Households in Williamsburg pick apples and bananas from trees each period. Annual data for apples and bananas picked, and the prices of apples and bananas in Williamsburg in 2021, 2022 and 2023 are provided below:

Year Quantity
of Apples Price
of Apples Quantity
of Bananas Price
of Bananas
2021 25 $1.00 30 $2.50
2022 26 $1.02 31 $2.57
2023 29 $0.97 27 $2.95

(a) What are the growth rates of real GDP in Williamsburg in 2022 and 2023? Assume that the base year for prices is 2021.

Growth rate of
real GDP in 2022 Growth rate of
real GDP in 2023

(b) What is the inflation rate in Williamsburg in 2022 and 2023?

Inflation rate
in 2022 Inflation rate
in 2023

(c) You predict that inflation in 2024 and 2025 will be 5.5 percent and 4.5 percent, respectively. What will be the value of the GDP deflator in 2024 and 2025?

GDP deflator
in 2022 GDP deflator
in 2023

(d) Can we use growth in nominal GDP to estimate an increase in quality of life of a nation? Explain
briefly why we can, or we can’t.

(e) Has the quality of life for the above economy increased in 2023? Explain briefly why or why not.

Eastern Island is an economy with a lumber (forestry and wood processor) company, a camper van builder, and some consumers. For simplicity, assume there is no government in this island economy. In a given year, the lumber company produces 20 thousand tons of lumber (wood) and sells it for $60 per ton. The lumber company pays $600,000 in wages to consumers.
The camper van builder uses only wood, 25 thousand tons of wood to be exact, as an input into camper van production. Of this, 15 thousand tons of wood come from the domestic lumber company at $60 per ton, and the rest, i.e., 10 thousand tons are imported at $40 per ton from the nearby Pitcairns Island. The camper van builder produces 1,000 camper vans, of which domestic consumers buy 800 camper vans for $2,000 per camper van. The remaining 200 camper vans are exported at $3,000 per camper van overseas. The camper van builder pays consumers $500,000 in wages.
Assume that all profits made by domestic producers are distributed to domestic consumers each year. Assume also that any production (of wood or camper van) not consumed in a given period is added to inventory. Lastly, assume that consumers easily catch fish for themselves and there is no market for fish. That’s why this figure for food and clothing does not enter into the GDP calculation.
(a) Draw a sketch (diagram) of the circular flow of dollars for this economy.

(b) Calculate each of the following values for the Eastern Island economy:

Consumption
Net exports
Total corporate profits
Nominal GDP

Consider an economy with the following Cobb-Douglas production function: 𝑌 = 126 ⋅ 𝐾0.32 ⋅ 𝐿0.68
Here 𝑌, 𝐾, 𝐿 represent real GDP, capital stock and labor force, respectively. In 2024, we have the capital stock at 𝐾 = 1375 and the labor stock 𝐿 = 855.
(a) What is the real wage (𝑊⁄𝑃) in this economy in 2024?
Report your answer in 2 decimal places such as 12.67, instead of rounding it to 13.
Hint: Formula for real wage:
𝑊 𝑌
= (1 − 𝛼)
𝑃 𝐿

(b) The following year in 2025, a new virus kills some of the labor force, which results in real GDP dropping by 20 percent. What is the real wage in 2025 after the viral disease? Assume 𝐾 remains the same.

(c) In part (a) and (b), you used the formula [𝑊 = (1 − 𝛼) 𝑌] to calculate real wages. What does the
𝑃 𝐿
factor 𝑌⁄𝐿 on the right-hand side of the formula denote?

(d) Based on this real wage formula provided above, what is the prescription you can give in general to the workers in an economy who seek higher wages? What would you recommend them?

Consider a Classical closed economy in a long run equilibrium in (i) goods and services (𝑌 = 𝐶 +
𝐼 + 𝐺) market and in (ii) loanable funds (𝑆 = 𝐼) market.
(a) What will be the effects of a tax cut (that is, a reduction in 𝑇) on equilibrium values for the following variables in this closed economy? [Write “Increase”, “Decrease” or “No change” in boxes next to each item below.]

Disposable income (𝑌 − 𝑇)
Consumption (𝐶)
Real output (𝑌)
National saving (𝑆 = 𝑌 − 𝐶 − 𝐺)
Interest rate (𝑟)
Investment (𝐼)

(b) The equilibrium in the loanable funds market is given in the chart below with loanable funds in the horizontal axis and interest rates in the vertical axis. The equilibrium point is initially at 𝑬𝟏 before the tax cut, where the saving and investment curves intersect. Show the shift in the saving and/or investment curves as a result of the tax cut above. Mark the new equilibrium point after the tax cut as “𝑬𝟐”. Also mark the new interest rate with 𝑟2 and investment with 𝑰𝟐.

Consider an economy with the following Cobb-Douglas production function: 𝑌 = 234 ⋅ 𝐾0.37 ⋅ 𝐿0.63, where 𝑌, 𝐾, 𝐿 represent real 𝐺𝐷𝑃, capital stock and labor force, respectively. The per worker production function can be represented as 𝑦 = 234 ⋅ 𝑘0.37.
At the beginning of year 1, the capital stock is 𝐾1 = 12,000 and labor stock is 𝐿1 = 80. Assume the saving rate is 15 percent, depreciation rate of capital is 10 percent, and population is stable and does not grow.
(a) What is capital per worker at the beginning of year 2 (i.e., a year later)?

(b) What are the steady state levels of the following variables?

Capital per worker
Output per worker
Consumption per worker

(c) We say that capital (𝐾) is a factor of production and it prominently features alongside labor (𝐿) in the production function. What does it represent? Give an example.

(d) Do you agree or disagree with the following statement?
“The large income gap between rich and poor nations is explained by differences in capital accumulation.”

(e) The US economy grew by 3% over the past 50 years in real terms. 1.3% and 1.1% of this growth are accounted for by capital and labor inputs, respectively. What is the third source of growth that accounts for 0.7% of the growth in US real GDP according to the Solow growth model?

Robinson and Friday produce and consume two goods: food and clothing. Both Robinson and Friday work 8 hours every day. Their production possibilities is given in table below:

Robinson Friday

Food 10/hour 7/hour
Clothing 8/hour 6/hour

In the absence of trade, both individuals work half of their day producing food and the other half producing clothing.
(a) What will be each individual’s production of food and clothing?

(b) What is the opportunity cost of producing food in terms of clothing for each individual?

(c) What is the comparative advantage of each individual? What do you recommend Robinson specialize in? What should Friday specialize in?

(d) Assume that Robinson will work 5 hours each day producing food and for the rest of the day for 3 hours he will produce clothing. Friday will produce food for 2 2 hours and clothing for 5 1 hours.
3 3
What will be overall production of each individual now?

(e) Should Robinson and Friday trade? Do they benefit from trade?

Consider a Classical open economy described by the following equations:

National Income Identity: 𝑌 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋
Real GDP: 𝑌 = 2,350
Private Real Consumption: 𝐶 = 300 + (0.75)(𝑌 − 𝑇)
Private Investment: 𝐼 = 600 − 2,000 ⋅ 𝑟
Government spending: 𝐺 = 1,100
Tax Revenue: 𝑇 = 900
Net exports: 𝑁𝑋 = 1,500 − 20𝜖
Real interest rate: 𝑟 = 𝑟∗ = 0.07

Here 𝜖 denotes the real exchange rate.
This economy is small in the sense that domestic real interest rate (𝑟) is determined in world capital markets (𝑟∗) due to capital mobility.

(a) Calculate national saving.
Hint: Use 𝑆National = 𝑆private + 𝑆public, where 𝑆private = (𝑌 − 𝑇) − 𝐶
and 𝑆public = 𝑇 − 𝐺
(b) Find the equilibrium real exchange rate, 𝜖. Hint: Start by finding 𝑁𝑋 = 𝑌 − 𝐶 − 𝐼 − 𝐺.
(c) In a recent act of the Congress, the government spending (𝐺) is increased to 1,250. Recall that 𝐺 was previously 1,100.
Find the new equilibrium real exchange rate (𝜖2).
(d) In addition to the government spending increase, the world interest rate also falls from 0.07 to 0.04 percent. What is the new equilibrium real exchange rate (𝜖3)?
(e) Recall that in a closed economy, an expansionary fiscal policy (say, an increase in government spending 𝐺) results in reduced savings (𝑆), increased interest rates (𝑟) which ultimately leads to reduced investment. As such it is not possible to stimulate the economic output 𝑌 fiscal policy in the long run. How about an expansionary fiscal policy in an open economy? Can policymakers stimulate long run economic output through expansionary fiscal policy? Explain the sequence of events in the space below.

Consider the following chart with US trade balance (net exports) as a percent of GDP (FRED ID: A019RE1Q156NBEA) and the US federal budget surplus or deficit as a percent of GDP (FRED ID: FYFSGDA188S). The two series are annual for the 1947-2023 period.

The figure above provides some visual evidence for the positive relationship between trade balance and federal budget surplus/deficit. In theory, explain the mechanism through which an expansionary fiscal policy (higher 𝐺 or lower 𝑇) can affect trade balance in the long run.

Download annual data of the two series (FYFSGDA188S and A019RE1Q156NBEA) for the 1947-2023 period from the FRED database. Make both series annual and the period is from 1947 to 2023.
We will now perform a regression analysis using MSFT Excel. We will have the trade balance as dependent variable (Y) and budget deficit (X) as independent variable.
Estimate the coefficients, 𝑅2, correlation coefficient (𝜌) of the regression equation 𝑌 = 𝛽0 + 𝛽1𝑋 + 𝜖.

Consider an economy with a labor force of 12,440,000 million, consisting of employed and unemployed workers. Assume population is fixed does not change over time. Labor reports for the month of September 2024 is recently published and the number of unemployed workers was 785,000. (Monetary policy tightening is expected to result in slight increases in unemployment over the next year or two.)
Below is the predicted job separation and finding rates in labor markets over the next 12 months. As an example, the number of unemployed who will be employed by next month should be 785,000 ×
(18.3%) = 143,655 while some of the workers who previously had a job will lose their job. To be more precise, we expect (12,440,000 − 785,000) × (2.1%) = 244,755 workers to join the unemployed club.

Month Separation rate (s) Job finding rate (f) Month Separation rate (s) Job finding rate (f)
Oct 24 2.1% 18.3% Apr 25 1.8% 19.9%
Nov 24 2.0% 18.8% May 25 1.8% 20.0%
Dec 24 1.9% 19.2% Jun 25 1.8% 20.1%
Jan 25 1.8% 19.5% Jul 25 1.8% 20.2%
Feb 25 1.8% 19.7% Aug 25 1.8% 20.3%
Mar 25 1.8% 19.8% Sep 25 1.8% 20.3%

(a) How many employed workers will there be in October 2024? What is the unemployment rate?

(b) Fill out the missing spaces in the table below for monthly unemployed and unemployment rate:

Month # of workers unemployed Unemployment Rate (U/L)

Month

of workers unemployed Unemployment Rate (U/L)

Sep 24 785,000 6.31%
Oct 24 886,100 Apr 25
Nov 24 May 25
Dec 24 Jun 25
Jan 25 Jul 25
Feb 25 Aug 25
Mar 25 Sep 25

(c) Economists expect a steady state in labor markets will be reached in about two years from today with a steady-state job separation rate (s) of 1.75% and job finding rate of 20.5%. What will the unemployment rate be equal to when the economy reaches its steady state? Show work.

Let’s change the assumption of a “fixed population”. Assume, instead, a 0.05% increase in labor force each month into the foreseeable future. As a result, the labor force is expected to be 12,446,220 in October 2024. Any new additions to the labor force due to population increase will initially be included in the unemployed count. For example, the number of unemployed workers is expected to reach 892,320 in October 2024.
(d) Fill out the missing spaces in the table below for monthly unemployed and unemployment rate for this economy with a growing labor force.

Month # of workers unemployed Unemployment Rate (U/L)

Month

of workers unemployed Unemployment Rate (U/L)

Sep 24 785,000 6.31%
Oct 24 892,320 Apr 25
Nov 24 May 25
Dec 24 Jun 25
Jan 25 Jul 25
Feb 25 Aug 25
Mar 25 Sep 25

(e) What is the unemployment rate once this economy reaches its steady state? Is the unemployment rate higher or lower in this economy with population growth compared to previously? (As before, assume
𝑠 = 1.75% and 𝑓 = 20.5% in the steady state.) (Hint: An Excel worksheet can help!)

(f) Policymakers of this economy with a growing labor force are not happy with the steady state unemployment level. They would prefer a steady 7 percent rate of unemployment in the steady state. Policymakers are confident that, by reducing the number of weeks of unemployment benefit eligibility, the job finding rate (𝑓) can be improved. To what rate should the job finding rate increase so that the unemployment rate will be brought down to 7 percent in the steady state? Assume the job separation rate is fixed at 𝑠 = 1.75%.

(g) Instead of changing the eligibility rules for unemployment benefits, which they are afraid, can turn out very unpopular among the unemployed, policymakers decide to provide incentives to businesses that will reduce the cost of hiring workers (such as tax credit for each worker hired). As a result, job separation rate (𝑠) will fall. To what rate should the job separation rate fall to so that the unemployment rate will be brought down to 7 percent in the steady state? Assume that the job finding rate is fixed at 𝑓 = 20.5%.

Problem 10
The US economy grows at a historical annual rate of about 3 percent post-World War 2. The average unemployment rate is 5 percent and the Federal Reserve’s target inflation rate is 2 percent during the same period. Consider the following relationships that tie two of these three variables (𝑌, 𝑢, 𝜋) together:
Okun’s Law: Percent change in Real GDP = 3% − 2 × (Change in unemployment rate)
(a) Explain the significance of this formula.

Consider the following two policies that promote economic growth. Pick one of these policies, do some research about it and explain how that policy can potentially improve the economic output of a nation.
 Allocating the economy’s investment (through industrial policy).
 Establishing the right institutions (such as property rights).