2. Constructing an Equilibrium Households live two periods and have preferences U(C₁) + BU (C₂), where 0 < 3 < 1 and U is the utility function and satisfies our usual assumptions. There are Ñ households in the economy. N₁ 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 N131 in the first period and N₂92
Q: domestic economy
A: Globalization refers to the method of accelerated interconnectedness and interdependence among…
Q: Demand for microprocessors is given by P = 35 – 5Q , where Q is the quantity of microchips (in…
A: Business economics entails making judgments and allocating resources in complex market landscapes.…
Q: How might the confirmation tendency affect Nathan's decision and what could he do to mitigate the…
A: Nathan is faced with a decision-making scenario in which confirmation bias (also known as…
Q: Suppose that you, Jennifer, and Yusef constitute the market for CDs. Your demand for CDs is…
A: Demand is the desire of an individual ability and willingness to pay for a product. The demand is…
Q: Some of the most meaningful communications are neither spoken nor written select one: true or false
A: The point is to find out whether the statement "some of the most meaningful communication is neither…
Q: Suppose the demand curve for steale dinners is represented by P = 500- __Q and the marginal cost is…
A: The demand curve for steak dinners: P=500−12Q ..... (1)The marginal cost: MC=$60The market of…
Q: The next three problems are from Unit 10. You are provided with a pair of demand and cost functions.…
A: To find the maximum profits for the firm, we need to follow these steps:Determine the revenue…
Q: a. U(x,y) = 10 √ √xy. b. U(x, y) = xy. c. d. Which of the following utility functions represent the…
A: “Since you have posted multiple questions, we will provide the solution only to the first question…
Q: According to the "No, markets fail often" view, in the market for loanable funds OA. interest rates…
A: The loanable funds market provides a framework for understanding the borrowing process. Savings…
Q: Period Demand 1 8 where y Demand and x = Period. What is your estimate of the demand in period 7?…
A: The given data is shown in the table below:Period (x)Demand (y)18211310412510614
Q: Different Neighborhood in Town Rural Outlet Store Local Shoe Store 30 Juanita earns an hourly wage…
A: Opportunity cost is the amount of one good that is given up in order to produce one more unit of…
Q: A dress manufacturer is expecting higher prices for dresses in the near future. What would we…
A: The demand curve represents the quantity of a commodity demanded by consumers at different price…
Q: Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is:…
A: A production function is a mathematical equation that represents the relationship between the…
Q: In this Decision Point activity, you explored how the price elasticity of demand impacts business…
A: The elasticity of demand:The elasticity of demand is calculated as the proportional change in…
Q: Suppose you and a friend are stranded on an island and must gather firewood and catch fish to…
A: An opportunity cost is a potential benefit that someone loses out on when selecting a particular…
Q: If the demand for a pair of shoes is given by 2p + 5q = 200 and the supply function for it is p - 2q…
A: The demand curve illustrates the relationship between price and the quantity demanded of a good.…
Q: Olivia and Helen produce shirts and ties. The figure shows their PPF s . A graph…
A: The objective of the question is to determine if Olivia and Helen can achieve any gains from…
Q: How much will real GDP increase by if the Federal Reserve decrease the reserve ratio from 20% to 10%…
A: The investment multiplier gauges the influence of investment spending on the entire economy. It is…
Q: Daisy works for a candle manufacturer and has a great idea for a new product. She wants the candle…
A: The issue raised by Daisy's story has to do with product creation, pricing tactics, and possible…
Q: 6 01:10:00 The table below shows the market demand and supply schedules for pumpkins. (1) Price ($…
A: The demand, supply and shortage of the pumpkins in the market is given as PriceQuantity…
Q: 2. Let z = 1.3, s = 0.3, a = 0.35, et = 1 and 8 = 0.07. What is the value of capital in the steady…
A: Steady-state per worker capital refers to a concept used in economics to describe the long-term…
Q: Refer to Figure 7.3. Suppose a firm moves along the isoquant from point a to point b. The rate of…
A: The rate of substitution refers to the rate at which one input can be replaced by another input in…
Q: You have $10 to spend. You can buy burgers for $3 each or pizza for $1 per slice. Marginal utility…
A: The satisfying power of a commodity is known as utility. The individual's goal is to maximize…
Q: Consider a consumer with utility function u(x1, x2) = min(4 min{x1, x2}, x1 + x2} (a) Draw…
A: This can be described as the concept that provides the graphical representation of the combination…
Q: What is the unmet demand at equilibrium?
A: Unment demand is the demand which is not met, or excess demand. This occurs when there is excessive…
Q: Use the figure below to answer the following questions. Price (dollars per unit) 10 8 6 A 2 0 D 100…
A: Shortage = Quantity demanded - Quantity suppliedSurplus = Quantity supplied- Quantity demanded
Q: What is an external benefit? An external benefit is a benefit that OA. always equals external cost…
A: An external benefit refers to a positive impact or advantage that arises from an economic…
Q: The following graph contains four lines (A, B, C and D), each of which has a slope that is either…
A: The objective of the question is to understand the relationship between two variables and how it is…
Q: The demand for a good or service is determined by Question 30 options: 1)…
A: The objective of the question is to identify who determines the demand for a good or service in the…
Q: Find the profit function for the Cobb-Douglas production function f(x₁, x₂) = Ax¹x2² with A > 0, α₁,…
A: The Cobb-Douglas production function is the total input used to obtain a specific output level in a…
Q: Below is a hypothetical example of an estimated industry supply curve for automobiles. Qs = 4000P –…
A: The hypothetical industry supply curve is given as The value of PL is $30 per hour.The value of PT…
Q: Price per Movie ($) Quantity demanded Elasticity of Demand 2 3 4 5 6 7 8 1200 1100 1000 900 800 700…
A: Elasticity of demand (Ed) is a measure that quantifies how much the quantity demanded of a good or…
Q: Which of the following statements is not correct? A government-imposed price of $10 would be a bine…
A: Price ceiling is a situation when government sets the prices of goods and services to maintain…
Q: 2) Assume firms' marginal and average costs are constant and equal to c and that inverse market…
A: The firm marginal cost and average cost are equal to c. ⇒AC=MC=c where c>0Inverse market demand:…
Q: A real price is A price after deflation has occurred. O A nominal price plus the inflation rate. An…
A: The price level in an economy is determined where aggregate supply equates to aggregate demand. This…
Q: The following data shows the market for soccer balls: Price ($) 0 Demand 120 Supply 0 10 110 20 20…
A: Equilibrium price and quantity are determined by the intersection of demand and supply curves. An…
Q: If the firms each produce half the total number of units, each firm will earn a profit of $ (Enter…
A: The market inverse demand equation: P=204−4QThe marginal cost for the firm: MC=12Note: "Since you…
Q: Let 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded.…
A: Business economics requires making decisions and allocating resources in complex market…
Q: Consider two similar restaurants in close proximity to each other on either side of the U peso. The…
A: The objective of the question is to understand the impact of the devaluation of the dollar against…
Q: Diogo has a utility function: U = 100X0.920.1 The price of X is px = $5, the price of Z is p₂ = $14,…
A: Utility maximization problem: With the given prices and income, a consumer chooses his consumption…
Q: Over the past decade, medical costs have increased more rapidly than other prices. In order to…
A: The budget line is a Graphical Representation of the combination of goods, which a consumer can buy…
Q: Question 2 (i) Calculate the Nominal and Real Exchange Rate Indices for the pound sterling in…
A: The objective of the question is to calculate the Nominal and Real Exchange Rate Indices for the…
Q: In the short run, the cost of O a. capital; labor O b. labor; capital c. electricity; wages d. raw…
A: In economics, the analysis of costs for a firm may be carried out in the short run or long run. The…
Q: he graph shows the market for apple pickers in New England. estion Viewer mat is the equilibrium…
A: The dynamics of the supply and demand curves can be used to study the labour market in economics,…
Q: Question 8: Consider a utility function u(x₁, x₂)=√x₁+√√x₂. .. What is the optimal bundle with P₁,…
A: A consumer's satisfaction derived from the consumption of goods is defined as utility. Utility can…
Q: Question Price controls are set on infant formula. Calculate the shortage caused by the price…
A:
Q: Problem three For each of the following pair of goods, which good would you expect to have more…
A: The problem requires understanding the concept of interest rate elasticity and applying it to a…
Q: Which of the following would NOT be a cause for an increased American demand for the Mexican peso?…
A: Currency is the medium of exchange. Earlier the system of barter economy was prevalent where goods…
Q: Which of the following is true? O A. When & < -1, demand is considered inelastic. O B. When - 1 < &…
A: Elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in…
Q: Please solve for the marginal revenue function using the demand function: Q=1400-100p
A: Marginal Revenue (MR): The additional revenue generated from selling one more unit of a good. It's…
Step by step
Solved in 3 steps with 6 images
- 2. Constructing an Equilibrium Households live two periods and have preferences U(c) + BU(c2), where 0 0. The type 1 agent faces budget constraints Y1 c+s' rs' where consumption for the type i agent in period j is denoted c. The type 2 agent faces budget constraints G + s² Y2 +rs? = The resource constraints are N1c + N2c Nịc+ N2c (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.2. Constructing an Equilibrium Households live two periods and have preferences U(ci) + BU(c2), where 0 0. The type 1 agent faces budget constraints Y1 c+s' rs' %3D where consumption for the type i agent in period j is denoted c. The type 2 agent faces budget cOnstraints Y2 +rs2 = The resource constraints are N1c + N2c Nịc+ N2c (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(c) = 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…1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form U(C₁, C₂) = c₁²c₂². The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = y₁ − S and C₂ = y₂ + s(1 + r). a. Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in the first period? c. In the previous part, the interest rate remained at 1. Now, consider the savings function, that is, the relationship between the real rate of interest and the amount saved. The equilibrium interest rate is then determined as a market price in the Saving-Investment diagram. Given the typical shape…
- 1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) = X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y = 6 B: X = 14; Y = 19 show all work a) Suppose the price PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium. b) How much of each good does each consumer demand in equilibrium? Consumer A’s Demand for X: Consumer A’s Demand for Y: Consumer B’s demand for X: Consumer B’s demand for Y: c)What is the marginal rate of substitution for consumer A at the competitive equilibrium?Zach's preferences are representable by the utility function u = 90.3927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questions are rounded, where required, to two decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p2 = 30, what is the maximised value of Zach's utility? O Au= 6.74 O B. u = 5.39 O Cu = 5.65 O D.u = 7.56 O E. None of the aboveExercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, c²) = c(c²)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
- 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 and2. General Equilibrium. consumers, each with the same Cobb-Douglas preferences except with differ- ent parameters. Consumer 1 has utility function u(x, x)= (x})"(x})!-«, while Consumer 2 has utility function u(x, x;) = (xP(x)-P. The endowment of good j owned by consumer i is denoted w. The price of good 1 is p, and the price of good 2 is 1. In the superscript, we denoted the consumer i = 1,2; in the subscript, we denote the good j= 1,2. Consider an exchange economy with two Write the maximisation problem faced by each consumer i = (a) 1,2, taking care to define the objective function and the budget constraint. Set up the Lagrangian and find the first order conditions. (b) For each consumer i = 1,2 , use the first-order conditions to determine the demand functions for each consumer i = 1,2 and for each good j = 1,2, in terms of the price p. (c) Find the aggregate demand for each good j = 1,2 and clear the markets for each good. Hence, show that the equilibrium price pi is given by the…d) An exchange economy has two goods (apples, bananas) and two types of agents (1, 2). Endowment of agent 1 is (3 bananas, 3 apples), and endowment of agent 2 is (4 bananas, 2 apples). Both goods are divisible goods, so that it is possible to consume frac- tions of each good (e.g. 4.92 bananas and apples). Each type 1 agent's preferences are represented by the utility function U(x,x) = min{x, x}, where x and x denote the agent's consumption of bananas and apples, respectively. Each type 2 agent's preferences are represented by the utility function U(x3, x²) = 7min{x3, x4} where x and r² denote the agent's consumption of bananas and apples, respectively. Use an Edgeworth's Box to depict the set of Pareto efficient allocations in this economy. Please capture consumption of bananas on the horizontal axis.
- Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, ci) = c(ci)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.4. Consider an exchange economy of two goods and two individuals. Consumer A has an endowment of 100 units of good 1 and 12 units of good 2 wA = (100,12), while consumer B has an endowment of 100 units of good 1 and 3 units of good 2 wB = (100, 3). The consumers' utility functions are given by: UA х,4 + Inx,A and UB x,B + 2lnx,B %3D Which of the following allocations is not efficient? a. (x,4,x24) = (100,5), (x,³, x2³) = (100,10) b. (x,4, x24) = (50,5), (x,®, x,³) = (150,10) c. (x,4, x24) = (0,4), (x,³, x,") = (200,11) d. (x,4, x24) = (100,0), (x1",x,") = (100,15) %3DSuppose there are two consumers. A and B. The utility functions of each consumer are given by: U₁XX)-x²-y U₂XY)-x-² Therefore For consumer A: MUX-2XY: MU-X² For consumer B: MUx-Y²; MUy-2XY The initial endowments are: A:X-60; Y-150 B.X-45: Y-75 al Suppose the price of Y, Py-1. Calculate the price of X, P, that will lead to a competitive equilibrium. How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y Consumer B's demand for X: Consumer B's demand for Y d ts) What is the marginal rate of substitution for consumer A at the competitive equilibrium?