homework2(2010s) Recent site activity masaruinaba

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Macroeconomics ^宿題 2

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選択問題では、適切なものを一つ選びなさい。すべての問題について解答は答えだけでなく、その

答えを選んだ理由をテキストやノートを参考にして丁寧にわかりやすく書くこと。読んで理解でき

ない解説や，答えだけのものは採点しない．明らからに他の人の解答を写したものも，採点の対象

としない．

1 長期の理論：要素市場，財市場，貨幣市場

1.1 A competitive firm takes:

(a). outputs as given, but not inputs. (b). inputs as given, but not outputs. (c). both inputs and outputs as given. (d). neither inputs nor outputs as given.

(e). the prices of its outputs as given, but not the prices of its inputs. (f). the prices of its inputs as given, but not the prices of its outputs. (g). the prices of both its inputs and its outputs as given.

(h). neither the prices of its inputs nor the prices of its outputs as given.

1.2 A profit-maximizing firm will demand capital (K) up to the point where:

(a). marginal revenue equals zero.

(b). the real rental price equals the real wage.

(c). the marginal product of capital equals the marginal product of labor. (d). the marginal product of capital equals the real rental price.

(e). the marginal product of labor equals the real rental price. (f). the marginal product of labor equals the real wage.

1.3 According to Euler’s theorem, the sum of all factor payments will equal total

output if each factor of production is paid its marginal product and if:

(a). the production function displays diminishing marginal productivity. (b). the production function has constant returns to scale.

(c). the production function has increasing returns to scale. (d). the amounts of capital and labor employed are equal.

(e). a firm acts monopolistically. (f). all of the above.

(g). none of the above.

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1.4 Constant returns to scale occurs when:

(a). output remains constant over time.

(b). the marginal productivity of inputs diminishes as inputs increase.

(c). the marginal productivity of labor equals the marginal productivity of capital. (d). the marginal products of capital and labor do not change.

(e). output quintuples when the marginal products of capital and labor are quintuplicated. (f). output quintuples when the amounts of all factor inputs are quintuplicated.

(g). none of the above.

1.5 Profit is zero for competitive firms when:

(a). the production function is constant returns to scale. (b). Euler’s theorem is satisfied.

(c). the sum of all factor payments equals total output. (d). the difference of total revenue and total cost is zero.

(e). all of the above. (f). none of the above.

1.6 The FALSE statement below is:

(a). the extra revenue a firm gets from an extra unit of capital equals the marginal product of capital times the price of output.

(b). the extra revenue a firm gets from an extra unit of labor equals the marginal product of labor times real wage. (c). a perfectly competitive firm’s capital demand curve is the MPK schedule.

(d). constant returns to scale and profit maximization together imply that economic profit is zero. (e). none of the above.

===============================================

1.7 Suppose that the production function is Y = K

¹²

^L

¹²

, the consumption function

is C = 10 + 0.75(Y − T ), the investment function is I = 30 − 2r, the government

purchases is G = 10 and the tax is T = 20, respectively, K = 100, and L = 100.

Firms are competitive. P is the price level, R is nominal rental rate, and W is

nominal wage.

1.7.1 In this economy, compute Output(Y ), Consumption(C), Investment(I), and Real Interest Rate(r) in equilibrium. (4 points)

1.7.2 Given the amount of labor input L, derive the demand function for capital stock. 1.7.3 Given the amount of capital stock input K, derive the demand function for labor input. 1.7.4 Compute the real rental price (^RP) and the real wage rate (^WP) in equilibrium.(2 points) 1.7.5 Confirm Y = ^RP^K+^WP^L. (1 point)

===============================================

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1.8 Suppose that the production function is Cobb=Douglas type, Y = AK

^α

^L

^1−α

, where

0 < α < 1. Proof the statements as follow. (2 points each)

1.8.1 The Cobb=Douglas production function satisfies the constant return to scale (規模に関して収穫一定_).

1.8.2 The Marginal products of capital (MPK) is positive. (The Cobb=Douglas production function is an increasing function of K.)

1.8.3 The marginal products of labor (MPL) is positive. (The Cobb=Douglas production function is an increasing function of L.)

1.8.4 As K gets larger, the marginal products of capital (MPK) decreases. (The Cobb=Douglas production function satisfies the diminishing return to scale (限界生産力逓減).)

1.8.5 As L gets larger, the marginal products of labor (MPL) decreases. (The Cobb=Douglas production function satisfies the diminishing return to scale (限界生産力逓減).)

1.8.6 The Cobb=Douglas production function satisfies ”Euler’s Theorem.”

===============================================

2 ^{長期の理論：失業}

2.1 (2 points). Use the INTERNET to find monthly number of labor force and unem-

ployed person from January 1973 to March 2010. Draw a graph of the number of

labor force and unemployed person (use seasonally adjusted data).(Hint: A good

place to look for data is the Web site of the Statistics Bureau, Director-General

for Policy Planning (Statistical Standards) and Statistical Research and Training

Institute.

http://www.stat.go.jp/data/roudou/longtime/03roudou.htm)

2.2 (2 points). Use the INTERNET to find monthly unemployment rate from January

1973 to March 2010. Draw a graph of the unemployment rate (use seasonally ad-

justed data).(Hint: A good place to look for data is the Web site of the Statistics

Bureau, Director-General for Policy Planning (Statistical Standards) and Statis-

tical Research and Training Institute.

http://www.stat.go.jp/data/roudou/longtime/03roudou.htm)

2.3 (2 points). Use the INTERNET to find monthly ACTIVE JOB OPENINGS -TO-

APPLICANTS RATIO (有効求人倍率) from January 1973 to March 2010. Draw a

graph of ACTIVE JOB OPENINGS -TO- APPLICANTS RATIO (use seasonally

adjusted data).(Hint: A good place to look for data is the Web site of Ministry of

Health, Labor and Welfare.

http://www.mhlw.go.jp/toukei/list/114-1.html)

2.4 (2 points). Why was the unemployment rate in Japan lower than the other coun-

tries? Explain some hypothesis. (5 lines )

2.5 (2 points) Replicate a graph of UV curve in Japan in page 23 of lecture slide for

”Unemployment.” The sample period is from 1973 to 2009.

3

homework2(2010s) Recent site activity masaruinaba

Macroeconomics 宿題 2

選択問題では、適切なものを一つ選びなさい。すべての問題について解答は答えだけでなく、その

答えを選んだ理由をテキストやノートを参考にして丁寧にわかりやすく書くこと。読んで理解でき

ない解説や，答えだけのものは採点しない．明らからに他の人の解答を写したものも，採点の対象

としない．

1 長期の理論：要素市場，財市場，貨幣市場

1.1 A competitive firm takes:

1.2 A profit-maximizing firm will demand capital (K) up to the point where:

1.3 According to Euler’s theorem, the sum of all factor payments will equal total

output if each factor of production is paid its marginal product and if:

1.4 Constant returns to scale occurs when:

1.5 Profit is zero for competitive firms when:

1.6 The FALSE statement below is:

1.7 Suppose that the production function is Y = K

L

, the consumption function

is C = 10 + 0.75(Y − T ), the investment function is I = 30 − 2r, the government

purchases is G = 10 and the tax is T = 20, respectively, K = 100, and L = 100.

Firms are competitive. P is the price level, R is nominal rental rate, and W is

nominal wage.

1.8 Suppose that the production function is Cobb=Douglas type, Y = AK

L

, where

0 < α < 1. Proof the statements as follow. (2 points each)

2 長期の理論：失業

2.1 (2 points). Use the INTERNET to find monthly number of labor force and unem-

ployed person from January 1973 to March 2010. Draw a graph of the number of

labor force and unemployed person (use seasonally adjusted data).(Hint: A good

place to look for data is the Web site of the Statistics Bureau, Director-General

for Policy Planning (Statistical Standards) and Statistical Research and Training

Institute.

http://www.stat.go.jp/data/roudou/longtime/03roudou.htm)

2.2 (2 points). Use the INTERNET to find monthly unemployment rate from January

1973 to March 2010. Draw a graph of the unemployment rate (use seasonally ad-

justed data).(Hint: A good place to look for data is the Web site of the Statistics

Bureau, Director-General for Policy Planning (Statistical Standards) and Statis-

tical Research and Training Institute.

http://www.stat.go.jp/data/roudou/longtime/03roudou.htm)

2.3 (2 points). Use the INTERNET to find monthly ACTIVE JOB OPENINGS -TO-

APPLICANTS RATIO (有効求人倍率) from January 1973 to March 2010. Draw a

graph of ACTIVE JOB OPENINGS -TO- APPLICANTS RATIO (use seasonally

adjusted data).(Hint: A good place to look for data is the Web site of Ministry of

Health, Labor and Welfare.

http://www.mhlw.go.jp/toukei/list/114-1.html)

2.4 (2 points). Why was the unemployment rate in Japan lower than the other coun-

tries? Explain some hypothesis. (5 lines )

2.5 (2 points) Replicate a graph of UV curve in Japan in page 23 of lecture slide for

”Unemployment.” The sample period is from 1973 to 2009.

Macroeconomics ^宿題 2

^L

^L

2 ^{長期の理論：失業}