solving the macro economics problem set

• For this simple economy with three final goods:
  • Calculate the Nominal GDP and the Real GDP in 2015 and 2016. Recall that 2000 is the base year.
  • What was the growth rate in 2016?
  • How many years will it take this economy to double its Real GDP at the annual growth rate you found in (b)?
  • What was the growth rate in 2016 using the chain-weighted method?
  • What is the difference between real and nominal GDP and why do economists make this distinction?
• Multiple-Choice Question (Show your work for full credit): Using the data in the table above, gross domestic product equals
• Compute the average annual growth rate of per capita GDP in each country listed below. The levels are provided for 1980 and 2014, measured in constant 2011 dollars.
• Use the Solow Model with the production function: 𝑌_𝑡 = 𝐴̅𝐾^𝛼𝐿^{1−𝛼}, to determine which
  • Intuitively explain the transition to a new steady state.
  • Draw the Solow diagram with output showing the increase in the TFP. Identify the steady states.
  • Draw the dynamic responses over time of capital, output, consumption, and investment.
  • What is the per-worker production function, 𝑦_𝑡 = 𝑓(𝑘_𝑡)? Show your work.
  • Following the Solow model and assuming no population growth, solve for the steady-state capita per worker, output per worker, and consumption per worker, with 𝑠̅ = 0.4 and
• Suppose that two economies (A and B) have the same initial capital stock (𝐾₀), the same production function, and depreciation rate. However, the citizens of country A have a higher saving rate than the citizens of country B. Based on the Solow model:
  • Which country will have higher level of output per worker in the steady state?
  • Which country will have faster rate of growth of output per worker?
  • Draw in one graph (Solow diagram) the steady states in these countries.
• Use the Solow model with the production function: 𝑌_𝑡 = 𝐴̅𝐾^𝛼𝐿^{1−𝛼}. Now, assume that the labor
  • What is the per-worker production function, 𝑦_𝑡 = 𝑓(𝑘_𝑡)? Show your work.
  • Solve for the steady-state level of capital per worker, output per worker, and consumption per worker.
  • Calculate the growth rate of per worker output, per worker capital, and per worker consumption.
  • Draw the resulting Solow diagram.
• Consider the Solow model where the production function no longer exhibits diminishing return to capital accumulation. Assume the production function in now 𝑌_𝑡 = 𝐴̅𝐾_𝑡, the rest of the model is unchanged.
  • Draw the Solow diagram in this case.
  • Suppose the economy begins with an initial capital 𝐾₀, and show how the economy would evolve over time in the Solow framework.
  • What happens to the growth rate of per capital GDP over time?

2015 2016Prices (USD) in the

Final goodsPrice (USD)Quantity Price (USD)Quantity base year 2000

Apples	1.0	100	1.5	100	1.0
Oranges	0.8	100	0.3	90	1.0
Coffee	2.0	200	2.0	220	2.0

Corporate profits	$ 200
Net interest	$ 150
Indirect taxes less subsidies	$ 230
Depreciation	$ 250
Compensation of employees	$ 1,350
Proprietor’s income	$ 150
Rental income	$ 70
Personal consumption expenditures	$ 1,400
Government expenditure on goods and services	$ 500
Net exports of goods and services	$ 40

A) $1,920.

B) $1,940.

C) $2,150.

D) $2,400.

𝑡𝑡

country has the highest steady-state level of capital and output using the table below. For simplicity, assume that labor is fixed and equal to one (1) in all countries. Which country has the highest, and lowest, steady-state capital stock and output? What is likely driven your answer?

5)

𝑡

Given the production function: 𝑌
_𝑡 = 𝐴̅𝐾
^𝛼𝐿̅1−𝛼, with constant labor force (𝐿̅), saving rate(𝑠̅), and depreciation rate (𝑑̅). Suppose that the economy is initially at its steady state. Next, assume an exogenous increase in total factor productivity (TFP) from 𝐴̅ to 𝐴̅′.

6)Assume that production is a function of capital (𝐾_𝑡) and labor (𝐿_𝑡), and that the rate of saving and depreciation are constant. Further, assume that there is no population growth and the production function (𝑌_𝑡) is given by

𝑌= 𝐾1/2𝐿1/2

𝑡𝑡𝑡

𝑑̅ = 0.1.

7)Assume again that production is given by

𝑌𝑡

= 𝐾1/2𝐿̅1/2

𝑡

First, write the production function in per worker terms. Next, assume that the per person level of capital in steady sate is 4, and the depreciation is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? Show your work.

[Hint: you may want to use the Golden Rule]

𝑡 𝑡

force (𝐿_𝑡) grows at a constant rate 𝑛, while the saving rate and depreciation rate are constant parameters given by 𝑠̅ and 𝑑̅ respectively.

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