a. Express the production function in per worker. b. Assuming closed economy with no government, A = 1, labor growth rate being constant (GL) and depreciation rate is positive 8 > 0, show the step by step derivation of the fundamental equation of growth (using per worker capital, k) c. Find the steady-state values of capital per labor (kss), output per labor (yss) and consumption per labor (Css). Note: Take kss = 0 as given, you don't have to show that it is true.

a. Express the production function in per worker. b. Assuming closed economy with no government, A = 1, labor growth rate being constant (GL) and depreciation rate is positive 8 > 0, show the step by step derivation of the fundamental equation of growth (using per worker capital, k) c. Find the steady-state values of capital per labor (kss), output per labor (yss) and consumption per labor (Css). Note: Take kss = 0 as given, you don't have to show that it is true.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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Show that, when using a traditional economic production function,doubling our population can double our output if capital stocks alsodouble. Use the production function: Q = AK L , where A representstechnology in an economy, K capital, and L labor. Double K and L andshow that Q also doubles, assuming α=β=1/2. Now show that, when we incorporate natural capital into thediscussion, doubling the population does not increase output in thesame way (since natural capital cannot also grow). Use theproduction function: Q = AK L N , where N is natural capital. DoubleK and L and show that Q less than doubles, assuming α=β=γ=1/3.
The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − AL
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Assume that a country's production function is Y= AKº³Lº7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. a. What is the marginal product of capital in this situation? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital-output ratio or by using the fact that capital's share equals MPK multiplied by K divided by Y.) b. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by Y must provide for gross growth of (8 + n + g)K, where 8 is the depreciation rate.) c. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital? d. What must the saving rate be to achieve the Golden Rule level of capital?
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1. Evaluate the following claim in the context of the static general equi- librium model with production: “An increase in the wage causes labour demand to fall, and therefore makes households worse off.” explains in detail and not copy paste from the anywhere
The Black Death: (a) Wages were higher after the Black Death because of diminishing returns. Our production model exhibits diminishing returns to labor: each additional unit of labor increases output by less and less. So if the amount of labor is reduced, the marginal product of labor — and hence the wage — increases. The reason is that capital stays the same: each remaining worker is able to work with more machines, so his productivity rises. In fourteenth-century Europe, the marginal workers could move to better land and discard old broken-down tools. Graphically, this can be seen by considering the supply-and-demand diagram for labor in Figure 4.2(b). If the supply of labor shifts back (because a large number of workers die), the equilibrium wage rate increases. Draw this graph — including the shift in the labor supply curve — to see the result for yourself. Mathematically, the result can be seen in the solution for the wage rate in our production model,…