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Consider the expanding input variety model of Section 13.1. Show that it is possible for the equilibrium allocation to satisfy the transversality condition, while the optimal growth path may violate it. Interpret this result. Does it imply that the solution to the optimal growth problem is less compelling? Show that when the condition in Proposition 13.3 is satisfied, the optimal growth path satisfies the transversality condition and yields a finite level of utility for the representative household.
Proposition 13.3
In the above-described expanding input variety model, the decentralized equilibrium is always Pareto suboptimal. Moreover, provided that (1- θ)η(1- β)-1/ββL , starting with any N(0) > 0, the Pareto optimal allocation involves a constant growth rate of
which is strictly greater than the equilibrium growth rate g∗ given in (13.20).
Suppose that consumtion equals $500 bilion when disposable income is $0, and that each increase of $100 billion in disposable income causes consumption to increase by $70 billion. Draw a graph of the saving function using this information.
suppose that the interest rate on a one year bond is 7 percent today and the interest rates expected on one year bonds in the future are 6 percents in one year, 5 percent in 2-year , and 4 percent in three years bond. what are interest rate today ..
Consider a worker who is paid a wage of $20 per hour. The worker has a disutility h^2 of working h hours. Assume that the worker faces a tax rate t. Thus, his net (after-tax wage rate is $20 (1 - t)). (i) How many hours will the worker work if his..
Discuss both the economics and the political economy of this viewpoint.
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A firm that produces houses has a total costs function given by the following: TC = 144 + 4Q2. If the industry in which this firm operates is perfectly competitive, in the long run competitive equilibrium the number of houses the firm will produce..
Joe's t-shirt shop is located in a small college town. the majority of business is custom t shirts for university book stores. as a sideline, they also sell t-shirts locally. the local demand is Q=200-5P. calculate output, price, and profit under ..
compute the r and y in which the two markets are clearing.
Assume ZCorp has the following short run production function: Q = 500X - 2X2 where X is the only variable input used by ZCorp to product its product, Q. Because ZCorp sells its product in a perfectly competitive market, it can sell all the Q it produ..
Suppose the government transfers 100 units of B's good 1endowment to A. How will the consumers' choices of good 1 in competitiveequilibrium change? Explain. (You should answer without repeating the utilitymaximization calculations.)
Calculate total revenue, marginal revenue, marginal cost, and average cost at each level of sales fo the store. If Swim N Style is a profit maximizer, what number of suits will it sell per hour? What will its price and profit be? How can you tell wha..
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