1 Question 1 1 Jim s Nursery produces and sells 1100 worth of flowers Jim uses no intermediate inputs He pays his workers 700 in wages pays 100 in taxes and pays 200 in interest on a loan Jim s contribution to GDP is A 900 B 1000 C 1100 D 1800 Answer C the contribution is exactly what Jim sold minus the intermediate inputs he used which are zero Ask yourself where are the 1000 that are missing from the payments 2 All of the following increase total factor productivity except A new inventions B more capital C new management techniques D favorable changes in government regulations Answer B TFP measures the efficiency with which the factors of production such as capital and labor produce output so it cannot be an actual factor of production 3 We can express the per worker production function as a function of only per worker capital thanks to A the decreasing marginal return of capital B the decreasing marginal return of labor C the constant returns to scale D the impatience of households Answer C To convince yourselves try to do this when the production function is Y K N when is not equal to 1 4 Assume two firms that produce a single good in an economy with a constant returns to scale Cobb Douglas production function If N1 N2 then the allocation is necessarily inefficient True False Why Answer False Then can have different capital stocks that would make their marginal productivities of labor being the same and thus efficient Question 2 Argue whether the following statements are True False or Uncertain and explain your answers All of these question relate to the basic Solow growth model we discussed in class 1 1 A higher savings rate increases the economy s growth rate forever Answer False Only temporarily 2 A higher savings rate increases the economy s growth rate temporarily Answer True Only temporarily 3 Consider two economies with a cobb douglas produciton function that are identical in all of their parameters s n A Economy 1 has a lower initial amount of capital than Economy 2 Then a Economy 1 will grow faster than Economy 2 Answer True The MPK is higher when there is less capital so this economy will accumulate capital faster than economy 2 and thus grow faster b Eventually Economy 1 will converge to Economy 2 Answer True Given that they have the same parameters they will converge to the same steady state Question 3 1 Consider a one time change in the level of the labor force in an economy such as due to a new generous immigration policy Specifically assume it rises permanently and immediately i e over a very short period of time from N to N This is the only change in the economy Assuming the economy starts in its initial steady state use the Solow model to explain what happens to the economy in the following questions a What happens to the capital per person immediately as the labor force increases from N to N Answer It falls When the new workers arrive the stock of capital is given and cannot be changed immediately b What happens to the output per person immediately as the labor force increases from N to N Answer It falls Since capital per worker falls then output per works must fall 2 c What happens to the capital per person in the long run once the economy reaches to the new steady state relative to the capital per person that was before the increase in the labor force Answer It goes back to the original steady state value d What happens to the output per person in the long run once the economy reaches to the new steady state relative to the capital per person that was before the increase in the labor force Answer It goes back to the original steady state value e What happens to the growth rate of output per person while the economy is moving towards its new steady state relative to the growth rate it has before the change Answer It is positive and thus higher than the steady state value As the economy converges back to the steady state the growth rate of the economy while being positive declines until it stops when the eonomy reaches to the steady state f What happens to the growth rate of output per person in the long run once the economy reaches to the new steady state relative to the growth rate it has before the change Answer It goes back to the original steady state value i e a zero growth rate 2 Consider a Solow economy that begins with a capital stock of 10 and suppose its steady state level of capital is 20 The economy then receives a gift of foreign aid worth 5 of capital which can be put into production right away a How would the foreign aid affect the eventual steady state consumption relative to the steady state consumption that would have occurred absent a foreign aid Answer It will not effect 3 Consider a Solow economy that is at its steady state with a capital stock of 20 The economy then receives a gift of foreign aid worth 5 of capital which can be put into production right away 3 a How would the foreign aid affect the eventual steady state consumption relative to the steady state consumption that would have occurred absent a foreign aid Answer It goes back to the original steady state value so it will have no effect b What can you say about the path of consumption over time following the aid until the economy gets back to its steady state Answer As there is more capital then the steady state and the savings rate did not change then the is more consumption than the steady state So consumption will jump up and then as capital converges back to the steady state it will decline back to its original value while still being above it as it converges back 4 Assume there was variation in GDP per capita in 1950 and complete unconditional convergence by 2000 Make up data consistent with this observation for 3 countries and plot what this might look like in a diagram scatter plot where 1 GDP per capita in 1950 is on the horizontal axis 2 GDP per capita in 2000 is on the vertical axis and 3 each dot is a country Answer You will draw it as three dots on a straight line i e horizontal parallel to the X axis 5 Consider a Solow model where the production function is now Yt AKt a Assume that A is smaller than the depreciation rare What does output in the steady state equal to Answer It depends on whether sA in which case there is no steady state or alternatively if sA then the only steady state is one with zero capital Question 4 1 An economy has a Cobb Douglas production function with no population growth The government chooses the saving rate s according to the 4