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Consider the Solow growth model with Cobb-Douglas production function Y = z[KαL1-α], where Y is total output, z is total productivity, K is the total capital input, and L is the total labor input.
a. Show that in the competitive equilibrium, α is the fraction of national income that goes to the remuneration of capital and 1 - α is the fraction that goes to the remuneration of labor.
b. Use the (average) labor share in national income from your own country for the period 1990 to 2000 to find the value of α.
c. Use your answer to part b to calculate the ‘‘Solow residual'' z using the aggregate output, capital, and labor (Y, K, and L) from your country for each year in the period 1990 to 2000. How has this measure of total productivity evolved over time in your country? Is there a productivity slowdown? Explain the possible reasons of this evolution (inventions, government regulations, price of energy, etc.).
In 1970 and 1980, the nominal price of motor fuel rose much more rapidly than the general price level, pushing up the relative price of motor fuel. As we would expect, the quantity sold decreased. In 1981 and 1982, the relative price leveled off a..
What is the equilibrium price and quantity in this market?
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Suppose the demand curve for a monopolist is QD = 500 - P and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit. a. Find the monopolist's profit-maximizing output and price..
Recently, the owner of a Trader Joe's franchise decided to change how she compensated her top manager. Last year, she paid him a fixed salary of $65,000, and her store made $120,000 in profits (not counting payment to her top manager). She suspec..
Show, too, how sterilization operations are reflected in the central bank's balance sheet.
The profit on a gold necklace is $15 and the profit on the goldbracelet is $25. A jeweler's showcase has room for at most 60necklaces and bracelets combined. The demand for the necklaces isat least 3 times the demand for bracelets.
According to the profit-maximization goal, the firm should attempt to maximize short-run profits since there is too much uncertainty associated with long-run profits.
The price at point a is $70 and the price at point c is $10 per bag. The price at point d is $56 and the price at point e is $31 per bag. The price at point f is $67 and the price at point g is $32 per bag. Apply the formula for the area of a trian..
On a diagram, draw the marginal cost curves for the two factories, the average and marginal revenue curves, and the total marginal cost curve (i.e., the marginal cost of producing Q = Q1 + Q2). Indicate the profit-maximizing output for each factor..
During 2002, the working-age population increased by 353.0 thousand, employment increased by 364.2 thousand, and the labor force increased by 469.5 thousand. Calculate the labor force participation rate for 2002.
Find Todd's optimal consumption bundle and utility level at that price level, using the Lagrangian multiplier method. Assume the government decides to impose a tax of $5 per unit of x (so that the new price of good x is $10).
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