Chapter 3. Questions for Review 1. What determines the amount of output an econo
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Chapter 3. Questions for Review 1. What determines the amount of output an economy produces? 2. Explain how a competitive, profit-maximizing firm decides how much of each factor of production to demand 4. Write a Cobb-Douglas production function for which capital earns one-fourth of total income. 7. What makes the demand for the economy's output of goods and services equal the supply Chapter 3. Problems and Applications 1. Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the following events a. A wave of immigration increases the labor force b. An earthquake destroys some of the capital stock. c. A technological advance improves the production function. d. High inflation doubles the prices of all factors and outputs in the economy 4. Suppose that an economy's production function is Cobb- Douglas with parameter a. What fractions of income do capital and labor receive? b. Suppose that immigration increases the labor force by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?Explanation / Answer
1. The amount to be produced in the economy is dependent on its factor of productions i.e, the inputs and the production technology.The factors of productions are land,labour,capital and entrepreneurship.Among these four land is fixed factor of production while labour and capital are not constant.Therefore,Q=f(L,N,K,E) where Q is the output,L is land,N is labour.K is capital and E is entrepreneurship.
2.As discussed in Q1, output of a firm is a function of labour and capital.Now,employing 1 addiional unit of labour or capital will increase the cost of the firm.As we know,profit=revenue - cost ,increasing cost will lead to decrease in profit.Suppose price of 1 unit of output is 'p' and cost/wage of 1 unit of labour is 'w'.Therefore,if a profit maximising competitive firm employs 1 additional unit of labour ,this is going to fetch the firm p*MPL(Marginal product of labour) units/dollars of addiional revenue but this decision is also going to cost him w dollars of wage bill.Hence,the optimal decision for the firm would be to hire till the point where p*MPL=w or, MPL= w/p i.e, marginal product of labour = real wage.Similarly,MPk =w/r (where r= rent)i.e, marginal productivity of capital = real rent.
4.The general form of Cobb-Douglas production function is Q=ALalphaKbeta.where Q is output,L is labour,K is capital,A is tota factor productivity and alpha,beta are 2 respective output elasticities of labour and capital.If capital earns 1/4th of total income then beta=1/4 and since alpha is not menioned we can assume it to be zero.Hence,the production function will look like Q=AK1/4.
7.The aggregate demand side of an economy is constituted by consumption demand,investment demand and government expenditure where the aggregate supply is determined by the production function of the economy.As we know investment is a function of real interest rate ,if interest rate is high investment wil be lower and aggregate demand will fall.On the other hand money supply is a function of transaction demand for mone and speculative demand for money.If interest rate increases it will increase speculative demand for money and since money supply=transacion demand for money/ speculative demand for money ,money supply will fall in turn.Therefore,real interest rate maintains the equilibrium of demand and supply in the economy.
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