ECON3010 Topics in Macroeconomics 3

 

UNIVERSITY OF SOUTHAMPTON ECON3010W1

SEMESTER 1 TAKE-HOME FINAL ASSESSMENT 2020-21

ECON3010 Topics in Macroeconomics 3

Duration: 24 HRS

START: 10:00 am, 27/01/2021 – END: 10:00 am, 28/01/2021

This paper contains 3 questions

• Answer ALL questions.
• An outline marking scheme is shown in brackets to the right of each question.
• Explain concisely all steps you undertake to answer the questions. Please write clearly, only readable parts will be taken into account.
• This is an open book assignment. You may use notes, books, online resources or software (e.g. Excel) when answering these questions. You must always use your own words and calculations and you may not communicate to others or get help from any person be it private or online.
• Once you have finished, you should upload your answers as a single pdf file on the Assessment section of the Blackboard site.
• The submission deadline is 10:00 am on January 28th. Your work must be

uploaded onto the Blackboard website before this deadline.

• A submission is only complete with a submission number.
• See blackboard for detailed submission instructions.
• Submission of this work acknowledges that you have answered the questions individually and in accordance with University guidance on Academic Integrity.

Question 1

• Consider an economy populated by a representative household that lives forever. Time is discrete. Household’s preferences are given by  (1)

with β ∈ (0,1).

The budget constraint is

c_t + k_t+1 ≤ w_th_t + (1 + r_t − δ)k_t,        (2)

where all variables have the usual interpretation and δ ∈ (0,1). In each period t, static firms produce final goods with a neoclassical production function of labour and capital  where A > 0, and  and  are the demands for labour and capital inputs.

Firms sell final goods and hire labour and capital from the household in perfectly competitive markets. Feasibility requires that

c_t + k_t+1 ≤ Af(k_t,h_t) + (1 − δ)k_t.       (3)

• State the problem of the household. [5]
• The utility function is assumed to satisfy the Inada conditions. State these conditions and explain the implication of these con-

ditions for the problem of the household.      [5]

• Find the first order conditions that solve the problem of the

household.   [5]

• Find the first order conditions of the representative firm. [5]
• Find the market clearing conditions. [5]
• Show whether the equilibrium is efficient. [15]

Question 2

• Consider an economy with three goods and three types of people distinguished by what they are able to produce and what they are willing to consume. Figure 1 illustrates the three types.

Figure 1: An absence of double coincidence economy.

• List the bilateral meetings between different types that lead to

transactions with barter.    [5]

• List the bilateral meetings between different types that lead to

transactions when good 1 is a commodity money.      [5]

• List the bilateral meetings between different types that lead to

transactions when there is fiat money.        [5]

• List the bilateral meetings between different types that lead to transactions when there is perfect record keeping. [5]

Question 3

• Consider an economy populated by a representative household that lives forever. Time is discrete. Household’s preferences are given by

with β ∈ (0,1). They also have a unit of time in each period, which they entirely devote to work for any positive wage because they have no disutility from it. So they supply h_t = 1 if the salary w_t > 0.

The budget constraint is

c_t + k_t+1 ≤ w_th_t + (1 + r_t − δ)k_t          (5)

where c_t,k_t+1,h_t ≥ 0 for all t and δ ∈ (0,1).

In each period t static firms produce final goods through the following production function

.

where K is the total capital stock in the economy. This enters separately into the production function from K_t which represents

the firm demand of capital input. Instead K is not an individual choice. As usual, α ∈ (0,1) and A > 0.

Firms sell final goods and hire labour H_t and capital K_t from the household in perfectly competitive markets to maximize profits given by

.        (6)

• Show that the production function is consistent with there being a representative firm and a competitive equilibrium. [10]
• Write down the planning problem. [10]
• Show that the competitive equilibrium is inefficient. [10]
• Design a policy intervention such that the competitive equilib-rium achieves efficiency.   [10]

END OF PAPER