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The Solow Growth Model.

Consider the Solow model and assume that output (Y) is produced with inputs capital (K) and labour (L) according to the Cobb-Douglas production function

Labour grows at a constant rate n and the level of technology (A) grows at a constant rate g. Furthermore, capital depreciates at rate δ, and α is a parameter that is strictly between 0 and 1. The population saves a constant fraction s of output and the average growth in output is about 2% per year. The capital income share of GDP is 50% and the depreciation rate is 8% per year. The capital-output ratio is 2 in steady state.

(a) Define capital per effective worker

It can be shown that k(t) evolves according to is the production function per effective worker (which can be derived from equation (1)). Use equation (2) to derive an equation for the steady state values of capital per effective worker and output per effective worker with respect to saving rate, s. Illustrate the steady state(s) in a diagram, taking care to label all relevant quantities correctly. Is (are) the steady state(s) you found stable? Explain.

(b) What must the saving rate be in the initial steady state? What is the marginal product of capital in the initial steady state?

(c) What is the Golden Rule steady state level of capital? Marginal product of capital at the Golden Rule steady state? What must the saving rate be to reach the Golden Rule steady state?

- Credit Market Imperfection.

Suppose an economy in which credit markets are imperfect. In particular, assume that consumers can only borrow against the value of a collateral. Let this collateral be housing (with H denoting the amount of housing that a consumer owns).

(a) Derive the inter-temporal budget constraint of the consumer and illustrate it in a diagram. Make sure to introduce all variables that you employ in the derivation and/or diagram.

(b) What are the likely consequences of this credit market imperfection on a consumer’s optimal consumption bundle (consisting of consumption today and consumption tomorrow)?

(c) Assume that a housing bubble exists which leads to housing being generally overvalued. Discuss how the credit-constrained consumer is being affected if this bubble bursts and house prices adjust. How does your answer relate to the observed recession after the housing bubble in the US burst in 2007?

- Consider a two-period model. The representative consumer works and consumes in the current period and the future period. He or she has h units of time in eachperiodand divides this time between work and leisure in each period. Let w denote thereal wage and w’ the real wage in the future period, and r the real interest rate. Suppose that the government decreases current taxes, while holding government spending in the present and future constant.

(a) Using diagrams, determine the equilibrium effects on consumption, investment the real interest rate, aggregate output, employment and the real wage. What is the multiplier and how does it differ from the government expenditure multiplier?

(b) Now suppose that there are credit market imperfections in the market for consumer credit, for example due to asymmetric information in the credit market. Repeat part (a) and explain any differences in your answers in parts (a)

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