Question

Yp(Potential Output) = 10L^½ K^½; W = 10 + 1Ls; W = 60 – 1Ld( W = nominal wage rate) ; Total demand for goods and services1 (planned consumption + gross investment + planned government purchases + net exports) = 1600 – 10P ; short-run aggregate supply: Y = -400 + 10P; C = 60 + 0.9[Y – Tx] – 1P; Net Exports = 0; Government purchases = 50; Last year’s capital stock = 100; gross investment = 50; Net investment = 44; retained earnings = 10; average values for Ufrictional = 5%; Ustructural = 13%; Ucycled = 2%; Tax = 0 always.

5. The economy is initially in long run equilibrium.

What is the price level? __________

6. What is the unemployment rate in #5? _________

7. What is the value for consumption in #5? _______

8. Then government purchases increase and the AD1

curve becomes AD2 = 1800 – 10P. What is the

unemployment rate when the economy moves to its

new short run equilibrium? __________

9. What is the new value for G? ______________

10. Eventually, wages and prices rise and the economy returns to its long run equilibrium. What will

be the value for the nominal wage rate in this new long run equilibrium? __________

11. What is the value for total business saving in this economy? __________

Answer 1

5).

Consider the labor market here the demand the supply of labor are given, at the equilibrium the demand must be equal to supply.

=> 10 + Ls = 60 – Ld, where Ld=Ls=L.

=> 2*L = 50, => L=25 and the “K=100”. So, the potential output is, => Yp = 10*L^0.5*K^0.5.

=> Yp = 10*25^0.5*100^0.5 = 500, => Yp = 500. At the LR equilibrium the level of output should be at Yp. Now, the AD function is given by.

=> AD = 1600 – 10*P, => 10*P = 1600 - AD, => 10*P = 1600 – 500 = 1100, => P = 1100/10 = 110.

So, the price level is “P=$110”.

6).

In the LR an economy always at its potential level, => Yp = 500 and the unemployment rate should be at its natural level. Now, the “natural rate of unemployment” is the sum of “frictional unemployment rate” and “structural unemployment rate”, => u=5+13 = 18%.

7).

The consumption function is, => C = 60 + 0.9*(Y-T) - P, => C = 60 + 0.9*500 – 110, where “T=0”.

=> C = 60 + 0.9*500 – 110 = 400, => C = $400.

8).

Now, let’s assume the govt spending increases that increases the AD to “1800 – 10*P”. So, at the SR equilibrium AD must be equal to SRAS.

=> 1800 – 10*P = (-400) +10*P, => 20*P = 2200, => P = 2200/20 = 110. The equilibrium output is.

=> AD = 1800 – 10*P = 1800 – 10*110 = 700 > 500. So, as the output increases the unemployment should decrease by “2%”, because the cyclical unemployment rate is “2%”.

So, the unemployment rate should be “18-2=16%”.