For the production function Q = K0.3 0.7 and the budget 123 = 6K + 3L find the NEW LEVEL in the optimal employment of capital (K) after wages change by a factor of 1.1 while maintaining the same level of output. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
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- For the production function Q = K0.6L0.8 and the budget 125 = 3K + 5L find the NEW LEVEL in the optimal employment of labor (L) after wages change by a factor of 1.4 while maintaining the same level of output. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1). I Know that the correct answer is 12.4 +/- 1 I am just unsure how to get that answer.For the production function Q = K0.5L0.1 and the budget 137 = 5K + 2L find the NEW LEVEL in the optimal employment of labor (L) after wages change by a factor of 1.5 while maintaining the same level of output. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Consider the following model of a competitive labour market where both firms and workers have perfect foresight and symmetric information about the price level (that is, no misperceptions). Firms' technology is given by the production function y = a N ½ (production function) where a is a positive constant representing total productivity, N is employment and the elasticity of production to employed labour is 1/2. The government requires firms to pay pension contributions to the fiscal authority: the contribution is a small fraction x of the wage paid to each employed worker. Therefore, firms profits equal P y - W N - x W N and they are maximized taking the price level P, the nominal wage W, and the pension contribution rate x as given. Labour supply is given by: W = P b N where b is a positive constant. Answer all the following questions. a) Derive the labour demand schedule by solving the profit maximization problem of firms.
- in an economy with production function Y = 1.5 × K^0.3L^0.7, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. A) 0.5; 0.8 B) 7; 8 C) 0.9; 1.35 D) 1.4; 0.4 E) 0.6; 0.9Consider 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…Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
- With the Cobb-Douglass production function, the real wage will increase if: A. the supply of labor increases B. total factor productivity increases C. the price of output increases D. the amount of capital decreasesConsider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Calculate GDP (Y) for this economy. Does the production function exhibit constant returns to scale? Demonstrate with examples. Determine if the production function exhibits diminishing marginal returns to capital. Demonstrate with calculus What is the real wage in this economy? What share of GDP will go to labor in this economy?True or false: Equilibrium employment is given by the intersection of the wage and the profit curves
- Consider a consumer with the following utility function for consumption and leisure: U (R, C ) = 160 ln N + Y where N is the hours of leisure (“recreation”) consumed per day (24 maximum) and Y is dollars spent on consumption (p = 1). The consumer has an hourly wage w. (a) Assume the consumer derives all income from work at a wage rate w. Derive the labor supply function, LS(w). (b) For what values of w does the consumer work zero hours? (Hint: does a corner solution arise?) (c) Suppose that w = 10. How many hours does this consumer work? If the wage rate increases to w′ = 16, how many hours do they work? What is the total effect on the supply of labor?Non-backward-bending labor supply curve. Consider an economy populated by 100 individuals who have identical preferences over consumption and leisure. In this economy the aggregate labor supply curve is upward-sloping. For simplicity, suppose that throughout this question that the labor tax rate is zero. a. For such a labor supply curve, how does the substitution effect compare with the income effect? b. Using indifference curves and budget constraints, show how such a labor supply curve arises.A worker receives, when unemployed, an offer to work forever at wage w, where w is drawn from the distribution F(w). Wage offers are identically and independently distributed over time. The worker maximizes Where ct is consumption and lt is leisure. Assume Rt is i.i.d. with distribution H(R). The budget constraint is given by And lt + nt ≤ 1 if the worker has a job that pays wt. If the worker is unemployed, the budget constraint is at+1 ≤ Rt(at + z − ct) and lt = 1. Here z is unemployment compensation. It is assumed that u(·) is bounded and that at , the worker’s asset position, cannot be negative. This assumption corresponds to a no-borrowing assumption. Write the Bellman equation for this problem.