**Q1. Evaluate the validity of the following statements (Attempt any 2 parts):**

(a)If country A has a population growth that is lower than country B, then the average women in country A has less children than her counterpart in country B.

Answer:- **False**. It depends on the age distribution of the population. It is possible for the fertility rate in one country to be lower than in another country, and yet for the population growth rate in the former country to be higher.

(b) If total mortality among children remained constant, but the incidence of that mortality shifted from late childhood to early childhood, fertility rates should decline.

Answer:- **True**. Use the idea of a shift from hoarding to targeting, as the incidence of mortality shifts from late to early childhood. When infant mortality falls, couples can choose a wait-and-watch strategy. But if mortality was prevalent in late childhood, then couples have to hoard a target number of children right in the beginning, as they themselves might cross the reproductive age by the time their children cross the late child morality barrier.

**Q2. Ali and his three brothers own a small farm in the agricultural sector of the Region Q. They work equally hard, and the value of their output measured in the local currency, nice, is 4,000 nice, which they divide equally. The urban sector of Q has two kinds of job. There are informal jobs which anybody can get (which pay 500 nice), and there are formal jobs which pay 1,200 nice. The probability of getting these jobs is determined as in the Harris-Todaro model.**

**Assume that Ali compares his own expected returns in the two sectors and there are no costs of migration. Calculate the threshold proportion of formal jobs to urban labor force that will just deter Ali from migrating.**

Answer:- Let the probability of getting a formal job be p. This is also the ratio of formal jobs to urban labour force, i.e. Lf/(Lf+LI)

Use Harris Todaro equilibrium condition for making Ali indifferent between migrating and staying in agriculture:

Here p = Lf/(Lf+LI), 1-p = LI/(Lf+LI), wa = 4000/ 4 (as wages in agriculture as decided by average sharing rule), wages in informal sector, wi = 500 and wages in formal sector w̅ = 1200

The threshold value of p is implicitly given when the expected wage from migration is just equal to her current income: 1200p + 500(1 − p) = 1000

Thus solving for p we get p = 5/ 7

**Q3. Are the following statements true, false or uncertain? Provide a brief explanation to back up your answer. (Attempt any 2 parts)**

(a) Migration restrictions alone lead to too many people in the informal sector.

**False.** As long as migration restrictions are effectively implemented, the informal sector will not exist.

(b) In the Harris-Todaro model, an increase in the formal sector labor demand at a fixed wage rate must lower the percentage of people in the informal sector, as a fraction of the urban labor force.

Answer:- **True**. At the equilibrium,

If we fix W̅ and Wi, then Wa must increase when total labor demand increases. Then Li/(Lf+Li ) must be lower than before.

(c) If government cannot tax agriculture, the supply curve of labor to industry in the Lewis model is always upward sloping.

Answer:- **True**

**4. In this chapter, we studied a model where a family wants one surviving child to provide old-age security. Let us say that the probability of any one child living to look after its parents in old age is 1/ 2 (i.e., 50– 50). However, the family wants this security level to be higher, say a probability of q > 1/ 2.**

**a) Describe the family’s fertility choices for different values of q, by first writing down a model that captures this story, and then examining the results for different values of q.**

Answer:- In this question the probability that a child will look after its parents in old age is given at 1/2. The tolerance probability is denoted by q. By the argument used for equation 9.1 in text, the couple will try to have n kids, where n is the smallest number such that 1-(1-1/2)^{n} ≥ q

We can rewrite this as (1/2)^{n} ≤ 1- q

Now the closer the value of q to one (meaning, the more averse to risk that the couple is), the larger will have to be the value of n.

**b) Calculate the expected number of surviving children for this family, under various values of q.**

The expected number of “surviving children”, that is, children who grow to look after their parents is clearly n/2 (simply the smallest number of children (n) that the couple will have to satisfy 9.1 equation multiplied by the probability of each child growing up to look after their parents)

So the parents will, on average, have more children than they need. Their risk aversion and high tolerance probability will lead them to have a large number of children in the first place.

**5. Consider a labor surplus economy producing a single output, which can be consumed (as food) or invested (as capital). Labor, once employed, must be paid a fixed wage of w which is fully consumed. All surpluses from production are reinvested.**

**a) Draw a diagram showing how output is distributed between consumption and reinvestment for some chosen level of employment. Show the profit-maximizing employment level: call it L*.**

Answer:- This question is simply Lewis-model re-worded. So there is labor that can either be employed in production of food (agriculture sector) or in production of capital (industrial sector). So to show L* simply draw the agricultural production function, the wage bill line and depict Lewis model labor allocation for agriculture and industrial. Mark L* at the point C where the MR = MC for production function.

**b) Reinvested surplus raises consumption tomorrow. Suppose that a social planner cares about consumption today and consumption tomorrow. Show that she will always wish to choose an employment level not less than L*.**

Assuming that all agricultural surpluses are taxed away, the industrial sector can re-invest surplus (shown by shifting of demand curve) comfortably till the point L*.

**c) Suppose that the planner wishes to employ units of labor, where L > L*. Carefully describe a subsidy scheme to profit maximizing employers that will make them choose this level of employment.**

Answer:- When we try to take out one extra unit of labour, beyond L* (where MR = MC) from agriculture and shift it to industries, there is a greater loss of agricultural surplus. Thus to move from agriculture to industry, the subsidy must be equal to the difference between the surplus at level of employment L and surplus at L*

**6. Why is sharecropping considered to be an economically inferior contractual system? Despite this, why does sharecropping enjoy enduring popularity in real world practice? (5,10)**

Answer:- Reasons for popularity of sharecropping:

- A. Risk averse tenants prefer sharecropping over fixed rent
- B. The double incentive problem : Sharecropping as a compromise solution
- C. Cost sharing of Inputs
- D. Limited Liability
- E. Sharecropping as Screening tool : low ability tenants will choose sharecropping

**7. I) Explain how a policy of lending by the formal sector to economic agents who would use these funds to lend in the informal markets, can have mixed effects on its impact on the interest rate charged to the small borrowers.**

Answer:- An expansion of credit from formal sector to economic agents who can lend in informal sectors is not bound to fail, but it cannot be simply assumed that that such expansion will lower interest rate for small borrowers. Following are the potential pitfalls.

- A. Costs of Monitoring
- B. Collusion
- C. Differential Information

**II) The following table gives default risks for various loan sizes in an informal credit market. Suppose that the rate of interest in the informal sector is 18% per year and that in the formal sector (with no default) is 10% per year. Calculate the maximum loan size that will be offered in the informal-sector credit market. For what minimum rate of interest will loans in the $ 250– 300 category be offered?**

Answer

Loan size ($) | Loans defaulted (%) |
---|---|

50-99 | 5 |

100-149 | 10 |

150-199 | 20 |

200-249 | 25 |

250-300 | 30 |

>300 | 50 |

To calculate the maximum loan size :

Let L be the maximum loan size,

Loan size ($) | Loans defaulted (%) | Expected Repayment | Return on Informal Loan |
---|---|---|---|

50-99 | 5 | 0.95 * L*(1+0.18) = 1.121L | (1.121L-L)*100 = 12.1% |

100-149 | 10 | 0.90 * L*(1+0.18) = 1.062L | (1.062L-L)*100 = 6.2% |

150-199 | 20 | 0.80 * L*(1+0.18) = 0.944L | (0.944L-L)*100 = -5.6% |

200-249 | 25 | 0.75 * L*(1+0.18) = 0.885L | (0.885L-L)*100 |

250-300 | 30 | 0.70 * L*(1+0.18) = 0.826L | (0.826L-L)*100 |

>300 | 50 | 0.50 * L*(1+0.18) = 0.59L | (0.59L-L)*100 |

Only for loan size in 50-99 range, the return in informal sector (12.1%) is higher than the return in default-free formal sector (10%), thus the maximum loan size offered will be $99. For any larger loan size, the return in formal sector is higher than the return in informal sector.

Minimum rate of interest for $250-$300

For loans in range $250-300 to be offered, the rate of interest charged in informal sector must compensate for the default risk.

Thus : expected repayment in informal loan = formal sector return

0.70 * L * (1+ r) = 1.10*L

Then r = 57%

**8. In the land of Xena, there are three inputs to production: capital, physical labour and mental labour. Men in have more physical labour power than women, but both men and women have the same amount' of mental labour power.**

**(a) Who earns more in Xena, men or women? What do these differences depend upon?**

Answer:- Payments in Xena would be to three factors of production: capital, mental labor and physical labor. Men have greater relative endowment of physical capital, they would be paid more once we add up all sources of income. It depends on the assumption that all capital is held jointly by families, and all income is paid to married individuals

**(b) Imagine that the technology is such that more capital raises the marginal product of mental labour faster than it raises the marginal product of physical labour. As the economy grows over time, its stock of physical capital is steadily increasing: How would you expect the relative wage of men to women to change over time? Explain.**

Answer:- If physical capital increases, the marginal products of both physical and mental labor rises, but because mental labor is more complementary to technology, one would expect the return to this input to rise relative to the return to physical labor. As a consequence, one would expect the relative wages of women to rise.

**(c) Women have one unit of labour time that they can allocate between raising children and being part of the workforce. How would this allocation be affected by the changes over time that were found in answer to part (b)? Explain.**

Answer:- A higher relative wage of women tends to reduce fertility. Based on all the three parts talk about why richer countries will tend to have lower rates of fertility.

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