The production of new ideas in the Romer model Select one: Oa. increases in the efficiency of creating knowledge and the fraction of labor in research and development. Ob. decreases in the efficiency of creating knowledge and increasing the fraction of labor in research and development. Oc. increases in the efficiency of creating knowledge and decreasing in the fraction of labor in research and development. Od. increases in the population growth rate and capital accumulation. Oe. decreases in the efficiency of creating knowledge and in the fraction of labor in research and development.
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A common specification is A_dot = δ A L_A (more generally A_dot = δ A^φ L_A), where A_dot is the flow of new ideas, δ is the research productivity (efficiency of creating knowledge), A is the existing stock of knowledge, and L_A is labor employed in research (the Show more…
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A variation on the Romer model: Consider the following variation: Yt = At^(1/2)Lyt, ΔAt+1 = zAtLat, Lyt + Lat = L, Lat = sL. There is only a single difference: we've changed the exponent on At in the production of the output good so that there is now a diminishing marginal product to ideas in that sector. (a) Provide an economic interpretation for each equation. (b) What is the growth rate of knowledge in this economy? (c) What is the growth rate of output per person in this economy? (d) Solve for the level of output per person at each point in time.
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Consider the following Romer model: Yt = At^alpha * Lyt delta At+1 = zbar * At * Lat Lyt + Lat = Lt Lyt / Lat = xbar where Yt is output at time t, At is knowledge, Lyt is the number of workers producing output, Lat is the number of workers producing knowledge, Lt is the total number of workers in the economy, and alpha, zbar, and xbar are parameters. Suppose Lt = Lbar, alpha in (0, 1], and xbar > 1. (a) Derive the expression for the growth rate of knowledge. (b) Derive the expression for the growth rate of output per worker, yt = Yt / L. (c) Let A0 denote the initial value for knowledge. Derive the expression for the level of output per worker at any time t as a function of A0 and parameters. (d) Draw a diagram with output per worker on the vertical axis (using a ratio scale) and time on the horizontal axis. Suppose there is a one-time permanent reduction in the workforce because of out-migration. Show graphically what will happen to output per worker over time.
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