Understanding GDP: Limitations and Inflation Measures Explained
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Course
AA 1
Subject
Economics
Date
Dec 10, 2024
Pages
8
Uploaded by oooni
Conceptual Questions 1.Read the article “Rethinking GDP” by Diane Coyle. Give three reasons why GDP is not a perfect measure of well-being and explain why their omission is important. •GDP includes goods whose production processes create externalities like pollution or noise. Additionally, some goods, such as weapons or drugs, may actually diminish well-being, yet they are still counted in GDP, despite reducing overall welfare. •GDP struggles to account for technological advancements. Improvements in the quality of goods, which enhance welfare, are often not fully captured in GDP measurements. •GDP does not reflect inequality. If GDP increases but the gains are concentrated among the wealthy, the overall improvement in welfare may be minimal. 2.Read the article “Making Sense of Inflation Measures” by James Bullard. Explain the differences are between the following 4 measures of inflation: CPI, PCE, Core PCE, and trimmed mean PCE. Which measure does the Federal Reserve target? What is their target rate? The Consumer Price Index (CPI) reflects a fixed basket of goods that requires periodic manual updates. In contrast, Personal Consumption Expenditures (PCE) inflation is automatically adjusted each month to reflect actual consumer spending patterns. Core PCE excludes the often volatile food and energy prices, while the trimmed mean PCE excludes items with the most extreme price changes, both high and low. The Federal Reserve currently aims for a long-term average inflation target of 2% based on PCE inflation.3.Read the article “Inflation Is Best Explained by This Underrated Economic Theory” by Tyler Cowen. Why does the author think the quantity theory didn’t hold up in the Great Recession? What evidence do they offer that current inflation was peaking at the time of the article? Cowen argues that during the Great Recession, the velocity of money declined partly because the Federal Reserve began paying banks interest on reserves, encouraging banks to hold onto excess funds instead of lending them out. In contrast, during the COVID-19 pandemic, inflation was closely linked to a rapid expansion of the money supply. The author suggests that the recent slowdown in M2 money supply growth indicates that inflation may be reaching its peak.
Analytical Questions1.In each of the following scenarios, calculate the total increase in US GDP this year caused directly by the given information a)An individual purchases an old used car from their friend for $6,000. They buy a new engine for the car for $1,000, replace the brakes for $500, and paint it for $200. They then sell the car for $10,000. Assume all improvements were completed this year. We don’t need details about the intermediate inputs to calculate the improvements. All that matters is that the enhancements added $4,000 of value to the car. As a result, the increase in GDP is $4,000. b)A computer manufacturer in the US buys parts for its computer from Japan. The cost of these parts is $500. It produces and sells a computer for $700 using these parts. The value added by the US is $700 - $500 = $200 c)A child is running a lemonade stand. They purchase 20 lemons for $3 each and 500 grams of sugar for $0.01 per gram. Using these ingredients, they make and sell 50 cups of lemonade for $2 each and at the end of the day they have 5 lemons and 100 grams of sugar remaining (that they do not sell and eventually consume themselves). The lemonade is a final good, so we count 50 units sold at $2 each, resulting in $100 from the lemonade. Additionally, the leftover materials that were consumed should also be included. This gives us another (5 x 3) + (100 x 0.01) = 16. Therefore, the total GDP increases by ($100 + $16 =$116). d)A video game company prints 2 million copies of a game that sells for $60. It sells 1.8 million of these this year and the remainder the following year. The timing of when the game is sold doesn’t matter—what counts is when it is produced. Therefore, GDP increases by 2 million units at $60 each, totaling $120 million. In terms of GDP components, the copies sold this year would be classified as consumption, while the unsold copies would be recorded as an increase in inventories.
e)A sandwich shop buys $1000 of ham, $500 of cheese, and $300 of bread. It also buys a new meat slicer for $300. Using these, it produces and sells $2000 of sandwiches. There is no ham or cheese remaining after production, but the meat slicer is still in perfect condition. Since the ham and cheese are intermediate inputs, we don’t need to include them, so the sandwiches contribute $2,000. The meat slicer is considered an investment, so we include that as well, bringing the total to $2,300. 2.A consumer has a utility function over two goods x and y given by U(x, y) = ln(x) + β ln(y), where β is an arbitrary positive constant. Assume the price of x and y are both equal to 1 and the consumer has an income of 100. a)Write down a Lagrangian that represents this consumer’s utility maximization problem given their budget constraint. ℒ= [ln(x) + β(ln(y)) − λ(100 − x − y)] b)Solve for the utility maximizing values for x and y as a function of β ⎩⎪⎪⎨⎪⎪⎧࠵?࠵?࠵?࠵?= ࠵?࠵?࠵?࠵?࠵?= ࠵?࠵?࠵?࠵?࠵?= ࠵?⇒⎩⎪⎨⎪⎧࠵?࠵?+ ࠵? = ࠵?࠵?࠵?+ ࠵? = ࠵?࠵?࠵?࠵? − ࠵? − ࠵? = ࠵?⇒ 2࠵?࠵? = ࠵?࠵? + ࠵? = ࠵?࠵?࠵?⇒⎩⎨⎧࠵? =࠵?࠵?࠵?࠵? + ࠵?࠵? =࠵?࠵?࠵?࠵?࠵? + ࠵?c)How does β relate to the demand for x and y? (i.e. as β increases, what happens to the demand for x and y?) As β increases, the amount that the consumer likes y relative to x increases. Therefore, the higher the β, the more the consumer will want to consume y (and the less they will want to consume x 3.Assume an economy can be represented by a single firm that has a production function described by Y = 27K1/3 L1/3a)Does this firm have increasing, constant, or decreasing returns to scale? Show how you know using the definition. Multiplying both inputs by a constant z,
27(zK)1/3(zL)1/3= z2/3(27K1/3L1/3) = z 2/3Y < zY Therefore the production function is decreasing returns to scale b)Calculate the marginal product of capital and labor for this firm. What happens to each marginal product as capital is increased, holding labor fixed? What happens to each marginal product as labor is increased, holding capital fixed? ࠵?࠵?࠵? =࠵?࠵?࠵?࠵?= ࠵?࠵? 9࠵?࠵?࠵?!࠵?࠵?; ࠵?࠵?࠵?= ࠵? 9࠵?࠵?࠵?;࠵?࠵?࠵?࠵?࠵? =࠵?࠵?࠵?࠵?= ࠵?࠵? 9࠵?࠵?࠵?!࠵?࠵?; ࠵?࠵?࠵?= ࠵? 9࠵?࠵?࠵?;࠵?࠵?From these equations we can see that as capital increases, MPK falls while MPL rises and as labor increases, MPL falls while MPK increases. c)Find a wage and rental rate such that the firm wants to hire exactly 27 units of labor and 8 units of capital when it maximizes its profit. ࠵? = ࠵?࠵?࠵? = ࠵? 9࠵?࠵?࠵?࠵?;࠵?࠵?= ࠵?࠵? = ࠵?࠵?࠵? = ࠵? 9࠵?࠵?࠵?࠵?;࠵?࠵?= ࠵?. ࠵?࠵?
In [1]:importpandas aspdimportseaborn assnsimportmatplotlib.pyplot aspltIn [2]:# Load the CSV filesgdp_df =pd.read_csv('/Users/OscarIroh_1/Downloads/GDPC1.csv')pce_df =pd.read_csv('/Users/OscarIroh_1/Downloads/PCEPI.csv')unrate_df =pd.read_csv('/Users/OscarIroh_1/Downloads/UNRATE.csv')# Convert 'DATE' columns to datetimegdp_df['DATE'] =pd.to_datetime(gdp_df['DATE'])pce_df['DATE'] =pd.to_datetime(pce_df['DATE'])unrate_df['DATE'] =pd.to_datetime(unrate_df['DATE'])# Set 'DATE' as the indexgdp_df.set_index('DATE', inplace=True)pce_df.set_index('DATE', inplace=True)unrate_df.set_index('DATE', inplace=True)# Resample PCE and UNRATE data to quarterly frequencypce_quarterly =pce_df.resample('Q').mean()unrate_quarterly =unrate_df.resample('Q').mean()# Align GDP data to the end of the quarter (instead of the start)gdp_df.index =gdp_df.index +pd.offsets.QuarterEnd()# Filter to the common date rangestart_date =max(gdp_df.index.min(), pce_quarterly.index.min(), unrate_quartend_date =min(gdp_df.index.max(), pce_quarterly.index.max(), unrate_quartergdp_filtered =gdp_df.loc[start_date:end_date]pce_filtered =pce_quarterly.loc[start_date:end_date]unrate_filtered =unrate_quarterly.loc[start_date:end_date]# Combine the three datasets and drop rows with missing valuescombined_df =gdp_filtered.join([pce_filtered, unrate_filtered], how='inner# Rename columns for claritycombined_df.columns =['GDP', 'PCE', 'UNRATE']# Display the resulting dataframecombined_df.head()Out[2]:11/10/2024, 17:03MACRO PS 1 F24localhost:8888/nbconvert/html/MACRO PS 1 F24.ipynb?download=false1/4
In [3]:# Calculate the percent change from 1 year ago (4 quarters ago for quarterlycombined_df['GDP_Growth_Rate'] =combined_df['GDP'].pct_change(periods=4) *combined_df['PCE_Inflation_Rate'] =combined_df['PCE'].pct_change(periods=4)# Drop rows with any NaN valuescombined_df_clean =combined_df.dropna()# Display the updated dataframe with the new columnscombined_df.head()Out[3]:In [4]:# Plot for the full datasetplt.figure(figsize=(10, 6))sns.regplot(x='GDP_Growth_Rate', y='UNRATE', data=combined_df, scatter_kws={plt.title('Okun\'s Law: Relationship between GDP Growth and Unemployment (Fuplt.xlabel('GDP Growth Rate (%)')plt.ylabel('Unemployment Rate (%)')plt.grid(True)plt.show()# Filter data since COVID (Q2 2020)covid_period =combined_df.loc['2020-04-01':]# Plot for the COVID periodplt.figure(figsize=(10, 6))sns.regplot(x='GDP_Growth_Rate', y='UNRATE', data=covid_period, scatter_kws=plt.title('Okun\'s Law: Relationship between GDP Growth and Unemployment (Siplt.xlabel('GDP Growth Rate (%)')plt.ylabel('Unemployment Rate (%)')plt.grid(True)plt.show()11/10/2024, 17:03MACRO PS 1 F24localhost:8888/nbconvert/html/MACRO PS 1 F24.ipynb?download=false2/4
In [5]:# Plot for the full dataset (Phillip's Curve: Inflation vs Unemployment)plt.figure(figsize=(10, 6))sns.regplot(x='PCE_Inflation_Rate', y='UNRATE', data=combined_df, scatter_kwplt.title('Phillip\'s Curve: Relationship between Inflation and Unemploymentplt.xlabel('PCE Inflation Rate (%)')plt.ylabel('Unemployment Rate (%)')plt.grid(True)plt.show()# Plot for the COVID period (since Q2 2020)plt.figure(figsize=(10, 6))11/10/2024, 17:03MACRO PS 1 F24localhost:8888/nbconvert/html/MACRO PS 1 F24.ipynb?download=false3/4
sns.regplot(x='PCE_Inflation_Rate', y='UNRATE', data=covid_period, scatter_kplt.title('Phillip\'s Curve: Relationship between Inflation and Unemploymentplt.xlabel('PCE Inflation Rate (%)')plt.ylabel('Unemployment Rate (%)')plt.grid(True)plt.show()In [ ]:11/10/2024, 17:03MACRO PS 1 F24localhost:8888/nbconvert/html/MACRO PS 1 F24.ipynb?download=false4/4