Quiz 1 Econ 463 September 9 Name 1 In The Malthus

Quiz1 Econ 463 September 9 Name 1 In The Malthu

In the Malthusian model, let the production function be y = 10 - 0.1L, the death rate schedule be 60 - 10y, and the birth rate be 40 per thousand. Draw the production function (y on the horizontal axis and L on the vertical axis), and put numbers on the axes. Draw the death rate function (y on the horizontal axis and death rate per thousand on the vertical axis). Also draw the Rate of Natural Increase (RNI) function and put it below the production function.

a. What is the equilibrium income (y*)? Show your calculations.

b. What is the equilibrium level of population (L*)? Show your calculations.

c. If the population is currently at 70, is the economy in equilibrium? If not, will the population rise or fall? Will per capita income rise or fall?

2. Assume the economy is at the equilibrium that you found in question 1. Now let the production function change to y = 12 - 0.1L. What will happen to income and population in the next few periods? Be as precise as you can. What will happen to income and population in the long run?

3. New question. Let the production function be y = 8 - 0.1L, the death rate be DR = 60 - 10y, and the birth rate be BR = 30. What is y? What is L? Show your work. Draw the production function graph. Put numbers on your graph. Also draw the graph of the Death Rate function and the Birth Rate line. Now suppose the society discovers a way to reduce the deaths from infectious disease (say by draining swamps to reduce the incidence of mosquito-borne fatal illness). How will the new steady state compare with the old one? Will y be higher or lower? Will L be higher or lower? Can you explain why?

Paper For Above instruction

Analysis of the Malthusian Model: Equilibrium, Policy Impacts, and Population Dynamics

The Malthusian model provides a classical framework to understand population dynamics and economic development based on the interaction between technological progress, natural resources, and demographic factors. This analysis explores the model's equilibrium conditions, the effects of changing production functions, and the consequences of policies aimed at reducing mortality rates. By examining the specific functional forms and parameters provided in the questions, we can derive key insights into the behavior of the system under different scenarios.

Understanding the Model Components

In this model, the production function is specified as y = 10 - 0.1L, where y represents per capita income and L is the population level. The death rate schedule, DR, depends on income: DR = 60 - 10y, indicating that higher income levels result in lower death rates. The birth rate, BR, is assumed constant at 40 per thousand in the initial scenario, and later it is changed to 30 to analyze demographic impacts.

Equilibrium Income and Population

To find the equilibrium income (y) and population (L), the key is to identify the point where the natural rate of increase (RNI) equals zero. RNI is calculated as the difference between the birth rate (per thousand) and the death rate (per thousand).

Calculations for Equilibrium

The initial production function: y = 10 - 0.1L

The death rate: DR = 60 - 10y

The birth rate per thousand: 40

a. Calculating y*:

At equilibrium, the natural increase is zero, so birth rate equals death rate per thousand:

40 = 60 - 10y

Solving for y:

10y = 60 - 40 = 20

y* = 2

b. Calculating L*:

Using the production function y = 10 - 0.1L and the equilibrium y* = 2:

2 = 10 - 0.1L

0.1L = 10 - 2 = 8

L* = 80

Assessment of Population at Current Level

If current population L = 70, which is less than L = 80, the population is below its steady-state level. Since the population is below equilibrium, the natural increase would be positive, causing the population to rise until it reaches L = 80. During this adjustment, per capita income, y, would tend to increase as population grows toward the equilibrium point, given the production function. Therefore, the economy is not in equilibrium, and the population will rise, with per capita income also increasing until reaching the steady state.

Impact of a Change in the Production Function

When the production function shifts to y = 12 - 0.1L, the new equilibrium income y* is found by setting the death rate equal to the new birth rate, which remains at 40 per thousand:

40 = 60 - 10y

As before, y* = 2, since the death rate function doesn't depend on y in this scenario and the birth rate remains unchanged, the income at equilibrium stays the same. However, the new production function allows higher income levels for the same population, indicating increased productivity.

Over the short run, income might rise due to improved technology and productivity, leading to a higher steady-state income level, provided birth and death rates adjust accordingly. In the long run, because the birth rate remains constant and the death rate depends on y, the population stabilizes at a new equilibrium determined by the intersection of the death rate and birth rate functions, which would potentially increase L* due to higher income facilitating better health and lower mortality.

Scenario of Reducing Infectious Disease Mortality

In the third scenario, the production function is y = 8 - 0.1L, the death rate is DR = 60 - 10y, and the birth rate is BR = 30 per thousand. Calculating y* involves setting the death rate equal to the birth rate:

30 = 60 - 10y

10y = 60 - 30 = 30

y* = 3

Correspondingly, the population at steady state is:

3 = 8 - 0.1L

0.1L = 8 - 3 = 5

L* = 50

Graphically, the production function y = 8 - 0.1L would be downward sloping, crossing the y-axis at 8 with a slope of -0.1. The death rate line DR = 60 - 10y declines as y increases, intersecting the horizontal line representing BR = 30 at y = 3, L=50.

Effects of Improved Health on Steady-State Conditions

By reducing death rates through improved disease control, the death rate schedule shifts downward, effectively lowering the death rate for any given y. This results in a lower equilibrium mortality, and thus a higher steady-state income y*, since the death rate at each income level decreases, leading to lower mortality at the same levels of income. The new steady state would have a higher y and L compared to the old one, as higher income levels reduce deaths further and support larger populations. This outcome demonstrates the positive impact of health interventions on demographic and economic growth, aligning with the Malthusian perspective on the importance of health improvements for sustainable development.

Conclusion

The analysis of the Malthusian model indicates that population dynamics and income levels are intricately linked, with equilibrium states determined by the intersection of demographic and productivity functions. Policy measures that reduce mortality, like combating infectious diseases, can shift the steady-state towards higher income and larger populations, illustrating the critical role of health in economic development. Furthermore, technological improvements reflected in the production function can lead to higher income levels, which influence population growth and stability. Understanding these mechanisms is essential for designing policies aimed at sustainable growth in developing economies.

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