Question

Need help with these questions. With explanations if possible!

1. Let the production function for an economy by given by Y=AK^1/2L^1/2 where Y is output, K is capital, L is labor and A is “ideas.”

a. If L=25, A=10, the savings rate is ¼ and the depreciation rate is ½, what will the steady-state values of output, capital and consumption be?

b. On a graph, show what will happen to steady-state output and capital of there is a decrease in the depreciation rate.

2. As capital increases, the marginal product of capital _________________________.

3. Country X and Country Y have identical population, institutions, and technology but country X has more physical capital. Which country will have a higher level of output and which will have a higher rate of growth?

Answer 1

This type of production function is called Cobb Douglas production function. The model given under to calculate steady state level of variables was given by Solow and Swan , known as Solow Swan Neo- classical m growth models. The steady state level of output, capital and consumption ( endogenous) variables are calculated from the following equation called as fundamental equation of Solow model :

Since it is difficult to type equations, i attached the photo shot of left over answer below. One thing need to consider that there is need of population level of country in order to calculate steady state level of capital , output, and consumption, which is missing in the equation , but i'll elaborate the question to possible extend that if you get the population data of a country you can easily calculate the respective variables easily.

a).

b). The fundamental equation of Solow model is given by

change in capital stock per worker with respect to time equals to total saving minus ( sum of population level and depreciation rate multilpy by capital), as

k^. = sf(k) - (n+ depreciation rate)k.

As shown in graph also , as depretiation rate comes down steady state level will change , and steady state level of capital will increase , but staedy state output level will come down.

c) As capital increases marginal product of capital deceases. Because of which marginal product of capital reaches to minnimum level where it enough to employ all labour force and rectify depreciation rate.

d). Given that two countries have same population level, identical  institutions, and technology but country X has more physical capital, then country X output will be more but country Y will have higher growth rate.

The basic idea and a proposition of Solow model is that irrespective of initial level any country can reaches to reaches to same steady state level if given population level, institutions and other exogenous variables like saving rate and depreciation rates are identical because countries further from steady state grow at higher rates than countries near to steady state.