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Econ 3200. Assignment 1 2023

Total Marks: 15

Due date: Monday, March 20th before 10 am

INSTRUCTIONS:

1. You will need to upload your answers to Blackboard.

2. You can upload multiple ﬁles in your submission, but you can only submit it once.

3. Files that can be uploaded: word, excel, pdf, jpeg, jpg, gif, png, bmp, etc.

1. The M1 Velocity of Money in the US and in Australia. Marks: 5.

(a) Go to the FRED website (https://fred.stlouisfed.org/), search for the Velocity of M1

Money Stock. Provide at least one reason that explains the pattern of the M1 velocity of money during the onset of the covid-19 pandemic (from Q1 2020 to Q2 2020). (1 mark)

(b) Go to the RBA statistics website (https://www.rba.gov.au/statistics/tables/), get the

series of nominal GDP and the series of M1 (all seasonally adjusted) from December 2021 to September 2022. The ﬁrst is in ﬁle H1 - Gross Domestic Product and Income ﬁle and the second in ﬁle D3 - Monetary Aggregates. The GDP series is quarterly while the M1 series is monthly. Delete the unnecessary months for M1, so that the new series is at the same months as the GDP series.

i. Compute and provide a graph of the M1 velocity of money for Australia from December 2021 to September 2022 (post-pandemic). (2 marks)

ii. Is the velocity of money constant in Australia? Provide at least one reason that explains the pattern of the velocity of money in words (in less than 8 LINES) and by providing a graph of another series (which you choose) in order to back your argument (2 marks).

2. Monetary Exchanges in a simple Search and Money Model. Marks: 5. Consider the following values α = 0.50, β = 1, r = 1, µ = 0.5, x = 0.70, U − ∈ = 100. As in the Appendix of Lecture 2, the values of being a producer, commodity holder and money holder

are given by

r + α

Vm = ( 1 − BD )(U − ∈),

with

A = r + β(1 − µ)x2 ( ) + βµxπ* , B = r + β(1 − µ)x2 ( ) + βµxπ* ,

β(1 − µ)xΠ α

(a) Compute V0 , V1 , and Vm for (i) Π = 0.80, π* = 0; (ii) Π = 0.80, π* = 1; (iii) Π =

0.60, π* = 0; and (iv) Π = 0.60, π* = 1. What is the optimal π * for each Π? Explain the results (in less than 3 LINES). (4 Marks)

(b) In Australia, 8 banknotes out of 1 million genuine banknotes are found to be counterfeits

annually (see A7 of the RBA Statistical Tables, March 2022). Would your answer to (a) change if there was a positive probability of money being fake? (1 Mark)

3. CBDC (Central Bank Digital Currency). Marks: 5. Many Central Banks around the world are now considering whether to start issuing CBDC in addition to ﬁat money. Consider the set of equations:

rV0 = α(V1 − V0 ) − γZ (µd ) ,

rV1 = βµm x max πm (Vm − V1 ) + βµd x max πd (Vd − V1 ) − γZ (µd ) ,

Tm Td

(S.0)

(S.1)

rVm = max πm4d(Vd − ∈m4d − Vm ) + (1 − πm4d)βµ1 xΠm (U − ∈m + V0 − Vm ) − γZ (µd ) , (S.m)

Tm4d

rVd = max πd4m(Vm − ∈d4m − Vd ) + (1 − πd4m) [yd + βµ1 xΠd (U − ∈d + V0 − Vd )] − γZ (µd ) ,

Td4m

(S.d)

which deﬁne the value functions of being at state 0 (production), state 1 (commodity seller), state m (money trader - commodity buyer), state d (digital money trader - commodity buyer). Notation and assumptions are similar as in the lecture. If CBDC is issued, it would be legal tender. In the above, ∈m4d ( ∈d4m) is the exchange cost of money for CBDC (CBDC for money). One advantage of CBDC is that, as it is digital (not physical), it is less costly to transfer, ∈d < ∈m , and moreover it could earn an interest or dividend yd . One risk is that as CBDC does not require commercial banks, it would reduce bank deposits and then the funds available for loans and other bank services. This negative externality is modeled above as −γZ (µd ) , where γ is the probability the agent requires bank services, and Z (µd ) is the cost which increases with the amount of digital-money traders. Please answer the questions below explaining your answer and referring to the above model: