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Let us return to Example 6.4.
(a) Prove that the law of motion of capital stock given by (6.37) monotonically converges to a unique steady-state value of k∗ starting with any k0 > 0. What happens to the level of consumption along the transition path?
(b) Now suppose that instead of (6.37), you hypothesize that
Verify that the same steps lead to the conclusion that b = c = 0 and a = βa.
(c) Now let us characterize the explicit solution by guessing and verifying the form of the value function. In particular, make the following guess: V (x) = A log x, and using this form together with the first-order conditions, derive the explicit-form solution.
design two packages for the second-degree price discrimination case so that the first package has quantity 8 for the high demand and the second one has quantity 6 for the lower demand such that the low demand group has consumer surplus at least $5..
Consumer 1 has expenditure function e1(p1; p2; u1) = u1sqrt(p1p2) and consumer 2 has utility function v(x1; x2) =x1x2^(alpha) What are Marshallian (market) demand functions for each of the goods by each of the consumers
Clean Supreme is a corporation that produces and sells powdered laundry detergent in the U.S. The company has estimated the following regression equation for the demand of its Brand Z detergent:
Linear equations for the consumption and saving schedules take the general form: C = a + bY and S = - a + (1 - b)Y where C, S, and Y are consumption, saving, and national income, respectively. The constant a represents the vertical intercept.
What is the minimum increase in income necessary for the consumer to be as well off under price px = 1, py = 2, as she/he was at prices px = 1, py = 1 Explain why the percentage increase is smaller than the increase in the CPI for the consumer
Calculate the BIC with the command estat ic and what is the difference between the predicted values and actual for the AR(1), AR(2) and AR(3) models.
A cell phone company is considering investing in additional cell phone towers. It estimates that if it builds K towers, its benefit in terms of increased profits will be: B(K)=500K-K^2 in millions. Assume each tower costs $20 million to build.
Investigate the history of slavery and discuss the ways in which this history impacts contemporary society
benefit-cost analysisthe objectives of the assignment are to gain further experience in calculating net present values
Show that Q2 and U span the same subspace, where Q2 is the sub-matrix of Q with the first column removed. Under what circumstances will they be the same, up to sign flips?
Why have tech firms with near monopolies in their own sectors sought to compete with tech firms that have extremely strong, near-monopoly positions in other sectors?
Consider the log-linear model 0 1 1 2 2 ln(Y) β0+ β1X1+ β2X2 + u Suppose you think that the value of β2 (the effect of X2) was not constant, but rather increased when X1 increased.
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