# Consider an economy with the production function Y = L(1/3)

November 24, 2016

ECO 305 – HW2
(Due Date: October 21 – beginning ofclass)

Please show all your work for full credit. Make sure that all graphs are fullylabeled.

Question 1 (50Points)

Consider an economy with the production function Y = L(1/3)

a) Derive the Labor demandCurve

b) If Labor supply curveis wage, labor andoutput.

Ls =(w/p),calculatetheequilibriumlevelsofreal

c) Assume Ms= 45 and k= 3 . What is the equation of the aggregate demand curve for this example? What is the price level? What is the nominal wagelevel?

d) Show equilibrium in labor market / output market / money market by using the graphical analysis of “The Complete Theory of Aggregate Demand andSupply”

Question 2 (50Points)

Consider an economy where, consumer’s utility function is given as U(C,L)=C-(1/2)L2. where C is consumption and L is labor. The production technology is Y=(1.6)L-(1/2)L2. The turnover cost per labor is(0.36)/(w/p)

(a) What happens to t as real wage increases? Give a clearintuition

(b) What happens to t as labor increases? Give a clearintuition

(c) Write down the firm’s maximization problem and solve it. Find real wage,labor.

(d) Write down consumer maximization problem and solve it. Derive labor supply curve

(e) Find real wage, employment, output and unemployment in thiseconomy.

(f) Illustrate the solution graphically using Labor Supply / Labor Demand and Production Function diagrams.

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