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 completelylabe

Answer

the production fins is grew by- Y = KA. N - N/ = MING A- N S. the demand for labour is given by - Min= w whenhe w be the sual wage (lp ) AK - N = W labor supply curve is given by N1 = 50+4W 5 AK - ( 50 + 4 ( ) = W => AK - 50 - 4W = W ") AK -50 = 5W = = AK - 50 5 now A = 10 2 10 = K. . ex - 100-60 5 optimum N = 50+4 ( 4 ) = 50 + 4 (10) => N= 504 40 290 So at N= 90 , A = 10, k = 10 Y= AUN - N/ 2 = 10 (10) 70 - 90/2 NIM = 90 00 - 8100/2 - 4950 A W = 10 same - - look at the fig. where optimum choice of N will be determined Y A by the intersection 4 = F( N ) of Nd E NS. L the com Cit is given by A. 4950 and at 1qin Nas go * at NON 42 4950 N= 90IS - Curve CA = 740 + 0:5(4-7) - 5007 If = 1000 - 500 , G= 800, =100 the is carve is given by - Y = ed + Id + G = ( 790 + 0. 5 7 - 0. 5 T - 5 0or ) + (1000 - 50or) 208 - WA + 800 2 790 +0-54 - 0-5 ( 100) - 50or + 1000 - 50or + 800 O.54 = (790 - 50 + 1003 + 807 - 1000Y 0-5 4 = 2590 - 10004 = ) 1000 8 + 0-54 = 2540 be the IS exsThe no that clean the good market. ( since IS Curve shows good market eging landtion) so we need to find out at y= 4950 JOO07 - 25 40 - 0. 5 ( 4950) = 65 65/ 1050 = 0-065 6-5 % 1=15%will clear the goods market.the money supply eng is given by - M' = 5008 4 719 - 2% =0:01 *He demand care of money is givenby - MyP = 110 + 0:54 - 5000 (1+ the) So - = 110 + 0.5( 4950) - 10007- 1050 (0-02) 2 2585 - 1060 (0 065) - 105 (0-02) = 2560 P = Md 500 0 250 0 2500 P= P'- 2 be the Price level that clean the money market.Since Da LM Carive shows the aqm bed Condition in money most let 5000 P 2506 2 110 + 05 4 - 1080 ( 7 + The ) = 2500 =1 140 + 0.54 - 10507- 1000 (0.02) = 2500 31 0 .54 - 1000 - 2500 + 20 - 410 = 2410 0.54- 1000 = 2410 this is the one for LM Curve