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Consider the following discrete-time optimal growth model with full depreciation:
Assume that u(.) is strictly concave and increasing for c ≥ 0, and f (.) is concave and increasing.
(a) Formulate this maximization problem as a dynamic programming problem.
(b) Prove that there exists a unique value function V (k) and a unique policy rule c = π(k), and that V (k) is continuous and strictly concave and π(k) is continuous and increasing.
(c) When will V (k) be differentiable?
(d) Assuming that V (k) and all other functions are differentiable, characterize the Euler equation that determines the optimal path of consumption and capital accumulation.
(e) Is this Euler equation enough to determine the path of k and c? If not, what other condition do we need to impose? Write down this condition and explain intuitively why it makes sense.
Using a method similar to the consumer price index, compute the percentage change in the overall price level. Use 2009 as the base year, and fix the basket at 1 karaoke machine and 3 CDs.
if a consumer has indifference curves that are convex to the origin but have a kink in them (similar to the perfect complements example, except the angle at the kink is greater than 90 degrees) how can we determine the optimal bundle
What is Bob's average annual earnings. In the previous question, what is the standard deviation of the annual salary? What is the probability that John will get 2 tickets during the week (Monday-Friday)?
A profit-maximizing firm is producing where MR=MC and has an average total cost of $4, but it gets a price of $3 for each good it sells. b) What would you advise the firm to do if you knew the average variable costs where $3.50
How can the Fed reduce inflation? How would this policy affect the nominal interest rate
Can any information be derived from one that cannot be derived from the other?
A perfectly competitive firm faces a market price of $10 for its output X. It owns two plants, A and B, whose total costs are TCA = 10+2X+.25X2,TCB = 15+.4X+.1X2. How many units should each plant produce to maximize profit at that price
a bakery operating in the short run has found that when the level of employment in its baking room was increased from 4 to 10,in increments of one, its corresponding levels of production of bread
If the Canadian production function is Cobb-Douglas with capital's share in total output 0.3, output growth is 3 percent per year, depreciation is 4 percent per year, and the capital-output ratio is 2.5,
"Between 1997 and 2001, many apple farmers switched from traditional to organic growing methods, increasing production of organically grown apples from 1.2 million boxes per year to more than 3 million boxes."
a. If the interest rate is 35%, what is the maximum you can spend in the current period b. Id the interest rater was lower, you probably would be able to spend more than that. What would be the max interest rate that would allow you to spend $225 ..
How would your policy have affected interest rates and real output during the period in question? What would be the benefit of your policies?
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