homework 4

Supposed you are an economist in the Council of Economic Advisers. You believe the current unemployment rate in the US is too high. And the unemployment rate can be lower if national output (GDP) increases. You want to know what policy to pursue to increase aggregate output by $600 billion. If you have the value of marginal propensity to consume (MPC) is 0.75. Please finish the following questions and provide your policy recommendations.

(1) What is the value of government purchase (spending) multiplier?

(2) What is the value of tax multiplier.

(3) What is your policy recommendation for government purchase or tax policy to increase national output (GDP) by $600 billion.

(4) How to intuitively explain the difference between magnitude of the tax multiplier and government purchase multiplier?

Question 2. (20 points)

Suppose in country A, its production function which is a combination of total capital (K) and total labor input (L), can be expressed as a function of total national output (Y),

Y = F(K, L) = K(1/4) * L(3/4).

Now, use the above equation to finish the following questions.

(1) In country A, does its production function have constant returns to scale, increasing return to scale or decreasing return to scale? And why? (show your work)

(2) What is the production function at per-worker level or f(k) in term of capital per work (k)? Here k = K/L and output per worker y = f(k).

(3) What is the principle of capital accumulation, following the equation ∆k = s*f(k) – δ*k? Here we use s to indicate saving rate and δ as capital depreciation rate.

(4) If we have s = 0.25 and δ = 0.2. How much will be the steady state capital per worker (k*)?

(5) Find the level of steady state output per worker (y) and consumption per worker (c).

Question 3. (20 points)

The following table shows you the annual real GDP growth rate (%) of the United States over recent five years. Use the information from the table and finish the following question.

Source: U.S. Bureau of Economic Analysis

(1) Use yearly GDP growth rate and calculate the five-year average growth rate of the US.

(2) Due to the Covid-19 pandemics, the US national output (GDP) shrank 3.5 percent in 2020. It is reasonable that economists could treat this year as an outlier because this change was largely caused by an unprecedented health crisis. Now use GDP from 2016 to 2019 to calculate 4-year average GDP growth rate. How much is the average yearly growth rate?

(3) Based on the average 4-year growth rate (2016-2019), how long it takes to double US GDP?

(4) For country B, its GDP is now about 60 percent of the US. You are trying to forecast GDP of this country relative to the US in the next 10 years. The US GDP growth rate is about 1.8 percent in the next 10 years. And GDP growth rate country B is about 3.5 percent. Then how much GDP of country will be relative to the US GDP after 10 years?

Question 4. (20 points)

Suppose in a country A, its economy can be described as the following equations,

· Y = C + I + G; national output or GDP.

· C = 20 + 0.8 (Y-T); consumption, marginal propensity to consume MPC = 0.8.

· I = 15; investment (as a given value here).

· G = 100; government spending.

· T = 100; tax.

(1) What is the equilibrium level of income according to the Keynesian Cross?

Suppose, now we have some new information. For example, investment (I) is a function of interest rate (r), as below.

· Y = C + I + G; national output or GDP.

· C = 20 + 0.8 (Y-T); consumption, marginal propensity to consume MPC = 0.75.

· I = 40 - 5 * r; investment which is a negative function of real interest rate (r).

· (M/P)d = Y - 35 * r; real money demand which is adjusted by price level (inflation).

· G = 100; government spending.

· T = 100; tax.

· M = 1,100; money supply.

· P = 5; price level.

(2) Using the information above, try to derive the IS curve.

(3) Use the same equations, now try to derive the LM curve.

(4) What are the equilibrium level of national output (Y) and the equilibrium interest rate (r)?

Question 5. (20 points)

Suppose there are two cities in Arkansas. They are 40 miles apart on an inter-state highway. In history, the two cities were similar in several aspects before the 1980s, including infrastructure, demographics and industries. For example, both cities had about 5,000 total population and roughly $10,000 of average household income in the mid-1970s. After 40 years, one city still has about 5,000 people and with $28,000 average household income. The other city, however, has expanded into a decent metro-area with 30,000 residents and $50,000 average household income.

(1) Could you explain the change of the two cities from the a respective of long-run economic growth? You can present your answer intuitively (in your own words) or graphically.

(2) From the story above, can you find any evidence to support or invalidate the Solow growth model, which is the core of modern economic growth theory.

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