In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q =f(L,K), q=6LK+4L² ²-(3) ₁². where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the character.)

Consider the production function: F(L, K) = L0:2K0.7. %3D The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. (a) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L, K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination? r (b) Compute the quantity of labour and capital that this firm would use to produce y = 2 at the minimum cost. How much would this cost be? What is the average cost and the marginal cost for that production level? Hint: for this part, you can use directly (without providing the derivation) any results derived in the lecture or tutorials. (c) Derive the equation of the isoquant for y = 2 (with K in the…

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.

When labor is doubled and capital is tripled, a firm's output increases 2.5 times. Which of the following is true? We need more information to determine the degree of returns to scale of this firm's production function. This firm's production function must exhibit increasing returns to scale. This firm's production function must exhibit decreasing returns to scale. This firm's production function must exhibit constant returns to scale.