(a) Construct and explain the lifetime budget constraint of a house-hold.(b) Derive and interpret the household's optimality conditions withrespect to consumption and leisure in the two periods.(c) Derive the optimality conditions of the firm with respect to thelabour input in the two periods.(d) Provide a definition of competitive equilibrium for this economy.(e) Imagine there is a positive temporary shock to the price of en-ergy. How can this shock be interpreted in the context of themodel above? Use the solution to the model to analyse theequilibrium effects of this shock on the real interest rate, con-sumption, leisure, hours worked, profits and the real wage inboth periods. Explain your answer intuitively.(f) Use a graphical analysis to separate income and substitution ef-fects. Which of these two effects prevails in equilibrium? Discusswhether the dynamics implied by shocks to the price of energymatch the stylized facts of the business cycle. 2. Consider an economy that lasts for two periods, populated by firmsand households. Markets are competitive. There is no government.Households' utility function is well-behaved and defined asU(C, 1) = u(C, 1) + Bu(C", l')where 0 < 3 < 1 is the preference discount factor, C and 1 isconsumption and leisure in the first period, while C' and l' areconsumption and leisure in the second period. h, the number ofhours available to households, is normalised to 1. The per-periodutility function is given by:u(C, 1) =Cl-n1-n— v(1 - 1)where n > 0 and > 0. Firms produce output hiring labour fromhouseholds. The first period production function is defined asY = zNdwhere Y is output, Nd is the demand for labour and z is the to-tal factor productivity in the first period. Second period output isproduced using the same technology as in the first period.Page 3 of 4Copyright 2022 v01 Ⓒ University of SouthamptonECON2004 W1(a) Construct and explain the lifetime budget constraint of a house-hold.(b) Derive and interpret the household's optimality conditions withrespect to consumption and leisure in the two periods.

Intertemporal decisions in economics involve economic trade-offs across different time periods. It…

Answered: (a) Construct and explain the lifetime…

Business

Economics

(a) Construct and explain the lifetime budget constraint of a house- hold.

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

Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of good 1 and ₂ units of good 2, their utility is given by u(x₁, x2) = aln x₁ + ln x2, where a > 0 is a free parameter. (i) How does the parameter a affect the marginal rate of substitution between goods 1 and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter a increases.
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…
3(b)Consider the following social choice problem in the setting of consumption of two goods by two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1 consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(q). The social endowment consists of 15 units of tillip and 20 units of quillip. a. Suppose that a social dictator has social welfare functional of the following form: social welfare, as afunction of (u",u") is a weighted sum with weight 2 on the lesser of u' and u' and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner? b. What is the set of all feasible, Pareto efficient allocations of the consumption good for this society? %3D
part C D
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
part B C D urgently
2. Consider a small island economy where the government is contemplating imposing a tax on bananas to raise revenue for public projects. The islanders' utility from consuming bananas (B) and coconuts (C) is given by the Cobb-Douglas utility function: U(B, C)=B°C1-a where a = 0.3. (a) Write down the consumer's optimization problem and derive the demand functions for bananas and coconuts. (b) Suppose the initial prices are PB $2 and Pc = = $4, and the consumer's income is I = $100. Calculate the initial quantities of bananas and coconuts consumed. (c) Calculate the compensating variation (CV) and equivalent variation (EV) for a tax rate of t = $0.50. Interpret your results in terms of the impact on consumer welfare. (d) Determine the tax revenue per consumer after the tax is imposed, assuming supply is perfectly elastic so the tax falls entirely on consumers. (e) Compare the impacts on consumer welfare between a flat tax equal to the revenue found in part (d) and the per-unit tax.
3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?
1
2) Two consumers R and S share an endowment (x, y) of goods X and Y. The consumers' utilities from consumption can be written as UR = aln(XR) + bln(YR), and Us=aln(xs) + bln(ys), where XR, XS, YR, and ys are the quantities which each consumes, and a and b are parameters, for which a + b =1. Write a report in which you a) Define the concept of the contract curve, and show that for these endowments, it will be the upward diagonal of the Edgeworth box, which shows all possible divisions of the endowment. b) Assume that in the initial endowment, XRE = XE and ysE=yE. R begins with the endowment of X and S begins with the endowment of Y. By setting up a constrained maximisation problem for each consumer, obtain their offer curves, and hence obtain the Walrasian equilibrium. c) State the two welfare theorems, and explain how they apply in this case.
8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x, y) U(2,2) defines y as a function of x in a %3D neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?