/2. (a) Show that if x is an allocation in the y-core of an economy, then any two agents of the same type must receive the same bundles, provided the preferences of the agents are convex, strongly monotonic and continuous. (b) Suppose that an apple orchard is located next to a bee keeper. The orchard produces A apples and the bee keeper produces H units of honey. The cost function of the apple orchard is C(A) = A² and the cost function of the bee keeper is C,(H) = H² – A. Show that the socially efficient supply decisions involve apple orchard producing more apples than it would if it only considered its own costs. %3D

/2. (a) Show that if x is an allocation in the y-core of an economy, then any two agents of the same type must receive the same bundles, provided the preferences of the agents are convex, strongly monotonic and continuous. (b) Suppose that an apple orchard is located next to a bee keeper. The orchard produces A apples and the bee keeper produces H units of honey. The cost function of the apple orchard is C(A) = A² and the cost function of the bee keeper is C,(H) = H² – A. Show that the socially efficient supply decisions involve apple orchard producing more apples than it would if it only considered its own costs. %3D

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

Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation?
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U = X11X 12 U2 = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) W3= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x= (1,2), x2= (8, 4), X3= (1,4) C. Show that x is not in the core.
12
image attached
= 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.
Consider a pure exchange economy with two goods k = 1,2 and two households i = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively. Utility functions for households A and B are UA (TA1, A2) = TA1TA2 and UB(B1, B2) = XB1T32. (a) Find an expression for the Pareto optimal set. (b) Assume e A = (4,4) and eg (5,8) are A and B endowments, respectively. Find the competitive equilibrium. (c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this result should not surprise us?
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.
5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u4(x4) Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xg, q = 0, 1, 2, ...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. rA + 3r and uB(xB) 4x? + x. (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.