Consider a two-period small open economy populated by households and firms with a single good each period. = The preferences of the representative household are described by the utility function u(c₁c₂): (c₁c₂)² where c₁1 and c₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ = 1. In period 2, the household receives profits, denoted by T₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + bh = 9₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 41.5, where Q₂ and 1₁

Consider a two-period small open economy populated by households and firms with a single good each period. = The preferences of the representative household are described by the utility function u(c₁c₂): (c₁c₂)² where c₁1 and c₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ = 1. In period 2, the household receives profits, denoted by T₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + bh = 9₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 41.5, where Q₂ and 1₁

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.5P

See similar textbooks

Similar questions

Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium.
Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function: u(c, r) = cr, where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c = avL, where a is some constant, and L is labour. Suppose that a=2. Finally, there is a time constraint: r+L=21 for the consumer. Also the consumer has income of 9. Consider a competitive labour market. Given the wage rate, w=1, the consumer would like to supply 2 decimal places.) units of the labour input. (Answer just the number up to
The question is a descriptive question in Microeconomics. Consider an economy inhabited by identical agents of size 1: A representative agent's preference over consumption (c) and labour supply (l) is given by the utility function u(c,l) = ca (24-l)1-a for 0<a<1 Production of the consumption good c is given by the production function c = Al; where A > 0 is the productivity of labour. Both the commodity market and labour market are perfectly competitive: the buyers and sellers take the price as given while taking demand and supply decisions. Let us denote the hourly wage rate by w > 0 and price of the consumption good by p > 0: A competitive equilibrium is given by the allocation of consumption andlabour, (cCE,lCE) and the relative price ratio, w/p, such that for given w and p, a representative agent decides her labour supply, lS, and consumption demand, cD; to maximize her utility; A firm decides its labour demand, lD; and supply of consumption good, cD; to maximize its…
(2) Consider a Robinson Crusoe's economy, where he has 10 hours to spend on gathering coconuts (L), or a leisure (R). That is, L + R = 10. He can produce coconuts based on the production function given by C = 4√L, where C is the number of coconuts. He does not enjoy gathering coconuts, but does enjoy his leisure time and eating coconuts. His utility function is given by u(C, R) = CR. (a) Find the optimal allocation (C*, L*), in which Robinson Crusoe acts as a social planner. (b) Now consider a de-centralized economy. That is, think of this economy that consists of many individuals with the identical taste and technology. First, consider a firm's decision problem. The firm produces coconuts (C), employing workers (L). The firm hires L in a competitive market, given the wage rate (w). Without loss of generality, assume the price of coconuts to be Pc = 1. Given the market wage rate (w), how much labour would a firm hire in order to maximize its profits? Label your answer as L, and note…
Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(x1, x2) = In ¤1 + In x2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf, y½) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (y7, vž) = (38, 12(1 – B)). The hunter-gatherers now have the possibility of opening up their economy to free trade. In world markets, 1 unit of meat can be exchanged for 2 units of berries, and the country would be a price-taker. Which of the following statements is correct? O a. Only agents of type g benefit from free trade. O…
Consider a two-period small open economy populated by households and firms with a single good each period. The preferences of the representative household are described by the utility function u(c₁c₂) = (C₁C₂)² where ₁ and ₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ = 1. In period 2, the household receives profits, denoted by T₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + b =q₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 410.5, where Q₂ and 1₁ denote…
Consider a two-period small open economy populated by households and firms with a single good each period. The preferences of the representative household are described by the utility function u(c₁c₂) = (C₁C₂)² where c₁ and c₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ 1. In period 2, the household receives profits, denoted by T₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + b = 9₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 410.5, where Q₂ and 1₁ denote…
5. Suppose the economy consists of a representative agent with the following utility function: P U = Cα ( M )1−α. Labor is supplied exogenously at level L¯. Output is sup- plied by a perfectly competitive representative firm, which has production function Y = Lη . Any profits are remitted to the representative agent. There is a government, which purchases amount G of goods and services. This amount is financed by a lump-sum tax, of level T and seigniorage. Money is the only asset in the economy; initial money holdings are given by M l. Money is supplied exogenously by the government. Assume both prices and wages are flexible. (a) Write down the consumer’s and the firm’s intertemporal maximiza- tion problems. (b) Solve for expressions for aggregate demand and supply (that is, out- put as a function of the price…
Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to l = 24 – h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and It hours of work can be represented by the utility function U(c, h) = c- (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours of work h*(w, 1 - T, Y) and con- sumption c*(w, 1 - T, Y). (c) Repeat part (b) for a consumer with the utility function U(c, h) = alog(c) - Blog(h).
Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier.
Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h'+p U(C,h) = c-B- 1+ p where ß> 0 and p > 0 are parameters. TENTO COITS ar answer aneren ananm pally. p (j) Suppose instead that the consumer's utility function was U(c, h) = min(c, -h). Would the EB from a unit excise tax be larger or smaller compared with the original utility function. Explain your answer in 4 sentences.
Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h²+p U(c,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ P a) What is this consumer's budget constraint? (e) Suppose now that the income tax liability is increased to T = 0.3. Calculate the consumer's utility at their new utility maximizing consumption and labour supply bundle after the tax change. (h) Using the excess burden formula, calculate…