Question

In: Economics

In Monetaria real GDP is growing at 2% per year and the money supply is growing...

In Monetaria real GDP is growing at 2% per year and the money supply is growing at 5% per year. suppose that the velocity of the money has been constant.
A) Find the Inflation Rate.

B) The nominal interest rate is 10%. Find the real interest rate, assuming that inflation will remain the same.

C) Suppose you are a small hats retailer. To simplify the analysis, lets assume that the only costs of doing business is paying for the merchandise you are selling. Suppose that you need to pay for the hats in December 2019 and you sell them a year later in December 2020. (Realism is not the point) Suppose that the wholesale price of a hat is $10, you expect to be able to sell a hat for $12 in December 2020 and you need to borrow money to buy the hats.
What is the profit per hat? (Hint: The interest you pay on the loan is part of your costs).

D) Suppose that inflation rose unexpectedly to 10%. suppose that you are able to raise your prices by the additional inflation. The interest rate on your loan remains unchanged. Now what is your profit per hat?

Bonus) The profit per hat you computed changed with unexpected inflation, but the value of the money also changed. Compare the profit per hat under the 2 scenarios (Parts C and D) in 2019 dollars.

Solutions

Expert Solution

Real GDP growth 2% per year

Money supply growth 5% per year

Velocity of money is constant.

Use Quantity Theory of Money: MV = PY

Using the chain rule,

% change in (XY) = % change in X + % change in Y

Thus,

%change in M + %change in V = %change in P + %change in Y

A) Find the Inflation Rate.

Using the above equation,

5% + 0 = %change in P + 2%

%change in P = 3% per annum

Thus, inflation rate is 3% per annum

B) The nominal interest rate is 10%. Find the real interest rate, assuming that inflation will remain the same.

Real interest rate = Nominal interest rate minus Inflation

= 10% - 3%

= 7%

Real interest rate = 7%

C) Suppose you are a small hats retailer. To simplify the analysis, lets assume that the only costs of doing business is paying for the merchandise you are selling. Suppose that you need to pay for the hats in December 2019 and you sell them a year later in December 2020. (Realism is not the point) Suppose that the wholesale price of a hat is $10, you expect to be able to sell a hat for $12 in December 2020 and you need to borrow money to buy the hats. What is the profit per hat? (Hint: The interest you pay on the loan is part of your costs).

Borrow $10 in 2019, at 10% per annum

This loan grows to $11 in 2020

Sell hats for $12 in 2020

Thus, Profit = Total Revenue minus Total Costs

= 12 - 11

= $1 per hat

Profit is $1 per hat

D) Suppose that inflation rose unexpectedly to 10%. suppose that you are able to raise your prices by the additional inflation. The interest rate on your loan remains unchanged. Now what is your profit per hat?

Borrow $10 in 2019, at 10% per annum

This loan grows to $11 in 2020

The selling price per hat rises by 10%, to $13.2 per hat.

Sell hats for $13.2 in 2020

Thus, Profit = Total Revenue minus Total Costs

= 13.2 - 11

= $2.2 per hat

Profit is $2.2 per hat

If all values are converted to 2019 dollars, and inflation effects are removed, the profit per hat under both the scenarios remains the same. This is because inflation raises the prices, but lowers the value of money.

The $13.2 selling price gets deflated by 1.1 (2019 prices), and it is brought back to $12.

Rahul Sunny answered 1 year ago
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