A profit maximizing firm produces output using capital, K, and labour, L, in the following production technology: Y = 2*K^0.5*L^0.5 The rental rate of capital is r=0.10. What is the capital-labour ratio of the firm?

Consider the production function: Y = z.f(K,N,L) where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land.

The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…

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Can you please help solve question 9 a,b and c  please show full working so I can compare it to my own work Thank you

suppose Mark operates the production of lawnmowers at Mark Mowers and Bros. Using inputs like labor (L) and capital (K). over his time as a production manager, he has found out that the production function, in the long run, is Q=500*min (L,7K). Given this information, help him determine the following. b. Assume for the time being that he has only one unit of capital to employ in this factory. What would be the total product, the marginal product, and the average product of the labor curve? Draw all three of them. Also make sure that you create a table using the different combinations of L and K that helps you in determining the shape of these curves.