Kindly solve these for me

Consider the standard version of the Solow growth model discussed in class. The production function is Y (t) = F(K(t), A(t) I(t) ), (1) while the rate of change of capital is given by K (t ) = BY (t) - 8K (t) . (2) Labor L (t) and the "effectiveness of labor" A (t) are assumed to grow at the exogenous rates n and 9, respectively. (a) Assuming that (1) exhibits constant returns to scale, show that the production function can be written in intensive form as y (t ) = 1 (k (t) ), (3) where y ( t ) = Y (t) / ( A (t) L (t)) and k (t) = K (t) / (A (t) L (t)). (b) Show that (2) can be written in intensive form as k ( t ) = of ( k (t) ) - (n+ g + 8) k(t). (4) What is the interpretation of (4)?Acme Widget, Inc., has the following production function, Find the MPN for each level of employment. Workers Widgets MPN 17 23 28 32 6 35 Acme can get $6 for each widget it produces If the nominal wage is $49, Acme will hire workers " the nominal wage is 531, Acme will hire workers If the nominal wage is $19, Acme wil hire workersProblem 4 - Optimal production The Acme Corp produces widgets using labor (L) and capital (K) according to the production, Q = F(L, K) = LINK1/4. A widget sells at price P = 16. A unit of labor costs W = 1 and a unit of capital costs R = 4. In the short run, the firm's capital is fixed at K = 1/2 and only labor can be set freely. In the long run, both capital and labor can be chosen freely. There are no fixed costs. 1. In the short run, if Acme Corp wants to produce an output level. Q, solve for its labor demand LSR (Q) 2. Using your expression for LSR(Q), solve for the firm's short run cost function, CSR(Q). 3. Solve for the short run marginal cost function, ACS?(Q). With this, find Acme's optimal short run output level QSR. 1. In the long run. Acme can change both capital and labor as it pleases. Find the optimal long run capital and labor input choices for a given output level. Q. Denote the optimal long run input choices by L(Q) and K (Q). State the long run cost function C(Q). 5. Determine Acme's optimal output choice in the long run, Q". How much labor does Acme demand in the long run. L"? Compare with your answer to question 3. Explain the difference.Acme widget company has the plant capacity to produce 100 widgets or 100 zercs. Acme's current production mix is 55 widgets and 45 zercs. What is the total cost of producing 55 widgets? A. 45 zercs C B. 55 zercs C C. I zerc D. There is not enough information to tell. What would be the marginal cost of producing the fifty sixth widget? (Curl)