Suppose that we are in the basic Solow model without technological growthor population growth. The only difference is that people live for two periods(working age and retirement). In the working age, they work and choose howmuch to save for retirement. In the retirement age, they don't work and spendtheir savings instead.The utility of someone working in period t is given by:U = (Ct) ³ (Ct+1)¹-B1. Interpret 3. Regardless of their income, what fraction of their incomewill the agent save? (Hint: this is a Cobb-Douglas utility function. Theexponents are very much related to optimal the share of spending on thedifferent goods.)2. Suppose the income of each agent is the wage wt. How much total savingswill there be at time t if the total working-age population is Lt, as afunction of wt, B and Lt?3. Supposed that the production function is the usual one (Yt = A(Kt) a (Lt) ¹-a)and that the wage is equal to the marginal product of labor (why shouldit?). What are the total savings in the economy as a function of B, a andYt?4. Write down the 4 key ingredients of this particular growth model in theaggregate (production function, aggregate ressource constraints, aggregatebehavioral equation, law of motion). This economy is equivalent to theSolow model, with a specific value of the savings rate. What is this savingsrate?5. Under what condition is the (endogenously chosen) saving rate equal tothe golden rule rate? What happens if 3 is too high or too low?

Utility function U=ctβct+11-β Production function: Yt=A(Kt)α(Lt)(1-α)

Suppose that we are in the basic Solow model without technological growth or population growth. The only difference is that people live for two periods (working age and retirement). In the working age, they work and choose how much to save for retirement. In the retirement age, they don't work and spend their savings instead.

Suppose that we are in the basic Solow model without technological growth or population growth. The only difference is that people live for two periods (working age and retirement). In the working age, they work and choose how much to save for retirement. In the retirement age, they don't work and spend their savings instead.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Some analysts claim that the economy is subject to a “paradox of thrift.” That is, increases in saving will cause consumption and GDP to fall. In support, they point to the fact that consumer spending is more than ⅔ of GDP. (a) Does the Solow model (described in Chapter 28 of Cowen and Tabarrok), show the paradox of thrift? Explain. (b) What about the real world? Do the data in Figure 28.8 below suggest a paradox of thrift? Explain.
In the Solow model in which y=Akα (where y is GDP per worker and k is capital per worker), compare the poverty trap model to the incentives model. Discuss whether the following statements are true or false in each model, using graphs and equations to explain and prove your conclusions:a. There exists some level of aid sufficient to get any poor country out of povertyb. There exists some threshold above which aid can be discontinued.c. A country’s long-run per capita income depends on where its per capita income is now.d. When the country is open to capital flows in or out, the main determinant of development is government policies and institutions e. Two pieces of evidence support the existence of poverty traps: (1) Growth of poor countries is slower than that of richer countries, and (2) Growth accelerates when a poor country exits poverty (explain why the poverty trap model predicts (1) and (2) and whether these predictions are confirmed by the data).
Recent studies investigating the inter-generational evolution of income distributions show that in the long run inequality in wealth is bad for economic growth even if we start out with an equal wealth distribution. Use the Galor and Zeira model to show how the mechanism works.
4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.
Suppose the economy of an island behaves as the Solow model (Y=AK1/2L1/2), version 1.0 (constant population). Suppose that the productivity parameter is A=90, the depreciation rate is d=1/10, the savings (investment) rate is s=0.10, and the labor force is equal to 2 million (and constant over time). 1-Due to climate change, from 2011 onward, every year the island is hit by hurricanes of increasing force that destroy capital. As a result, the depreciation rate doubles. What will be the new long-run (steady state) value for income per worker (Y/L)? Pick the closest value. Also label the new steady-state GDP as point C in the diagram. Between 75 and 85 None of the other options Between 4,500 and 5,200 Between 8,000 and 8,500 Between 44 and 49 2-In year 2021 investors recognize that the depreciation rate is higher than a decade earlier. They also recognize that the actual returns to their investments in physical capital over the previous decade have consistently fallen below their…
Consider the basic Solow model with no population growth and no technological progress and a production function of the form F (K, H ), where H denotes the efficiency units of labor (human capital) given by where N is the set of all individuals in the population, and hi is the human capital of individual i. Assume that H is fixed. Suppose there are no human capital externalities and factor markets are competitive. (a) Calculate the steady-state equilibrium of this economy. (b) Prove that if 10% higher h at the individual level is associated with a% higher earnings, then a 10% increase in the country’s stock of human capital H will lead to a% increase in steadystate output. Compare this result to the immediate impact of an unanticipated 10% increase in H (i.e., consider the impact of a 10% increase in H with the stock of capital unchanged).
This model begins from the assumption that savings is a constant proportion of income.a. Harrod-Domar Modelb. Rostow’s Stages of Growth Modelc. Solow Modeld. Power Balance Model
. Using the Solow growth model suppose that there is a hurricane coming toward a city. Because it is fully anticipated a lot of the people can leave and come back safely, but a lot of physical capital (K) is destroyed (buildings cannot move). Show graphically what the Solow model predicts will happen to the steady state. Does the poverty trap model have any different predication? Compare this graphically.
B. The rate of technological progress rises. 2. Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model: a. The rate of population growth falls. B. The rate of technological progress rises. C. The production function is Cobb-Douglas, F(K,AL) = K" (AL)1-" , and capital"s share, ", rises. D. Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.
Suppose an economy described by the Solow model is in steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. total output and total capital grow at 3.6 percent per year. suppose further that the capital share of output is 1/3. if you used the growth accounting equation to divide output growth into three sources- capital, labor, and total factor productivity- how much would you attribute to each source? compare your results to the figures we found for the united states in tables 9-2.
Please, I urgently need this exercise. Area of expertise is macroeconomics: Solow growth model.
Q)If half of the capital decreased,what will be the new steady state level of capital per capita? Draw a picture.(Solow Model) Explains in detail and correctly