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ECON20001

Creation date：2025-02-12 15:30:51

Belonging category：经济Economics

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Assignment #2

The assignment is marked out of 25 points. The weight for each part is indicated following the question text.

Style requirements: This assignment requires the submission of a spreadsheet. Please keep THREE decimal places in your answers and include your spreadsheet as an appendix. You can use Excel, Google Sheets, Libre Offfce etc. in your calculations. Please also take care in presenting your work and answers clearly. (1 point)

Question 1 [4 points]

Convergence in two samples of economies. Go to the website containing the Penn World Table (https://www.rug.nl/ggdc/productivity/pwt/) and collect data on real GDP (expenditure-side real GDP at chained PPPs (in mil. 2017 USD)) and population from the earliest year available (usually, but not always, 1950) to the latest year (usually, but not always, 2019) for Australia, Japan, South Korea, Italy, Taiwan, China, Brazil, Albania and South Africa. Then construct real GDP per person each year as the ratio of its real GDP per person to that of Australia for that year (so that this ratio will be equal to 1 for Australia for all years.)

(a) Plot these ratios for Japan, South Korea, Italy, and Taiwan over the period for which you have data. Does your data support the notion of convergence with Australia? Give a brief explanation to rationalize your ffnding. (2 points)

(b) Plot these ratios for China, Brazil, Albania, South Africa, and Australia. Does this data support the notion of convergence with Australia? Give a brief explanation to rationalize your ffnding. (2 points)

Question 2 [20 points]

Solow growth model with capital utilization. In this question, you will explore how changes in the capital utilization rate and savings rate affect an economy.

Consider a version of the Solow (neoclassical) growth model in which the total capital stock K may not be fully utilized. Denote the capital utilization rate as u with 0 ≤ u ≤ 1 so that the aggregate production function is Y = (uK) α (AN) 1−α where as before, K is total physical capital stock and N is employment.

Further, assume that the depreciation rate is an increasing function of the utilization rate and given by,

δ(u) = δu β , where 0 < δ < 1, β > 0

Thus, the capital accumulation equation (in per effective worker terms) is,

(1 + gA + gN )(kt+1 − kt) = syt − (δ(u) + gA + gN )kt

where k ≡ K/AN is capital per effective worker, y ≡ Y/AN is output per effective worker

(1) Using the parameter values in Table 1, calculate the steady-state values of capital per effective worker k ≡ K/AN, output per effective worker y ≡ Y/AN and consumption per effective worker c ≡ C/AN. Also calculate the growth rates of output per worker and consumption per worker along the balanced growth path. (2 points)

(2) Using the parameter values in Table 1, calculate the golden rule savings rate that maximizes steady state consumption per effective worker. (1 point)

(3) Suppose that the economy is initially in steady-state. In year t = 0 the capital utilization rate increase from u = 0.75 to u = 0.80 (i.e., from 75% to 80%) while all other parameters have their benchmark values.

(i) Calculate the new steady-state levels of capital per effective worker, output per effective worker and consumption per effective worker. Does long-run capital per effective worker increase? Explain. Does long-run output per effective worker increase? Explain. (3 points)

(ii) Also calculate the long run growth rates of output per worker and consumption per worker? Do the long-run growth rates of output per worker and consumption per worker increase? Explain. (1 point)

(iii) Using equations, describe how you can calculate the time-paths of capital per effective worker, output per effective worker and consumption per effective worker. Plot the time paths of capital per effective worker, output per effective worker and consumption per effective worker for 100 years (t = 0, 1, ...., 100). (2 points) (iv) Describe and explain the dynamics of capital per effective worker and output per effective worker that you plotted in

(iii). Discuss which variables move in the short-run and why. In your explanation, you should describe how effective investment and effective depreciation are impacted in response to an increase in capital utilization. You may use a diagram to aid in your explanation or alternatively describe how the effective investment and effective depreciation curves will be impacted following an increase in u. (4 points) Note: You will probably want to use a spreadsheet program to implement these calculations.

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LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 FINC5090 MATH1052 SciComp Elec4622 FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 MAT 237 BISM2201 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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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