Considerthefollowingmodeloftheeconomy

Productionfunction: Y=AKN-N2/2Marginalproductoflabor:MPN=AK-N.

wheretheinitialvalues ofA= 10and K =10.

The initial labor supply curve is given as: NS = 50 + 4wInitialconditionsinthegoodsmarket

Cd=790+.50(Y-T)-500rId=1000-500r

G=800

T= 100

Md/P=110+0.5Y-1000(r+e)

NominalMoneysupply M= 5000

Expectedinflationisequalto2%(e=0.02)

1a) (6points)Solvefor the labormarketclearing realwage(w*),the profitmaximizinglevel of labor input (N*), and the full employment level of output (Y*). Please show work.Drawtwodiagramsvertically withthelabor market onthe bottomgraphandtheproductionfunctiononthetopgraph. Besuretolabel everythingincludingthis initialequilibriumpointaspointA.(10pointsfor completelylabeledand correctdiagrams)

Answer

Since Da LM Carrive shows the age bed Condition is money most lut Md 5000 2560 2 110 + 0.5 4 - 1000 ( 7 + Te ) = 2500 =1 140 + 0.54 - 10507- 1000 (0 02) = 2500 31 0 .54 - 10007 = 2500 + 20 - 410 = 2410 = ) 0.54 - 1000 = 2410 this is the one for LM Curve,the production firs as given by YERAN - N/2 ) MINE A-N So the demand for labour is given by- Mraz as white to be the real wage (it) AK - NEW Labor supply curve is given NJ = 50 + 40 5 AK - ( 50 + 9 ( ) = W > AK - 50 - 4W = W ") AK -50 = 5W LY = AK - 50 5 NOW A = 10 2 10 = K. 5. 5 3 optimum N = 50+4 ( 1) = 150 + 4 (10) => N= 504 40 290 So at NERO , A = 10, K = 10 YE AKIN - N/U. = 10 (10) 90 - 90 / 2 Nim = 9000 - 8100/2 -4950 A 1= 10 same -to look at the fig. NAIM wheree optimum choice of N will be determined YA by the intersection 4 = P(N) of N ENS. L thi com 4950 K at NON 42 4950IS - Curve CA = 340 + 0.5(4-7) - 5007 Id = 1000 - 500 G= ROD, T=400 the Is Cave is given by- Y = Cat Id + G = (790 + 0.57 -0. 5 T - 5 0or ) + (1000 - 50or) + 800 = 190 +0-54 - 0-5 (100) - 50or + 1600 - 50.Y + 860 240 - 50 + 1000 4 507 - 1600Y O.54 5 9590 - 10001 10807 +0-54 = 2540 be the ISthat clean tie good market cans andTim o me need to find out T at y= 4950 JOO07 - 25 40 - 0-5 (4950 ) = 65 65 = 0. 065 6.5%the money stopply egg is given by - M = 5000 & The= 2%:20.01 *the demand care of money is givenby - MyP = 110 + 0:54 - 1000 (1+ te) So -= 410 + 0.5(4150) - 10007- 1050(0-02) 2585 - 1060 (0 065) - 10 (0-02) = 2560 560 0 P = 250 0 2500 P=P = 2 be the Price level that clean the money market.int. rated (0 ) . Sd = 0.54 - 740 - 5008 4 1B I d = 100 - 500r Id, 1680 output ( y ) At equilbrium, S d - Id 0. 54 - 740 - 5085 = 100- 5007 0 . 54 - 840 y - 1680 Putting 1680 in egn D . 0 .5 x 1680 - 740 - 560r = 100- 5008IS - LM LM A 6. 57- - 15 3910 7 y IS = LM govDo + 0 sy = 25 40 2 0154 - 1 (DOT : 2410 9 coo x 6 . 8 85 + 0 . 54 = 2540 5 85 + 0. 5 4 = 2840 0.54 = 1955 y 1955 3810P Date ..... / .... / ...........mal LM LM 1 2 15 ' 15 3910MS 3 output 3970 Map - 110+ 0. sy 1830 - 1000 (8+ 0.02) 110 + 0. 54 - 1000 (27+ 0.02 ) = 1830 1850 + 0.54 - 10005 + 2 00 2 1830 110 + 0 .54 - 1000 = 2030 O . sy - 1coot = 1920 0 .54 - 100 0 *0 065 = 1920 0 . sy - 65 = 1920 0 . 54 - 1520 +65 o.sy - 1985 3 9 7 0