Help with number 4 my attays to the costa ¹= 1: N(t) remains constantAs we see, there are only two options for solution of linear difference equations: ever-fastergrowth or decay to zero or another constant value. The exponential growth of populationsis also known as Malthusian after the early population modeler Thomas Malthus. He useda simple population model with constant growth rate to predict demographic disaster due tothe exponentially increasing population outstripping the growth in food production. In fact,human population has not been growing with a constant birth rate, and food production hasonly as good as the assumptions that underlie them.(so far) kept up pace with population size, illustrating yet again that mathematical models are10.2.4 ExercisesVFor the following scenarios for a population: 1) Construct a dynamic model by writing down adifference equation both in the updating function form (N(t+1) = f(N(t))) and the incrementform (N(t+1) - N(t) = g(N(t))) and specify the time step; 2) find the solution of the lineardifference equation with a generic initial value and check that it satisfies the difference equationand predict the future.by plugging the solution into your equation (in either form); 3) plug in the given initial value1. Zombies have appeared in Chicago. Every day, each zombie produces 3 new zombies.days?Suppose that initially there is only one zombie, how many zombies will there be in 72. Suppose hunters kill 50 deer in a national forest every hunting season, while the deer bypredict how many there will be in 5themselves have equal birth and death rates. If there are initially 500 deer in the forest,years.3. The number of infected people in a population grows by 8% per day and those whowill be infected in 45 days?become infected remain infected. If initially there are 8 infected, how many individuals4. Suppose bacteria in a population divide in 2 every hour and 90% of the current populationdies after reproduction, not including the new offspring. If the population initially has10 million bacteria, predict how many there will be in 12 hours.5. In a rabbit population, each pair produces 1.2 offspring every year (i.e. 0.6 per capita)and the adults have a 0.5 annual death rate after reproduction (and assume the wholemany there will be in 5 years.population is paired up into mating pairs.) If initially there are 100 rabbits, predict how6. Consider the same rabbit population, but now a python that lives nearby eats exactly 1years?rabbit a month. If initially there are 100 rabbits, how many do you predict will be in 1016216

Bacteria Divides in 2 every hour .Also 90% of current population dies .Therefore ,If a current…

will be infected in 45 days? 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 12 offenning cted, how many individuals

will be infected in 45 days? 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 12 offenning cted, how many individuals

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 4SCQ: Assume there are two countries: South Korea and the United States. South Korea grows at 4 and the...

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Exercise 2: Growth and developmentCountries 1 and 2 have the production function: Yt = AiKαt L1−αt , where country 1 hasTotal Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35for both. In the two countries population is constant and there is no technological progress.Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, andcountry 2 saves 20%.a) Write down the function of production per unit of labor. Suppose the two countriesstart with an initial capital stock (per unit of labor) of 500, what are the initial income andconsumption per unit of labor in both countries?b) Determine their steady state levels of capital, income and consumption per unit oflabor.c) Determine the difference in their steady state level of income per unit of labor, andhow much of that difference is due to differences in TFP and how much is due to differencesin capital per unit of labor.d) Suppose now that country 2 suddenly has access to the country 1…
Country Z INDICATOR NOW 1 YEAR AGO GDP growth rate 3.7% 3.5% Explain if each country is healthy. Click True for Healthy Click False for Not Healthy O True O False
Assume there are two countries: South Korea and the United States. South Korea grows at 4 and the United States grows at 1. For the sake of simplicity, assume they both start from the same fictional income level, 10,000. What will the incomes of the United States and South Korea he in 20 years? By how many multiples will each countrys income grow in 20 years?
0.25 0.10 0.20 0.15 0.25 If your initial distribution of countries from lowest GDP to highest GDP is shown above, and you then estimate a Markov steady state and show that in the future, the distribution will look like this, you have evidence of what? 0.50 0.50 O Economic Convergence O Economic Divergence O Spatial Dependence O Temporal Homogeneity
120 100F NOR ARE SGP CHE HKG SWE TWN Na. A VEN 40 60 80 100 120 Relatiwe GDP per enpita to the US lewel - 1970 In the figure above, GDP per capita relative to the US level for a large group of countries is plotted for years 1970 (in the horizontal axis) and 2000 (in the vertical axis). Which one of the following statements is correct? O Income per capita of countries on the 45 degree line has grown at a similar rate than income per capita of the US in each year. O Income per capita of each country is plotted according to how strongly it correlates to the income per capita of the US in each year. O The income per capita of those countries below the 45 degree line has grown the fastest in between years 1970 and 20 O The income per capita of those countries on the 45 degree line has not grown in between years 1970 and 2000.
Country Z INDICATOR NOW 1 YEAR AGO GDP growth rate 3.7% 3.5% Explain if each country is healthy. Click True for Healthy Click False for Not Healthy O True O False
The world was growing at a constant growth of 0.00007% rate between 100,000 BC and 1750AD. If birth rates per thousand averaged 35 during this period , what was the average death rate in equilibrium. (approximately) A. 31 B. 40 C. 35 D. 30
An economist fits the following production function to data from Australia and New Zealand, Y = AK" L1-« She estimate that for Australia, a = = 0.7. She estimates that for New Zealand, a = = 0.2 Based on this information, which of the following statements is most likely to be correct. There is not enough information to comment on the relative capital intensities Production wilI be relatively more capital intensive in New Zealand than in Australia Production will be relatively more capital intensive in Australia than in New Zealand Production will be equally as capital intensive in each country since they both experience constant returns to scale
Use the following information to answer the next question. While studying a population of rats in a colony, a student recorded the change in the number of rats year by year. He found that after a few years the population size of the rats became constant. The student mentioned in his report that the rat population was showing exponential growth O abnormal growth O logistic growth O per capita growth
Examining the sub-national variation in development for many countries, such as Brazil, China, or Mexico, reveals O development is closely related to access to energy supplies. O there are no substantial variations in wealth at the regional scale. variations exist between regions that are isolated and those connected to international trade. O wealth is concentrated in the cooler, mountainous regions. cities are relatively underdeveloped compared to the agricultural lands. Clear sele
Session 2 Questions 44 and 45 are open-response questions. ws BE SURE TO ANSWERAND LABEL ALL PARTS OF EACH QUESTION. Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. If you do the work in your bhead, explain in writing how you did the work. Write your answer to question 44 in the space provided in vour Student Answer Booklet. The graph below shows the birth rate and the death rate of a mouse population ovet a three-year period. The immigration rate and the emigration rate of the population are equal. 44 Birth Rate and Death Rate of a Mouse Population Year 3 Year 2 Year 1 Time Key Death rate Birth rate a. Describe what happens to the size of the population for each year shown on the graph. Explain your answers. b. Identify three factors that could affect the death rate of the mouse population, and explain why each factor affects the death rate. 100 rient. Birth and Death Rates
onsider an imaginary economy that has been growing at a rate of 3% per year. Government economists have proposed a number of policies to increase the growth rate but first need to convince the president that the policies will pay off. To do so, they want to present a comparison of the number of years it will take for the economy to double, depending on the growth rate. Using the rule of 70, determine the number of years it will take the economy to double at each growth rate. Growth Rate Years Required to Double (Percent) (Nearest whole number of years) 3 4 5