1. Consider a perfectly competitive economy with K' amount of capital and L' amount of labour. All factors of production are fully employed. Technology is described by a Cobb-Douglas production function given by:
Y' = F (K-, L-) = (K-)a(L-)b
a) For each of the following cases, indicate whether the production function exhibits increasing, decreasing or constant returns to scale. Demonstrate your result (by introducing a multiple z of the factors of production) and explain.
i) a = 0.4, b = 0.5
ii) a = 0.3, b = 0.7
iii) a = 0.6, b = 0.6
b) Suppose that a = 0.3, b = 0.7 . If factors are paid their marginal products, what is the share of income received by capital and labour, respectively? Show your result and explain.
c) What are economic profits and accounting profits in this economy? Explain.
d) Suppose that a natural disaster destroys 30% of this economy's capital stock but that the labour force remains unchanged. (Assume again that a = 0.3, b = 0.7 ).
(i) What is the percentage change in total output? Explain and draw a graph to illustrate.
(ii) What is the percentage change in the real rental rate? Explain and draw a graph to illustrate.
(iii) What is the percentage change in the real wage rate. Explain and draw a graph to illustrate.
In each case indicate the direction of change (increase or decrease) and derive the percentage change. Show your work. Explain in words. Draw a graph to illustrate the change in each case.
e) Now suppose that an improvement in health care permits the labour force to increase by 10% while the capital stock remains unchanged at its initial level (i.e., the level it had in parts 1(a)-1(c)).
(i) What is the percentage change in total output? Explain and draw a graph to illustrate.
(ii) What is the percentage change in the real rental rate? Explain and draw a graph to illustrate.
(iii) What is the percentage change in the real wage rate. Explain and draw a graph to illustrate.
In each case indicate the direction of change (increase or decrease) and derive the percentage change. Show your work. Explain in words. Draw a graph to illustrate the change in each case.
2. Suppose the government wants to reduce its budget deficit. Using the long-run model of the economy developed in Chapter 3, graphically illustrate the impact of the alternative fiscal policy measures indicated in parts (a) and (b) below. Be sure to label: (i) the axes; (ii) the curves; (iii) the initial equilibrium values; (iv) the direction curves shift; and (v) the final equilibrium values.
a) Suppose the government decides to reduce the government's budget deficit by reducing government expenditures. What happens to: (i) national saving; (ii) the real interest rate; (iii) investment; (iv) consumption; and (v) output? Illustrate graphically and explain in words why these variables change or why they do not change.
b) Suppose the government decides to reduce both government expenditures and taxes by the same amount (this is a "balanced budget" change). What happens to: (i) national saving; (ii) the real interest rate; (iii) investment; (iv) consumption; and (v) output? Illustrate graphically and explain in words why these variables change or why they do not change.
3. Consider the following model of an economy where the consumption and investment functions are given respectively by:
C = 300 + 0.75(Y - T-)
I = 1800 - 65r
Also, government expenditures are given by G- =1000, taxes are given by T- = 300, and where r is the interest rate.
(Here r is measured in percent. Use the values r = 1, r = 3 and r = 5 etc., rather than 0.01, 0.03 and 0.05.)
a) Find the equation for aggregate demand Y as a function of r.
b) Suppose that long run aggregate supply, Y-, is produced according to the following technology:
Y- = A(√K)(√L)
where the technology parameter A = 300, capital K = 25 and labour L = 36 units.
(i) What is the equilibrium interest rate r* ?
(ii) What is national saving?
(iii) What is the government budget deficit?
(iv) Draw a graph to illustrate the equilibrium in the financial (loanable funds) market. (Your graph does not have to be drawn to scale.)
Show your work in each part of the question. Round off numbers to the third digit after the decimal point (For ex. 2.5436 ≈ 2.544)
c) Suppose that technology improves so that now A = 350, while K and L stay the same.
(i) What is the new equilibrium interest rate r*?
(ii) What is the new level of national saving?
(iii) What is the new level of consumption? What conclusion about the impact of technological improvement do you draw from your results in 3(c)(ii) and 3(c)(iii) ?
(iv) Draw a graph to illustrate the impact of the improvement in the production technology. Show your work in each part of the question.
d) Suppose now that the government decides to reduce taxes to T- = 200. What is the new equilibrium interest rate r*? What is the new level of national saving? (Assume that Y- is the same as what you found in part 3(c)).
Show your work and draw a graph to illustrate the impact of the decrease in T-.