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宏观经济代写-ECOS 2002-Assignment 2

时间：2022-03-26

ECOS 2002

Assignment 2

Due: Week 6

Instructions: We are going to use this assignment to provide you a tutorial on how to

take the midsemester exam. There is a Canvas Quiz setup that asks questions related to

each of the problems in this assignment and it takes the exact form of our mid-semester

exam. Please submit your written work through the assignment submission

box as normal AND complete the quiz. Again, everything is based on effort and

not accuracy. Failure to complete both the Canvas Quiz and the submission will result

in a loss of marks.

Unknowns/Endogenous Variables Yt, At, Ly,t, La,t

Goods Production Function Yt = AtLy,t

Ideas Production Function ∆At+1 = z¯AtLa,t

Resource Constraint Ly,t + La,t = L¯

Allocation of Labour La,t = γL¯

Parameters: z¯, L¯, γ, A¯0

Table 1: The Basic Romer Model

1. Comparing the Romer Model to the Solow Model

(a) Give one economic phenomena that the Solow Model explains and one eco-

nomic phenomena that the Solow Model cannot explain.

(b) What is the main economic phenomena explained by the Romer Model.

2. Consider the basic Romer Model given in Table 1 of this document.

(a) Solve for the balanced growth path of GDP per capita. (Show your work)

1

(b) Illustrate using a graph the effect of a decrease in the proportion of labour

allocated to the ideas sector (γ ⇓). On the graph, label the level effect of this

change. Explain the intuition of the change in your graph.

3. Human Capital in the Romer Model: Let’s consider the possibility that human

capital is required to produce ideas. To add human capital, we assume the ideas

production function is

∆At+1 = z¯AtHtLa,t. (1)

Furthermore, let’s assume that human capital requires labour to produce:

Ht = Ls,t. (2)

The labour is now split into three groups Ly,t + La,t + Ls,t = L¯. For simplicity,

let’s assume Ly,t = 0.5L¯, La,t = .25L¯, and Ls,t = .25L¯. Assume L¯ = 100.

(a) What is the economic interpretation of using labour to produce human cap-

ital? (Hint: This is not a trick question. I am just looking for basically the

definition of human capital.)

(b) Solve for the balance growth path of GDP per capita in this model.

(c) Does the inclusion of human capital increase the rate of growth compared

to the standard model? Explain. (Hint: Think about the growth rate if

the extra labour used in Ls,t was just allocated to ideas production or goods

production in the basic model. How does that case compare to this case?)

4. The Bathtub Model and JobKeeper and JobSeeker: Consider the bathtub model of

unemployment given by

Et + Ut = L¯ (3)

∆Ut+1 = sEt − fUt (4)

where U¯ and E¯ denote the steady levels of unemployment and employment, re-

spectively.

(a) Solve for the steady state level of unemployment. (Hint: ∆Ut+1 = 0)

(b) What is the effect on steady state unemployment if the separation rate rises

(s ⇑)?

(c) The JobKeeper program was designed to provided a subsidy to firms to pass

on to their employees and is contingent on keeping the jobs intact. Use the

model to explain what effect is any this would have on measured unemploy-

ment.

(d) The JobSeeker program provides subsidies to workers currently out of work.

What parameter in the model would this policy likely affect? What is the

impact on unemployment?

5. The Minimum Wage: Consider the graphical model of the labour market. Evaluate

the following statement using graphs and justify your answer with figures:

“The introduction of a minimum wage ALWAYS increases the natural rate of un-

employment.”

Assignment 2

Due: Week 6

Instructions: We are going to use this assignment to provide you a tutorial on how to

take the midsemester exam. There is a Canvas Quiz setup that asks questions related to

each of the problems in this assignment and it takes the exact form of our mid-semester

exam. Please submit your written work through the assignment submission

box as normal AND complete the quiz. Again, everything is based on effort and

not accuracy. Failure to complete both the Canvas Quiz and the submission will result

in a loss of marks.

Unknowns/Endogenous Variables Yt, At, Ly,t, La,t

Goods Production Function Yt = AtLy,t

Ideas Production Function ∆At+1 = z¯AtLa,t

Resource Constraint Ly,t + La,t = L¯

Allocation of Labour La,t = γL¯

Parameters: z¯, L¯, γ, A¯0

Table 1: The Basic Romer Model

1. Comparing the Romer Model to the Solow Model

(a) Give one economic phenomena that the Solow Model explains and one eco-

nomic phenomena that the Solow Model cannot explain.

(b) What is the main economic phenomena explained by the Romer Model.

2. Consider the basic Romer Model given in Table 1 of this document.

(a) Solve for the balanced growth path of GDP per capita. (Show your work)

1

(b) Illustrate using a graph the effect of a decrease in the proportion of labour

allocated to the ideas sector (γ ⇓). On the graph, label the level effect of this

change. Explain the intuition of the change in your graph.

3. Human Capital in the Romer Model: Let’s consider the possibility that human

capital is required to produce ideas. To add human capital, we assume the ideas

production function is

∆At+1 = z¯AtHtLa,t. (1)

Furthermore, let’s assume that human capital requires labour to produce:

Ht = Ls,t. (2)

The labour is now split into three groups Ly,t + La,t + Ls,t = L¯. For simplicity,

let’s assume Ly,t = 0.5L¯, La,t = .25L¯, and Ls,t = .25L¯. Assume L¯ = 100.

(a) What is the economic interpretation of using labour to produce human cap-

ital? (Hint: This is not a trick question. I am just looking for basically the

definition of human capital.)

(b) Solve for the balance growth path of GDP per capita in this model.

(c) Does the inclusion of human capital increase the rate of growth compared

to the standard model? Explain. (Hint: Think about the growth rate if

the extra labour used in Ls,t was just allocated to ideas production or goods

production in the basic model. How does that case compare to this case?)

4. The Bathtub Model and JobKeeper and JobSeeker: Consider the bathtub model of

unemployment given by

Et + Ut = L¯ (3)

∆Ut+1 = sEt − fUt (4)

where U¯ and E¯ denote the steady levels of unemployment and employment, re-

spectively.

(a) Solve for the steady state level of unemployment. (Hint: ∆Ut+1 = 0)

(b) What is the effect on steady state unemployment if the separation rate rises

(s ⇑)?

(c) The JobKeeper program was designed to provided a subsidy to firms to pass

on to their employees and is contingent on keeping the jobs intact. Use the

model to explain what effect is any this would have on measured unemploy-

ment.

(d) The JobSeeker program provides subsidies to workers currently out of work.

What parameter in the model would this policy likely affect? What is the

impact on unemployment?

5. The Minimum Wage: Consider the graphical model of the labour market. Evaluate

the following statement using graphs and justify your answer with figures:

“The introduction of a minimum wage ALWAYS increases the natural rate of un-

employment.”