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Consider the basic Solow growth model with a constant saving rate s, constant population growth at the rate n, and no technological change, and suppose that the aggregate production function takes the CES form in (2.38).
(a) Suppose that σ > 1. Show that in this case equilibrium behavior can be similar to that in Exercise 2.22 with sustained growth in the long run. Interpret this result.
(b) Now suppose that σ → 0, so that the production function becomes Leontief:
The model is then identical to the classical Harrod-Domar growth model developed by Roy Harrod and Evsey Domar (Harrod, 1939; Domar, 1946). Show that in this case there is typically no steady-state equilibrium with full employment and no idle capital. What happens to factor prices in these cases? Explain why this case is pathological, giving at least two reasons for why we may expect equilibria with idle capital or idle labor not to apply in practice.
Inspect your graph to see that it displays diminishing MP.
An expenditure of $20,000 is made to modify a material-handling system in a small job shop. This modification will result in first-year savings of $2,000, a second-year savings of $4,000, and a savings of $5,000 per year thereafter.
Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe, in percent form), and return on the firm's stock (rose, in percent form):
The production function is given by W=F(L)=8*L^.5 and the marginal productivity MPL=4/L^.5. If widgets sell for $10, the price of labor is $8/hour, and there is a fixed cost of $25. What is the cost function C(W) for this production technology.
What is the unbiased estimate of the difference in height between boys and girls? Provide a formula and check the unbiasedness. Calculate the value of this estimate for the given sample
Consider a business cycle theory that combines the classical IS-LM model with the assumption that temporary changes in government purchases are the main source of cyclical fluctuations. How well would this theory explain the observed cyclical beha..
Suppose the individual demand for a product is given by QD = 1000 - 5p. Marginal revenues is MR = 200 - 0.4Q, and marginal cost is constant at $20 there are no fixed cost. A. The firm is considering a quantity discount. The first 400 units can be ..
Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x; y) = lnx + 2lny (MUx = 1=x;MUy = 2=y). Repeat part (b) for the case in which px..
a. If Firms B and C propose a merge, would the Antitrust Division likely challenge the merger Why or why not b. If firms G and H propose a merger, would the Antitrust Division likely challenge the merger Why or why not
A machine that costs $1,500,000 has a 3-year life. It will generate after tax annual cash flows of $700,000 at the end of each year. It will be salvaged for $200,000 at the end of year 3. If your required rate of return for the project is 13%, what i..
Find a solution of this equation in terms of the infinite history by inverting the appropriate lag polynomial. Prove that this solution is bounded. Find an explicit expression for ∂y/∂wt-j
Consider the following graph created be Heston and others. It shows per capita GDP growth rates of various countries (1960-2010) on the vertical axis and 1960 per capita GDP (in dollars) of those countries on the horizontal axis. The 1960 GDP numb..
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