Suppose an economy is on a balanced growth path in a simple Romer model, as described in the text, where aggregate output is: Y, = A,Lyt, law of motion of ideas (idea production function) is: AA+1= ZA“, Lar , labour resource constraint is: Ly +Lat = L, and the allocation of labour is: Lat = IL, %3D where z is a productivity parameter of the researchers, Ao is the existing stock of ideas at time, t = 0, L is the total population and assumed to be constant, and i is the constant fraction of population who works in the research sector. Suppose in year 2030, research productivity z rises immediately and permanently to the new level z'. а. How would the growth rate of ideas behave if a <1? b. Assuming a = 1, solve for the new growth rate of knowledge and growth rate of output per capita. %3D С. Assuming a = 1, sketch the graph of Iny; against time t. d. Why might research productivity increase in an economy?

Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain.  (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k).  (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6.  (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…

Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.

The aggregate production function is Y = 3KL. If there are 20 units of capital and 50 units of labor, what is capital productivity?   Group of answer choices 300 1000 600 150

Based on two period model: population growth results in a decrease in the relative amount allocated to the second period and a lower present value of the marginal user cost. True or False?

Given the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: = g> 0 (a) Obtain the marginal product of capital algebraically, also discussing the second derivative. (b) Transform the production function into efficiency-worker terms, showing how =ỹ depends AL on =k. K AL

Suppose the per-worker production function is: y = A(1-ga) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (ga/m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same O rise

Please see attached image.

None

Help me .....