3. Consider a one-consumer one-firm economy in which u(x) = aTz+1q, w = 1 and f(z) = z2.(a) Derive a competitive equilibrium for this economy.(b) Derive the Pareto set of this economy.

This question asked us to derive a competitive equilibrium and subsequently determine the Pareto set…

Answered: Consider a one-consumer one-firm…

Consider a one-consumer one-firm economy in which u(x) = axz+xq, w = 1 and f(z) = z². (a) Derive a competitive equilibrium for this economy. (b) Derive the Pareto set of this economy.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b) There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical…
The utility possibility frontier is defined as the set of maximum utility levels for all consumers that is feasible in the economy, given resource constraints and preferences. For a two-consumer economy, it is defined formally as the solution to: u (ūB) = max u A (xA) subject to ug(xB) > ūg and (xA, XB)feasible. For each of the economies above, find an equation for the utility possibilities frontier, and graph it.
There are two goods, Computers and Wheat, and two factors of production, capital and labor. Production in both sectors satisfies constant returns to scale. Production of computers is relatively more capital-intensive. Both input and final goods markets are competitive. Goods are freely traded internationally, but factors are immobile across countries. We will focus our analysis on the Home country. In the initial equilibrium, the Home country produces both computers and wheat, but only exports wheat. In our analysis, we will consider the following sequence of time-frames: In the short run, both factors are completely specific to their initial sectors of employ- ment. (i.c. both factors are used to produce both goods, but in the short run it is impossible to relocate the factors that are currently in use for production) . In the medium run, capital is specific but labor can relocate. . In the long run, both factors are mobile across sectors. • In each run, the prices of factors adjust…
The First Theorem of Welfare Economics can be expressed asA) the competitive equilibrium results only when no transactions costs exist.B) the competitive equilibrium does not involve reallocation of endowments.C) any efficient allocations can be achieved by competition.D) the competitive equilibrium is efficient.
Refer to Figure 14-7. Assume that the market starts in equilibrium at point W in graph (b) and that graph (a) illustrates the cost curves facing individual firms. Suppose that demand increases from D0 to D1. Which of the following statements is not correct? a. Point Z is a long-run equilibrium point. b. Point Y is a long-run equilibrium point. c. Points W, Y, and Z are short-run equilibria points. d. Point W is a long-run equilibrium point. PRICE Graph (a) MC ATC P₂ aa P Q Q QUANTITY PRICE P₂ a a a Graph (b) Q Qy Qx Qz QUANTITY Do D₁
Consider a two-good exchange economy with two types of consumers. Type A have the utility function And an endowment of 3 units of good 1 and k units of good 2. Type B has the utility function And an endowment of 6 units of good 1 and 21 - k units of good 2. a. Find the competitive equilibrium outcome and show that the equilibrium price p* = p1/p2 of good 1 in terms of good 2 is p* = 21+k/15. b. Find the income levels (MA; MB) of both types in equilibrium as a function of k. c. Suppose that the government can make a lump-sum transfer of good 2, but it is impossible to transfer good 1. Use your answer to part b to describe the set of income distributions attainable through such transfers. Draw this in a diagram. d. Suppose that the government can affect the initial distribution of resources by varying k. Find the optimal distribution of income if (i) the SWF is W = log(MA) + log(MB) and (ii) W = MA + MB.
How did the lauch of Apple's ipad effect the competitive market environment? High prices and high profits in a competitive generally lead to new suppliers entering the market, prices sliding down the market demand curve, the market supply curve shifting to the right, and significant product and technological innovation.
12
Please answer the question fully and completely else I will rate negative, thanks! Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with a unit of each good. The utility functions of each consumer are: A: 13 4 4 u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2 The firm B 1 A 1 1 2 produces good 2 using good 1 as an input, according to the production function f(y) = y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 If P₁ and P2 determine the utility maximizing demand of consumer are the per unit prices of goods 1 and 2, . B for each good as a function of p, and P2 · If P₁ P 2 1 and are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. Ifp, and p2 are the per unit 1 prices of goods 1 and 2, determine the utility maximizing demand of consumer…
An economy with many consumers (Amy, Hao, ...), many producers, two goods (A and B) and two inputs (L and K) is in a competitive general equilibrium. Which of the following conditions are satisfied in this economy? (Select all that apply) The absolute value of the slope of PPF (with good A on the horizontal axis) is equal to MCA / MCB, the ratio of marginal costs of producing goods A and B, at any point on PPF MRSAB = PA / PB for all consumers For every possible redistribution of goods among the consumers, some of them will be better off and some of them will be worse off. MRS = MRT MRS MRTS PA = MCA and PB = MCB MUAmy = MUHao A = PA MRTS = PA / PB MUAmy A = MCA and MUAmy B = MCB MRTS between labour and capital is the same for all firms, whether producing good A or good B. the ratio of input marginal products must be equal to the ratio of input prices MRT = MRTS for all firms, whether producing good A or good B For every possible redistribution of inputs among the firms, the quantity…
B) In his State of the Union address in 2003, President Bush supported the idea of changing from the use of internal combustion engines to fuel cells based on hydrogen as a way of reducing air pollution and the emission of greenhouse gases. Fuel cells are nonpolluting because they only emit water vapor. President Bush proposed having the government subsidize research and development of hydrogen fuel and fuel cell technology. The president did not propose raising taxes on gasoline as a way of encouraging the use of fuel cells and reducing greenhouse gases. Currently, hydrogen is more expensive than gasoline.
= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.