where x and y denote, respectively, the number'of hours of skIlled and current labor force consists of 35 hours of skilled labor and 49 hours of unskilled labor. Find the marginal rate of technical substitution.
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- F (L, K) = L0.2K0.7， The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. Derive the equation of the isoquant for y = 2 (with K in the vertical axis and L in the horizontal axis). Use the first and second derivative to show that this curve is decreasing and convex. Provide a graphical representation of the isoquant indicating at least one combination of labour and capital in this curve.If output is produced according to Q = ( KL) 3/4, then this production process exhibits: a.first decreasing and then increasing returns to scale b.first increasing and then decreasing returns to scale c.increasing returns to scale d.decreasing returns to scale e.constant returns to scale Hedge Fun is a landscaping firm that specializes in topiary. Last year, the firm had 60 employees and served 120 customers. This year, it had 70 employees and served 140 customers. The average product of labor is at a maximum when the number of customers is: a.equal to 120 b.greater than 140 c.equal to 140 d.between 120 and 140 e.less then 120A car wash firm calculates that its daily production (in numbers of cars washed) depends on the number of n workers it employs according to the formula P=30n-0.05n^2 cars. (a) Calculate the marginal product of labor at employment level of 50 workers. ___ cars/workers. Interpret the results. This means that, at an employment level of 50 workers, the firm’s daily production will increase at a rate of ____ cars per additional worker it hires.
- why is 1-l1 hours worked and not just l1 as it states in the questionConsider the following model of the factors that influence a person's annual wage: Y = β0 + β1X1 + β2X2 + β3X1X2 + β4X3 + u where Y = annual wage, in dollars X1= years of formal education X2 = age, in years X3 = variable equal to 1 if male, 0 otherwise U = error term Which of the following is the interpretation of β1 alone? The effect of X1 on Y when X2 = 0 The effect of X1 on Y when X2 is at its median value. The effect of X1 on Y, holding all else equal. The effect of X1 on Y when X2 is at its mean value.Consider the augmented production function Y equals A K to the power of 1 divided by 3 end exponent open parentheses H N close parentheses to the power of 2 divided by 3 end exponent, where Y is output, A is total factor productivity, K is capital, N is the number of workers, and H is average years of education. Suppose that A=2, K=8, and N=1000. What is the average product of labor (or output per worker) if H is 15.7?
- Cowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…Let a firm's production function Q (L)=12L^2-1/20L^3 (i.e. output as TL orthe amount of production depends on the workforce, L, as Q is the number of people with a single production input). This functionlet be the foreground 0 ≤ L ≤ 200 for. Accordingly,A) What is the number of labour force (L*) that will make output (Q) the highest?B) what is the number of workers (L**) who will make the maximum amount of output per employee(i.e. Q (L)/L)?c) in both cases the output of the L* and L** values you find and the output per employee at the mosthow can you be sure it's high? Show me.Suppose the price of manufactured goods is 2, price of food goods is 5. The production function for Qm=Lm^0.60 and QF=5*LF^0.60. The total number of workers, L, is 4986. What is the number of workers in the manufacturing sector?
- Himig has two part-time jobs, as an assistant worker in a fast food chain (Job 1) and and as a receptionist at a small hotel (Job 2). Due to her heavy load in her studies, Himig can only render 12 hours a week in her jobs. She has determined that for every hour she works at Job 1, she needs 2 hours of preparation time, and for every hour she works at Job II, she needs one hour of preparation time, and she cannot spend more than 16 hours for preparation. If Himig makes Php 40 an hour at Job 1, and Php30 an hour at Job 2, how many hours should she work per week at each job to maximize her income? (Let x = Job 1; y = Job 2).In a certain factory the production is Q = 120K1/2L1/3 units, where K represents the capital investment measured in units of $ 1,000 and L the size of the labor force measured in worker-hours. Currently, the capital investment is $ 250,000 and 400 worker-hours are employed. Apply the total differential of Q to estimate the resulting change in output, if the capital investment increases by $ 500 and labor increases by 2 hours-worker.10. If over the range of positive marginal product, the short-run total product of factor A in the production of X is given by the equation: X=aA +b A2 – A3 Where a, and b are positive constants, and if the average product of A is maximized when X=100, then the marginal product of A must be greater than the average product when X=50. True or False ?. Prove your answer.
