Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function: u(c, r) = cr, %3D where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c = avL, C = where a is some constant, and L is labour. Suppose that a=2. Finally, there is a time constraint: r+L=21 for the consumer. Also the consumer has income of 9. Consider a competitive labour market. Given the wage rate, w-1, the consumer would like to supply 2 decimal places.) units of the labour input. (Answer just the number up to

Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function: u(c, r) = cr, %3D where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c = avL, C = where a is some constant, and L is labour. Suppose that a=2. Finally, there is a time constraint: r+L=21 for the consumer. Also the consumer has income of 9. Consider a competitive labour market. Given the wage rate, w-1, the consumer would like to supply 2 decimal places.) units of the labour input. (Answer just the number up to

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Solve for first order conditions of the representative agent. Write down the market clearing condition (resource constraint) for the aggregate economy.
You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the following parameters. The maximum amount of money available to spend is $340 where the price of K=8 and the price of L=4. That is Pk=8 and Pl=4. The function is given as q=K0.4L0.6 . What is the constraint equation?
solve this all these three subparts early i upvote
You are told that q = 12 can be produced by (L,K) = (5,6) and (L′,K′) = (4,5). Explain whether each of the following two statements is true, false, or uncertain. (a) (q, L, K) = (12, 5, 6) represents an efficient production plan. (b) (q, L′, K′) = (12, 4, 5) represents an efficient production plan.
= 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.
Answer please with added diagrams b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b it is not optimal to work, say, 10, or 6 hours per day.
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 we have one consumer with a Cobb Douglas utility function for consumption, x, and leisure, R : u(x, R) = a ln a+(1-a) In R. The consumer is endowed with one unit of labor/leisure and there is one firm with a constant-returns to scale technology: a = aL. Determine r(p, w) and R(p, w).
Consider an economy with one consumer and one firm. The firm produces the output C from the labour L according to the production function f(L)=L/182. The consumer provides labour to the firm and consumes the good C. The consumer can work a maximum of 18 hours a day. Her utility function is u(Le,C)=2C+Le where Le=18-L is her leisure time. What is the time L the consumer should work at the Pareto efficient allocation? None of the other answers. O a. Ob. L=0 O c. L=9 O d. L=3 O e. L=6 thomnt
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?
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Consider a representative consumer with preferences over consumption e and leisure I given by u(e,l) = 1/4 * ln(c) + 3/4 * ln(l) Assume that the price of consumption is normalized to p = 1 and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 24 The consumer also receives dividend (profit) income of pi = 39 and pays lump-sum taxes of T = 7 (a) Write out the consumer's budget equation, and draw a graph of the budget constraint. (b) Solve for the optimal decisions e and 1. How many hours per day is the consumer working? (c) Suppose the consumer's wage decreases to w = 16 Solve for the new optimal choices of c and I". Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the wage changes in part e, determine whether the consumer experiences an income effect, a substitution…