price.1 Suppose that there is another village, Village B. Unlike Village A, Village B was not affected by the drought. Both villages have the custom of virilocality: i.e., a bride moves to the groom’s family and join his household upon marriage. Find the minimum value of bride price that the households in Village A would accept and marry off their daughters to Village B in order to overcome hunger. Briefly explain in words the incentives the households in Village A have in marrying off their daughters. (7 points) Question 4) Suppose that the households in Village A received the minimum value of bride price found in Question 3 and married off their daughters to Village B in response to the drought. The sons in Village A now consider whether to work in Village C where there are two different sectors: formal and informal. They aim to increase the total family income. Formal jobs pay 4 and informal jobs pay 1 in Village C. The wages are in the same unit of household income. The probability of getting a formal job is 40%. One who fails to be hired in the formal sector is automatically offered an informal job. Assume that there is no migration cost. Do you think that the sons in Village A will migrate and search for a job in Village C? Rationalise your answer. (5 points) Question 5) Suppose that the drought caused crop failure in Village A, but child mar- riage (daughters) and child migration (sons) have not happened yet. The government seeks not only to prevent child marriage and migration but also to resolve the issue of child labour in Village A. A policymaker suggests combining two policies: banning child labour and pro- viding emergency aid. Do you agree with the idea? Rationalise your answer. (5 points)
There is Village A where the luxury axiom and the substitution axiom are satisfied (as discussed in Chapter 6). In this village, 200 households and 100 firms exist. Each household is composed of 4 household members: two adults and two children. One of the children is a teenage daughter and the other is a teenage son. The subsistence level of consumption for each individual is s = 2.5.
One of the two adults in each household works on its private land and produces the value of agricultural output a = 3. The other adult earns a wage by working for a firm and decides whether to work at the firm with the two children. Regarding the labour input for firm’s production, one unit of child labour is equivalent to 0.5 units of adult labour. Accordingly, the child wage is half of the adult wage.
Each firm produces output according to the following production function.
Output = 16(Adult Equivalent Labour)^(1/2)
We assume that the adults working on their private lands cannot work for firms. Wages, firms’ output, agricultural output, income, and consumption are measured in the same unit.
Question 1) Find whether there is a unique equilibrium or multiple equilibria in Village A. Does child labour exist in equilibrium in this village? (For Question 1, you do not need to consider a case in which only one of the two children works.) (5 points)
Question 2) Suppose that a drought shock hit Village A. The shock did not affect the firms, but all households experienced crop failure and produced zero agricultural output. Explain why the households in Village A suffer from hunger in this case. (3 points)
Question 3) Corno et al. (2020) find that droughts increase the hazard ratio of child marriage in countries with bride price.1 Suppose that there is another village, Village B. Unlike Village A, Village B was not affected by the drought. Both villages have the custom of virilocality: i.e., a bride moves to the groom’s family and join his household upon marriage. Find the minimum value of bride price that the households in Village A would accept and marry off their daughters to Village B in order to overcome hunger. Briefly explain in words the incentives the households in Village A have in marrying off their daughters. (7 points)
Question 4) Suppose that the households in Village A received the minimum value of bride price found in Question 3 and married off their daughters to Village B in response to the drought. The sons in Village A now consider whether to work in Village C where there are two different sectors: formal and informal. They aim to increase the total family income. Formal jobs pay 4 and informal jobs pay 1 in Village C. The wages are in the same unit of household income. The probability of getting a formal job is 40%. One who fails to be hired in the formal sector is automatically offered an informal job. Assume that there is no migration cost. Do you think that the sons in Village A will migrate and search for a job in Village C? Rationalise your answer. (5 points)
Question 5) Suppose that the drought caused crop failure in Village A, but child mar- riage (daughters) and child migration (sons) have not happened yet. The government seeks not only to prevent child marriage and migration but also to resolve the issue of child labour in Village A. A policymaker suggests combining two policies: banning child labour and pro- viding emergency aid. Do you agree with the idea? Rationalise your answer. (5 points)
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