Another economy has the production Y = A * K^0.5 * L^0.5, the marginal product MPL = 0.5 * A * K^0.5 / L^0.5, in which K = 144 and the supply of labor w = 5 * EP/P *L^0.5 Productivity is A=50. In absence of shocks and policies, EP/P=1, the number of jobs is L = 60, and wage is w = 38.73. But now inflation is slower than expected, with EP/P=1.2. Find the new equilibrium number of workers. 2. Find the new equilibrium wage at EP/P=1.2 3. Graph the change in the labor market equilibrium. Mark the before and after equilibria with E0 and E1. Label axes and curves, map relevant values onto axes. 4. Now let's consider this same scenario in terms of the accelerationist Phillips curve. The labor force is N=64. Find the rates of unemployment before and after as (N-L)/N and map them into our surprise inflation indexes, EP/P. Label the natural rate of unemployment, show the cyclical rate of unemployment. Step 1: Given information: Y = AK0.5L0.5 -------> Production function. MPL = 0.5A (K / L)0.5 ---------> Marginal product of labor. K is fixed at 144, i.e., K = 144 ---------------- Labor supply: w = 5*(EP/P)*L0.5 Where EP / P = 1 => w = 5L0.5 -----------> labor supply equation when EP/P = 1 -------------------- arrow_forward Step 2: Calculation of new equilibrium workers: (1) Suppose initially, A = 50 and EP/P = 1. In this case, the number of workers is L is 60 and w = 38.73 But now inflation is slower than expected, with EP/P=1.2 This will change the labor supply equation ----------------------- Deriving labor demand equation: MPL = 0.5A(K/L)0.5 Put A = 50 and K=144 => MPL = 0.5 * 50* (144 / L)0.5 => MPL = 25 * (12 / L0.5) => MPL = (300 / L0.5) -------------------- Labor demand equation: MPL = w Where w is real wage. => 300 / L0.5 = w => w = 300 / L0.5 -----------> Labor demand equation ------------------------ Deriving the new labor supply equation: w = 5 *(EP / P) *L0.5 Put EP/P = 1.2 => w = 5 * 1.2 * L0.5 => w = 6 * L0.5 ------------> Labor supply equation when EP/P = 1.2 ------------------------- At labor equilibrium, labor demand = labor supply => 300 / L0.5 = 6L0.5 => 300 / 6 = L0.5 * L0.5 => 50 = L => L = 50 Hence, the new equilibrium number of workers is 50. ------------------------------------------------------------------- arrow_forward Step 3: Calculation of new equilibrium wage at EP/P = 1.2 (2) Labor demand remain unchanged at w = 300 / L0.5 w = 300 / L0.5 Put L = 50 (i.e., the new equilibrium number of workers) => w = 300 / 500.5 => w = 42.43 Hence, the new equilibrium wage at EP/P = 1.2 is 42.43 --------------------------------- arrow_forward Step 4: Graphing the labor demand and supply curve. (3) When EP/P = 1 w = (300 / L0.5) --------> Labor demand w = 5L0.5 -----------> Labor supply L = 60 --------------> equilibrium number of workers w = 38.73-----------> equilibrium wage --------------------------------------------------------- When EP/P=1.2 w = (300 / L0.5)--------> Labor demand w = 6L0.5 -----------> Labor supply L = 50 --------------> new equilibrium number of workers w = 42.43-----------> new equilibrium wage

Another economy has the production Y = A * K^0.5 * L^0.5, the marginal product MPL = 0.5 * A * K^0.5 / L^0.5, in which K = 144 and the supply of labor w = 5 * EP/P L^0.5 Productivity is A=50. In absence of shocks and policies, EP/P=1, the number of jobs is L = 60, and wage is w = 38.73. But now inflation is slower than expected, with EP/P=1.2. Find the new equilibrium number of workers. 2. Find the new equilibrium wage at EP/P=1.2 3. Graph the change in the labor market equilibrium. Mark the before and after equilibria with E0 and E1. Label axes and curves, map relevant values onto axes. 4. Now let's consider this same scenario in terms of the accelerationist Phillips curve. The labor force is N=64. Find the rates of unemployment before and after as (N-L)/N and map them into our surprise inflation indexes, EP/P. Label the natural rate of unemployment, show the cyclical rate of unemployment. Step 1: Given information: Y = AK0.5L0.5 -------> Production function. MPL = 0.5A (K / L)0.5 ---------> Marginal product of labor. K is fixed at 144, i.e., K = 144 ---------------- Labor supply: w = 5(EP/P)L0.5 Where EP / P = 1 => w = 5L0.5 -----------> labor supply equation when EP/P = 1 -------------------- arrow_forward Step 2: Calculation of new equilibrium workers: (1) Suppose initially, A = 50 and EP/P = 1. In this case, the number of workers is L is 60 and w = 38.73 But now inflation is slower than expected, with EP/P=1.2 This will change the labor supply equation ----------------------- Deriving labor demand equation: MPL = 0.5A(K/L)0.5 Put A = 50 and K=144 => MPL = 0.5 50* (144 / L)0.5 => MPL = 25 * (12 / L0.5) => MPL = (300 / L0.5) -------------------- Labor demand equation: MPL = w Where w is real wage. => 300 / L0.5 = w => w = 300 / L0.5 -----------> Labor demand equation ------------------------ Deriving the new labor supply equation: w = 5 (EP / P) L0.5 Put EP/P = 1.2 => w = 5 * 1.2 * L0.5 => w = 6 * L0.5 ------------> Labor supply equation when EP/P = 1.2 ------------------------- At labor equilibrium, labor demand = labor supply => 300 / L0.5 = 6L0.5 => 300 / 6 = L0.5 * L0.5 => 50 = L => L = 50 Hence, the new equilibrium number of workers is 50. ------------------------------------------------------------------- arrow_forward Step 3: Calculation of new equilibrium wage at EP/P = 1.2 (2) Labor demand remain unchanged at w = 300 / L0.5 w = 300 / L0.5 Put L = 50 (i.e., the new equilibrium number of workers) => w = 300 / 500.5 => w = 42.43 Hence, the new equilibrium wage at EP/P = 1.2 is 42.43 --------------------------------- arrow_forward Step 4: Graphing the labor demand and supply curve. (3) When EP/P = 1 w = (300 / L0.5) --------> Labor demand w = 5L0.5 -----------> Labor supply L = 60 --------------> equilibrium number of workers w = 38.73-----------> equilibrium wage --------------------------------------------------------- When EP/P=1.2 w = (300 / L0.5)--------> Labor demand w = 6L0.5 -----------> Labor supply L = 50 --------------> new equilibrium number of workers w = 42.43-----------> new equilibrium wage

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Production And Growth

Section: Chapter Questions

Problem 5CQQ

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I just need assitance and a better understanding of 3 and mostly 4

1. Another economy has the production

Y = A * K^0.5 * L^0.5,

the marginal product

MPL = 0.5 * A * K^0.5 / L^0.5, in which K = 144

and the supply of labor

w = 5 * EP/P *L^0.5

Productivity is A=50. In absence of shocks and policies, EP/P=1, the number of jobs is L = 60, and wage is w = 38.73.

But now inflation is slower than expected, with EP/P=1.2.

Find the new equilibrium number of workers.

2. Find the new equilibrium wage at EP/P=1.2

3. Graph the change in the labor market equilibrium. Mark the before and after equilibria with E0 and E1. Label axes and curves, map relevant values onto axes.

4. Now let's consider this same scenario in terms of the accelerationist Phillips curve. The labor force is N=64. Find the rates of unemployment before and after as (N-L)/N and map them into our surprise inflation indexes, EP/P. Label the natural rate of unemployment, show the cyclical rate of unemployment.

Step 1: Given information:

Y = AK^0.5L^0.5 -------> Production function.

MPL = 0.5A (K / L)^0.5 ---------> Marginal product of labor.

K is fixed at 144, i.e., K = 144

----------------

Labor supply:

w = 5*(EP/P)*L^0.5

Where EP / P = 1

=> w = 5L^0.5 -----------> labor supply equation when EP/P = 1

--------------------

arrow_forward

Step 2: Calculation of new equilibrium workers:

(1)

Suppose initially, A = 50 and EP/P = 1. In this case, the number of workers is L is 60 and w = 38.73

But now inflation is slower than expected, with EP/P=1.2

This will change the labor supply equation

-----------------------

Deriving labor demand equation:

MPL = 0.5A(K/L)^0.5

Put A = 50 and K=144

=> MPL = 0.5 * 50* (144 / L)^0.5

=> MPL = 25 * (12 / L^0.5)

=> MPL = (300 / L^0.5)

--------------------

Labor demand equation:

MPL = w

Where w is real wage.

=> 300 / L^0.5 = w

=> w = 300 / L^0.5 -----------> Labor demand equation

------------------------

Deriving the new labor supply equation:

w = 5 *(EP / P) *L^0.5

Put EP/P = 1.2

=> w = 5 * 1.2 * L^0.5

=> w = 6 * L^0.5 ------------> Labor supply equation when EP/P = 1.2

-------------------------

At labor equilibrium, labor demand = labor supply

=> 300 / L^0.5 = 6L^0.5

=> 300 / 6 = L^0.5 * L^0.5

=> 50 = L

=> L = 50

Hence, the new equilibrium number of workers is 50.

-------------------------------------------------------------------

arrow_forward

Step 3: Calculation of new equilibrium wage at EP/P = 1.2

(2)

Labor demand remain unchanged at w = 300 / L^0.5

w = 300 / L^0.5

Put L = 50 (i.e., the new equilibrium number of workers)

=> w = 300 / 50^0.5

=> w = 42.43

Hence, the new equilibrium wage at EP/P = 1.2 is 42.43

---------------------------------

arrow_forward

Step 4: Graphing the labor demand and supply curve.

(3)

When EP/P = 1

w = (300 / L^0.5) --------> Labor demand

w = 5L^0.5 -----------> Labor supply

L = 60 --------------> equilibrium number of workers

w = 38.73-----------> equilibrium wage

---------------------------------------------------------

When EP/P=1.2

w = (300 / L^0.5)--------> Labor demand

w = 6L^0.5 -----------> Labor supply

L = 50 --------------> new equilibrium number of workers

w = 42.43-----------> new equilibrium wage

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