three money amp banking questions

Short Questions

1. [Okun’s Law] In the aggregate demand-aggregate supply (ADAS) model we assume increasing aggregate output is equivalent to reducing the unemployment rate. Now we examine this claim empirically.

(a) Plot the unemployment rate in the US from 1980-2018 (Hint: Use the FRED web site). What is the average unemployment rate in this period? What is the most recent unemployment rate in the US?

(b) Plot the percentage change (yearly) in the unemployment rate and the percentage change (yearly) in the real GDP from 1980-2018. What is the relationship between the fluctuations in the unemployment rate and the fluctuations in the real GDP?

2. [Monetary Policy] (a) Using the ADAS model, explain and demonstrate graphically the short-run and long-run effects of a decrease in the money supply.

(b) Using ADAS model, explain and demonstrate graphically the short-run and long-run effects of a temporary negative supply shock.

3. [Bitcoin’s Electricity Cost] In this exercise we estimate the electricity cost of Bitcoin mining.

The mining difficulty of Bitcoin is a measure of how difficult it is for a miner to mine a block. The number of hashes (each hash is one computation) to generate a block (i.e. solving a mathematical puzzle) is given by difficulty x (2^32). For example, if you use a computer that can process1 Giga hash per second, and if the mining difficulty is 20000, then on average it takes

20000 x (2^32)/(10^9 x 60 x 60) = 23.86 hours

to mine a block. If a miner successfully mines a block, then he or she is rewarded by certain amount of Bitcoin. The amount of Bitcoin rewards evolves over time and is predictable, see the data here.

  • Collect data on Bitcoin’s mining difficulty, price, and reward per block for 2013-2019. Plot these data in three figures.
  • Suppose to run a computer that process 1 Giga hash per second we need 0.079 Watts. What is the amount of electricity that we need to solve for 1 block (in units of kilowatt hour (kWh))? Show how this estimate evolves for 2013-2019.
  • Look up the cost of electricity in the US. Calculate the electricity cost for mining 1 block. What is the electricity cost of mining 1 Bitcoin? (hint: the cost of mining one Bitcoin is the cost of mining 1 block divided by the Bitcoin rewards).
  • Plot the electricity cost of mining 1 Bitcoin and the price of 1 Bitcoin for 2013-2019 in the same figure. Is the electricity cost justified by the price?
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