Suppose that a firm has production function F(L, K) = L2/3 K1/3 for producing widgets, the wage rate for labor is w = $400, and the rental rate of capital is r = $25. a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem. b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of this problem. c) Solve the two equations for the firm’s optimal choice. Show your work.

Please see the attached photo, and Only solve part d, e, and f

I need help on this question

None

Subpart 1-3

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost. a) Find the marginal product of each input. b) Determine whether the production function exhibits diminishing marginal product to each input. c) Find the marginal rate of technical substitution (MRTSLK) d) How does MRTSLK change as more L, is used holding output constant. e) Find the least costly combination of labour and capital to produce 3000 units.

Suppose function of Total Cost (TC) is the following: CT = 300 + 3Q + 2Q2 Where AT is total costo in USD y Q is number of boxes of manufactured devices  a) What are functions of Fixed Cost (FC) and Average Fixed Cost (AFC) ? Graph both b) What are functions of Variable Cost (VC) and Average Variable Cost (AVC) ? Graph both c) What is Marginal Cost (MC) Graph it

A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function:   f (L , K) = 6L1/3K1/6   If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.

In the following production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. What is the marginal product of input 1?

Suppose a firm has the following production function  Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8  = (16/Q)+ 4√?  (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.