Let us consider the cost implications of the short-run production schedule from assignment number 7, where capital was fixed at 2 units of capital. Labor:  0 1 2 3 4 5 6 7 8 9 Output:  0 6 24 60 120 170 210 240 260 270 In this scenario, since we only have two inputs (Capital and Labor), and since the amount of capital is fixed, the cost of total cost capital would also be Total Fixed Cost (TFC) and since labor is variable, the total cost of labor would be Total Variable Cost (TVC). In that context, assume that the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is also $30 per unit of labor per period. (a) Use this information set up a diagram (using excel) that shows total cost (TC) and total variable cost (TVC) of the firm per period in the short run with the level of output on the horizontal axi

Please answer in detail according to the picture. Show that the cost function is homogeneous of degree 1/(α+β) in output. How do the returns to scale (degree of homogeneity of the production function) relate to the propertiesof the cost function? Does this make sense to you? Explain clearly why.

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…

Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3)                  The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.