in the second, whereN = N1 + Ng.Households have access to a credit market where they can borTow (s < 0) or saves>0. The type 1 agent faces budget constraintsY = c+srs!where consumption for the type i agent in period j is denoted e. The type 2 agentfaces budget costraints2 +rsThe resource constraints areNye+ NạGNic+ NạNa2 =(a) State the maximization problem solved by each type of agent and derive the first-order and second-order conditions. Derive the solution using the implicit functiontheorem.(b) Determine the equilibrium conditions for the three markets using the resourceconstraints and the budget constraints. Provide a statement of the equilibrium.(c) Assume logarithmic utility U(e) = In(c) and derive a closed form solution forconsumption in both periods and savings for both types of agents.(d) Solve the social planning problem. Compare the solution of the social planningproblem with the competitive equilibrium. Demonstrate that the decentralizedsolution solves the social planning problem for a particular set of Pareto weights.Explain how this is an example of the First Welfare Theorem. 2. Constructing an EquilibriumHouseholds live two periods and have preferencesU(c) + BU(c2),where 0 < B < 1 and U is the utility function and satisfies our usual assumptions.There are Ñ households in the economy. N¡ of these households have endowment y,in the first period and no endowment in the second - these agents are called “Type 1".The remaining N2 have no endowment in the first period and y2 in the second period- these agents are called “Type 2." Hence the resources of the economy arein the first period and

Equilibrium is an economic concept, where two market forces, i.e. demand and supply equate each…

(a) State the maximization problem solved by each type of agent and derive the first- order and second-order conditions. Derive the solution using the implicit function theorem. (b) Determine the equilibrium conditions for the three markets using the resource constraints and the budget constraints. Provide a statement of the equilibrium. (e) Assume logarithmic utility U(e) - In(e) and derive a closed form solution for consumption in both periods and savings for both types of agents. (d) Solve the social pla

(a) State the maximization problem solved by each type of agent and derive the first- order and second-order conditions. Derive the solution using the implicit function theorem. (b) Determine the equilibrium conditions for the three markets using the resource constraints and the budget constraints. Provide a statement of the equilibrium. (e) Assume logarithmic utility U(e) - In(e) and derive a closed form solution for consumption in both periods and savings for both types of agents. (d) Solve the social pla

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: 8) Mark derives utility from watching movies and from playing computer games according to the…

A: Mark's utility function: U(c,m)=6c1/3m1/2 .... (1)Here c denotes the number of hours he plays…

Q: at the optimal output , what price will do drop in chrge and what will be its output?Price $ Output…

A: (1) At optimal output,

Q: 4. Consider the following utility function of a consumer: u(x₁, x₂) = a ln x₁ + (1 - a) ln x₂ where,…

A: Engle Curve: Engle curve for a good shows different combinations of demand for the good and…

Q: marginal utility for custard (U.). What is Amelia's marginal rate of substitution (MRS)? Give a…

A: Different utility levels of consumers are taken to be independent. This means that utility obtained…

Q: ;) Given preferences represented by the utility function u(x1, x2) = min{3x1, x2}. a) Write down the…

A: a) The given utility function is: U= min( 3x1, x2) This represents the utility function of perfect…

Q: ility representations = of the pairs of utility functions over X R2, state whether they erences. If…

Q: 2) For the following utility functions, using the budget constraint M = Pgx & Pyy, find the…

A: Compensated demand function: MRS = MUxMUy = 0.5x-0.52(0.5)y-0.5 = 1y0.52x0.5 equating MRS to price…

Q: You were presented with a utility maximizing rule which states: If you always choose the item with…

A: A state of maximal satisfaction is referred to as Consumer's Equilibrium. The consumer's equilibrium…

Q: max ixf exp(-pt)u(c(t))dt, subject to initial capital k(0) and law of motion of capital given by…

A: Think about the ideal control issue with the accompanying goal capability, starting capital, and law…

Q: .3 A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours…

Q: (4) Consider a Cobb-Douglas utility function U(1,2) = ria, where U is the utility level, x, and 2…

A: The utility maximization problem is to choose the amounts of commodities x1 and x2 to maximize the…

Q: With a high stress job that oversees the public health of a nation, Tony loves to eat pomegranate…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Which of the following utility functions represent preferences that always result in an interior…

A: Interior solution occurs when the optimal combination of goods and services have positive quantities…

Q: Assume a consumer with the utility function U = U (X, Y) = X2 Y2 and the typical budget constraint M…

A: Utility functions play an important role in economics because they assess individual happiness or…

Q: Suppose a consumer seeks to maximize the utility function U (x, y) = (x+2) (y + 1), where x and y…

A: For utility maximization the second-order condition we have to show the utility function is convex…

Q: The utility possibility frontier is defined as the set of maximum utility levels for all consumers…

A: The Utility Possibility Frontier (UPF) represents the maximum degree of total utility that can be…

Q: Answer both question (a) and (b) below. (a) State theWeak Axiom of Revealed Preference (WARP). (b)…

A: Revealed preference theory was given by Paul a Samuelson in 1938. Under this, theory, it is assumed…

Q: Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices…

A: The given utility function, U = min[4x,5y], which shows that both goods are complementary.…

Q: Which of the following utility functions represents preferences over consumption bundles (X, Y) that…

A: Marginal utility is extra amount of total utility in the market economy. Diminishing marginal rate…

Q: An individual's utility is given by: U (q1, q2) = a(q1)+ b(q2), where a and b are constants. When…

A: Given that, An individual's utility function is given by U(q1,q2) = a(q1)+b(q2) Here ,this is a…

Q: Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility…

A: Utility:The utility is want satisfying power of a commodity. It can be expressed in cardinal and…

Question

in the second, where
N = N1 + Ng.
Households have access to a credit market where they can borTow (s < 0) or save
s>0. The type 1 agent faces budget constraints
Y = c+s
rs!
where consumption for the type i agent in period j is denoted e. The type 2 agent
faces budget costraints
2 +rs
The resource constraints are
Nye+ NạG
Nic+ Nạ
Na2 =
(a) State the maximization problem solved by each type of agent and derive the first-
order and second-order conditions. Derive the solution using the implicit function
theorem.
(b) Determine the equilibrium conditions for the three markets using the resource
constraints and the budget constraints. Provide a statement of the equilibrium.
(c) Assume logarithmic utility U(e) = In(c) and derive a closed form solution for
consumption in both periods and savings for both types of agents.
(d) Solve the social planning problem. Compare the solution of the social planning
problem with the competitive equilibrium. Demonstrate that the decentralized
solution solves the social planning problem for a particular set of Pareto weights.
Explain how this is an example of the First Welfare Theorem.

2. Constructing an Equilibrium
Households live two periods and have preferences
U(c) + BU(c2),
where 0 < B < 1 and U is the utility function and satisfies our usual assumptions.
There are Ñ households in the economy. N¡ of these households have endowment y,
in the first period and no endowment in the second - these agents are called “Type 1".
The remaining N2 have no endowment in the first period and y2 in the second period
- these agents are called “Type 2." Hence the resources of the economy are
in the first period and

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Define equilibrium

VIEW

Step 2: State the maximisation problem

VIEW

Step 3: Determine equilibrium condition

VIEW

Step 4: Calculate logarithmic utility

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Let a consumer's utility function be U (x, y) = x'/²y/2. The consumer's income is I = 160 and prices for the two goods are, respectively, p, = 1 and py = 4. (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose now the price of good y is equal to p, = 16 (while the price of good r stays constant). Compute the new optimal consumption basket.
Which of the following utility functions represent preferences that are NOT homothetic? (a) U(X, Y) = 10X ² + y² (b) U(X, Y) = ln(X) + 42 ln(Y) + ² (c) U(X,Y) = 4X¾ +7Y (d) U(X,Y)= XY (e) All of the above utility functions represent homothetic preferences
Assume that U(X, Y) = Xa Yb Budget constraint is I = Px X + Py Y Please solve the above utility maximization problem (constrained optimization) using Lagrangian Method for the optimal quantities X* and Y* showing step-by-step solution.
Q3: Are the following utility functions quasi-linear, quasi-concave, quasi-convex, homogenous of degree 0, homogenous of degree 1? Show your working: 1) U(x,y) = min(x,y) 2) U(x,y) = (x" + yaja
Problem 2.3 Let the consumer's preferences over consumption bundles (x1, x2) be represented by the utility function u(x1,X2) = /x1 +1·(x2+1). Which of the following statements is correct? (a) The utility function v,(x1,x,) = In(x, + 1) + 3 ln(x, + 1) also represents the consumer's preferences. (b) The utility function v,(x1,x2) = In(x1 + 1) + In(x2 + 1)² also represents the consumer's preferences. (c) None of the statements is correct.
Q.3 A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours spent playing golf and y is the hours spent playing cards per month. Calculate the values of x and y for which utility is maximised, subject to the constraint 21x + 3y = 180
Question 3: Assume that U(X, Y) = Xa Yb Budget constraint is I= P, X+ P, Y Please solve the above utility maximization problem (constrained optimization) using Lagrangian Method for the optimal quantities X* and Y* showing step-by-step solution. ANSWER:
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…