Question

1.Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function:u(c,r)=cr,

where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c=a√L

where a is some constant, and L is labour. Suppose that a=4. Finally, there is a time constraint: r+L=18.

Consider a competitive labour market. Given the wage rate, w=2.0, a firm would like to hire     units of the labour input. (Answer just the number up to 2 decimal places.)

2.

Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function:u(c,r)=cr,

where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c=a√L

where a is some constant, and L is labour. Suppose that a=4. Finally, there is a time constraint: r+L=15. If Robinson acts as a social planner of this economy, how many units of coconuts will be produced and consumed? (Answer just the number up to 2 decimal places.)

Answer 1

Graph Labor (hours) Coconuts Production function 0 24 Feasible production plans Technology: Labor produces output (coconuts) according to a concave production function Econ 370 - Production 6 Robinson Crusoe’s Preferences • To represent RC’s preferences: – coconut is a good – leisure is a good • Yields standard indifference map with leisure • Yields indifference curves with positive slopes if plot laboor. Graph Leisure (hours) Coconuts More preferred 0 24 Econ 370 - Production 8 Robinson Crusoe’s Preferences: Graph Leisure (hours) Coconuts More preferred 24 0 Labor (hours) 3 Econ 370 - Production 9 Robinson Crusoe’s Choice: Graph Leisure (hours) Coconuts 0 24 Labor (hours) C* L* Econ 370 - Production 10 Schizophrenic Robinson Crusoe • Now suppose RC is both – a utility-maximizing consumer and – a profit-maximizing firm – And decides separately how much to produce or consume • Use coconuts as the numeraire good – So, price of a coconut = $1 • RC’s wage rate is w • Coconut output level is C Econ 370 - Production 11 Robinson Crusoe as a Firm • RC’s firm’s profit is π = C – wL • Isoprofit line equation is • π = C – wL ⇔ C = π + wL, in C-L space • Slope = + w • Intercept = π Econ 370 - Production 12 Isoprofit Lines: Graph Higher profit Slopes = + w C = π + wL (π1 < π2 < π3) Labor (hours) Coconuts 0 24 π1 π2 π3 4 Econ 370 - Production 13 Profit-Maximization: Graph • At optimum: – Isoprofit slope = production function slope – That is, w = p × MPL = 1 × MPL = MRPL Production function Labor (hours) Coconuts 0 24 π1 π2 π3 Econ 370 - Production 14 Profit-Maximization: Graph • As a firm, at wage w Robinson: – demands Labor L* – Produces C* coconuts – Gets π* = C* – wL* in dividends from the firm Labor (hours) Coconuts 0 24 C* L* π * Econ 370 - Production 15 Utility-Maximization: Introduction • Now consider RC as a consumer endowed with $π*, who can work for $w per hour • What is RC’s most preferred consumption bundle? • Budget constraint is: C = π * +wL Econ 370 - Production 16 Utility-Maximization: Budget Constraint Budget constraint: Labor (hours) Coconuts.