QUESTION 34Please answer the following three questions based on this modified Malthusian model: suppose individualshave the following utility function: u( C;i n,) = In( Ct )+0 In( nt), where Ct is consumption and nt is thenumber of kids, and 0> 0. The cost of raising children is entirely a goods cost, and is given by p (per child).Individuals have one unit of labor, and labor is paid a real wage, w.. Suppose the production functiondepends on the labor supply, Lp and is given by Y. = A.L,a , where 0 QUESTION 35Following from the model described in the previous question. What is the budgt constraint facing theindividual, and what is the optimal condition for individual choices of consumption and fertility?1The budget constraint is wt- pn; = C;i The optimal condition isCtpnt1The budget constraint is w, -p= C;; The optimal condition isCtnt1The budget constraint is Wt-p3 Ct; The optimal condition isCt%3DThe budget constraint.is w -p-n;= C; The optimal condition isCt = Opn;

34. Given : Yt=AtLtα Marginal Product of labor : =dYtdLt=d(AtLtα)dLt=αAtLtα-1 Hence,the correct…

34 Please answer the following three questions based on this modified Malthusian model: suppose individuals nave the following utility function: u( C;i n) = In( Ct)+0 In( nt), where Ct is consumption and nt is the number of kids, and 0> 0. The cost of raising children is entirely a goods cost, and is given by p (per child). Individuals have one unit of labor, and labor is paid a real wage, w Suppose the production function depends on the labor supply, L, and is given by y. = Ala, where 0< a< 1 and A, is the TFP. Labors ar paid a wage equal to the marginal product of labor. What is the expression for the wage rate? %3D Wt = AL;" a-1 %3D Wt = At At Lt %3D

34 Please answer the following three questions based on this modified Malthusian model: suppose individuals nave the following utility function: u( C;i n) = In( Ct)+0 In( nt), where Ct is consumption and nt is the number of kids, and 0> 0. The cost of raising children is entirely a goods cost, and is given by p (per child). Individuals have one unit of labor, and labor is paid a real wage, w Suppose the production function depends on the labor supply, L, and is given by y. = Ala, where 0< a< 1 and A, is the TFP. Labors ar paid a wage equal to the marginal product of labor. What is the expression for the wage rate? %3D Wt = AL;" a-1 %3D Wt = At At Lt %3D

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q3
Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium.
Suppose an individual makes consumption and savings decisions in two time periods (1 and 2). Its utility function is given by: U = In addition, the prices and income of said individual and the interest rate he faces are known: P1 = 1, P2=3; M1 = 100, M2 = 200 r=0.23 Determine: a) The budget constraint and plot b) Optimal demand functions c) The savings supply function d) In equilibrium, will the individual be a lender or a borrower?
Assume a primitive society that produces two goods: food and tools. There is a consumer that is currently willing give up 2 units of food to obtain 1 tool (MRSTF=2). The price of a tool is 3 coins, and the price of food is 1 coin per unit. Is this individual maximizing their utility? Explain Briefly.