Using the model for a closed economy, if the nominal wage is $40 and we have a Cobb-Douglas production function where a = 0.2, L = 400, and labor income + capital income = $2,000, what is the price of the output given the neoclassical theory of distribution holds? %3!
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- Consider an economy with production function given by Y = AK0:5L0:5 where A is the total factorproductivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is xed and equal to 1. Assume A=100.a. Write the rm's problem of choosing labor demand. Derive the demand for labor as a functionof the real wage.b. Assume labor supply is inelastic and xed at L= 100. Find the equilibrium values of the wageand the employment level for this economy. Display graphically the labor supply and the labordemand curves. Carefully label your graph.c. Suppose the economy faces a positive productivity shock and TFP is now A=200. Displaygraphically the new labor demand function. What are the equilibrium values of employment andthe real wage?d. Compute the total output when A=100 and when A=200. What is the output's growth rate?Compare that growth rate with the growth rate in A. How does the growth rate of output percapita compares to the growth rate in A? Explain…Why does modeling production as convex in inputs probably make sense in the real world?The labour market in an economy is characterised by the following equations: W = 0.7-0.9u ре Wage setting: W = 0.5 P Price setting: In which W is nominal wages, pe and P are expected nominal prices and nominal prices, respectively, u is level of unemployment. Consider a linear production function for firms such that Q = N, i.e., production for firms (Q) depends only on the number of employees (N). Considering this information, which of the following statements are CORRECT: U The price mark-up (u) for this economy is 1 (i.e. µ = 1). O If actual output is below potential output, actual unemployment rate is below 0.22, (i.e. uț < 0.22). The equilibrium unemployment in this economy is 0.22 (i.e. ue = 0.22). U If wage setters become less responsive to changes in unemployment (e.g., from -0.9 to -0.7), the equilibrium unemployment decreases.
- Why is the interest rate irrelevant in the one-period general equilibrium model? What is the mechanism for the interest rate affecting labour supply in the two period model?If the production function for GDP is Cobb-Douglas in labour and capital, with the exponent on capital is a space equals space 1 third, and assuming constant returns to scale, and a perfectly competitive goods market a. The marginal product of labour (vertical axis) will have a positive, concave slope when plotted against labour (horizontal axis) b. In equlibrium, wage will equal 2 over 3 y, where y is output per worker c. Labour and capital are complements so the derivative fraction numerator d squared Y over denominator d L d K end fraction less than 0 d. None of the answers is correct e. The marginal product of labour is: left parenthesis 1 minus a right parenthesis A open parentheses Lover K close parentheses to the power of aexplain the elasticities of production function for a neoclassical production function with the help of graph
- Economics Modify the Lewis model and assume that there is a strictly positive marginal product of labor in the traditional sector. Use figures with production functions in the traditional and the modern sectors to show what the equilibrium is when no one wants to move away from agriculture. What assumptions do you have to make about production functions to arrive at the conclusion that fewer people will end up in agriculture? Use the same starting point as in the above question. Derive the demand for labor in the traditional and in the modern sectors. Show graphically what the characteristics of the equilibrium would look like when no one wants to change sectors.Land is a factor specific to producing olives. When Padua starts to trade, it exports olives. Using the specific factors model, explain what happens to nominal and real rental rates of land.Recall that equilibrium in the static consumption-labor choice model is given by the following five equations: Y = AK"L-a R = aAKa-1L-a = (1- a)AKªL-a L= [N - () R] %3D R/P K %3D Y = C Suppose that A decreases. Construct a pair of well-labeled diagrams of equilibrium in the factor markets to show how the change in A affects the supply of capital, the supply of labor, the real wage, and the real rental rate. When A increases: O Y increases and C increases OY increases and C decreases OY decreases and C increases OY decreases and C decreases
- Consider again the canonical OLG model with log preferences and a Cobb-Douglas production function, but assume that individuals now work in both periods of their lives. (a) Define a competitive equilibrium and the steady-state equilibrium. (b) Characterize the steady-state equilibrium and the transitional dynamics in this economy. (c) Can this economy generate overaccumulation?Explain The difference between induced and autonomous investment in economics....Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total factor productivity, N D is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0 < t < 1). There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U(c, l) = ln c + ln l (1) (a) Write down the definition of a competitive equilibrium for the above economy. (b) Show that the Walras’ law holds for this economy. (c) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium. (d) Solve for the optimal allocation of leisure,…
