World Economy Final - Week 4

Front 1

The additional output produced by adding one extra unit of capital to the production process while holding everything else constant is called

a) total factor productivity
b) average output
c) the marginal product of capital
d) returns to scale
e) economies of scale

Back 1

C. THE MARGINAL PRODUCT OF CAPITAL

Front 2

Holding all other things constant, a firm has the following production schedule: [SEE CHART ON WORKSHEET]

This firm exhibits:
a) diminishing marginal product of labour
b) increasing labour productivity
c) technological innovation
d) depreciation of capital
e) a shortage of labour

Back 2

A. DIMINISHING MARGINAL PRODUCT OF LABOR

Front 3

Suppose the economy has TFP = 10, there are 400 hours worked, and 9 unit of capital and the Cobb‐Douglas production function is OUTPUT = TFP x HOURS^(1/2) x CAPITAL^(1/2)

Output is currently
a) 36,000
b) 600
c) 12,000
d) 1,800
e) 6,000

Back 3

B. 600

Y = 10 x 400^(0.5) x 9^(0.5) = 600

Front 4

Suppose the economy has TFP = 10, there are 400 hours worked, and 9 unit of capital and the Cobb‐Douglas production function is OUTPUT = TFP x HOURS^(1/2) x CAPITAL^(1/2)

The marginal product of labour is
a) 0.75
b) 1.25
c) 1.0
d) 10
e) 30

Back 4

A. .75

MPL = (1‐a)A(K/L)^a
MPL = 0.5 x 10 x (9 / 400)^(0.5) = 0.75

Front 5

Suppose the economy has TFP = 10, there are 400 hours worked, and 9 unit of capital and the Cobb‐Douglas production function is OUTPUT = TFP x HOURS^(1/2) x CAPITAL^(1/2)

If total factor productivity grows by 1% per year while capital and labour each grow by 2% per year, then output grows by
a) 1.5% per year
b) 3% per year
c) 5% per year
d) 1.67% per year
e) 4% per year

Back 5

B. 3% PER YEAR

%Change(Y) = %Change(A) + [a x %Change(K)] + [(1‐a) x %Change(L)]

%Change(Output) = 1 + [0.5 x 2] + [0.5 x 2] = 3

Front 6

Suppose the economy has TFP = 10, there are 400 hours worked, and 9 unit of capital and the Cobb‐Douglas production function is OUTPUT = TFP x HOURS^(1/2) x CAPITAL^(1/2)

For this hypothetical economy, the share of output paid to labour is
a) 70%
b) 30%
c) 50%
d) 10%
e) 90%

Back 6

C. 50%

a = share of GDP paid to capital
(1‐a) = share of GDP paid to labour = 1 – 0.5 = 0.5

Front 7

Consider an economy with a Cobb‐Douglas production function in which capital and labour receive equal shares of national income and labour input is constant. If the capital stock grows by 2% and output grows by 4%, then the most likely explanation is:

a) the marginal product of labour is increasing

b) the production function exhibits decreasing returns to scale

c) total factor productivity has increased by 3%

d) TFP has grown by 2%

e) There is a 2% change in the capital account balance

Back 7

C. TOTAL FACTOR PRODUCTIVITY HAS INCREASED BY 3%

%Change(Y) = %Change(A) + [a x %Change(K)] + [(1‐a) x %Change(L)]
4% = %Change(A) + 0.5(2)% + 0%
%Change(A) = 4 ‐1 = 3%

Front 8

The marginal product of capital may be decreasing because:

a) capital depreciates over time

b) each additional machine has fewer workers to operate it

c) new machines embody a different technology than old machines

d) at some point the economy reaches full capacity, beyond which output cannot expand

e) machines are often firm‐specific, with little resale value to another firm

Back 8

B. EACH ADDITIONAL MACHINE HAS FEWER WORKERS TO OPERATE IT

Front 9

The diminishing marginal product of capital implies

a) that as nations become poorer, the marginal product of capital declines

b) that an extra machine generates less extra output in a country with little capital than in a country with much capital

c) that additions to the capital stock produce more incremental output in poor countries than in rich countries

d) that wealthy economies will continue to grow richer while poor countries become poorer

e) a failure on the part of a nation’s investors to replace depreciated capital equipment

Back 9

C. THAT ADDITIONS TO THE CAPITAL STOCK PRODUCE MORE INCREMENTAL OUTPUT IN POOR COUNTRIES THAN IN RICH COUNTRIES

Front 10

Convergence refers to

a) the reunification of formerly divided countries such as East and West Germany

b) an equality between a country’s imports and exports

c) an economy reaching a steady state

d) poorer countries growing more rapidly than rich countries

e) agreement between economic historians of different political persuasions

Back 10

D. POORER COUNTRIES GROWING MORE RAPIDLY THAN RICH COUNTRIES

Front 11

By definition, the capital stock of a country is expanding if

a) gross fixed capital formation is positive

b) depreciation is positive

c) the marginal product of capital is positive

d) net investment is positive

e) the steady state has been achieved

Back 11

D. NET INVESTMENT IS POSITIVE

Front 12

For any economy with an existing capital stock of $800 million and annual depreciation of 5%, a steady state occurs if:

a) gross investment = $840 million

b) gross investment = $1600 million

c) gross investment = $40 million

d) net investment = $5 million

e)net investment = $800 million

Back 12

C. GROSS INVESTMENT = $40 MILLION

Steady‐state: sYt = δKt
sYt = δKt = 0.05($800 million) = $40 million

Front 13

The Golden Rule for achieving the highest sustainable long run level of consumption per capita is to equate:

a) saving with investment

b) investment with depreciation

c) depreciation with the marginal product of capital

d) the marginal product of capital with saving

e) output with investment

Back 13

C. DEPRECIATION WITH THE MARGINAL PRODUCT OF CAPITAL

Front 14

If the rate of investment exceeds the rate recommended by the Golden Rule,

a) the economy will not reach a steady state

b) long run consumption will fall below its Golden‐Rule level

c) the economy will experience sustained long run growth

d) the marginal product of capital will increase

e) the rate of depreciation will speed up

Back 14

B. LONG RUN CONSUMPTION WILL FALL BELOW ITS GOLDEN RULE LEVEL

Front 15

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

A. What is the share of labour income in output?

Back 15

The share of labour income is 73% and of capital is 27%.

Front 16

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

B. What happens to the share of profits (i.e. capital’s share in output) when there is a change in TFP? (Comment on your answer).

Back 16

These shares stay the same when there is a change in TFP; TFP is neutral with respect to income shares so both capital and labour share in its benefits. Clearly some forms of technical progress might not be like this and could favour labour relatively heavily or favour capital.

Front 17

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

C. What happens to the marginal product of labour if L increases by 10% with no change in other inputs?

Back 17

A 10% increase in L reduces the MPL by about 2.5% (and increases MPK by about 7.2%)

Front 18

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

D. What happens to the marginal product of capital if K increases by 15% with no change in other inputs?

Back 18

A 15% increase in K reduces the MPK by about 9.7% (and increases MPL by about 3.8%))

Front 19

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

E. What happens to the marginal product of labour if both L and K increase by 7%?

Back 19

MPK and MPL are unchanged if L and K rise by the same percentage

Front 20

Given the following Cobb‐Douglas production function: Y = TFPxK^(0.27)xL^(1‐0.27)

F. What happens to output per person employed if both L and K increase by 7%?

Back 20

Output per capita is also unchanged.

Front 21

Assume there are two countries, a poor country (P) with a small capital stock and a rich country (R) with a large capital stock. They have similar levels of employment and TFP (i.e. they have the same production function). A multinational wishes to invest a fixed amount of capital (K*) in one of these countries. Which country will experience the biggest growth in GDP from the investment? Draw a diagram to illustrate your argument.

Back 21

[SEE WORKSHEET]

Front 22

Draw a diagram to show the effect on GDP per capita of:

a) An increase in the savings rate (s)
b) An increase in the population growth rate (n)

Back 22

[SEE WORKSHEET]