1. Aerojet Rocketdyne, an American rocket engine design production company, has the following production function: F(Q) = 2.54L²³K^0.77. Rocketdyne is currently using 500 units of capital (servers and 3D printers) and has an average hourly wage of $85. Based on this information, calculate the following:

a). Calculate Rocketdyne's labour costs.

b). Calculate Rocketdyne's average labour costs.

c).Calculate Rocketdyne's marginal labour costs.

2.)At L = 3, and K = 2, the marginal product of labor is 4 and the marginal product of capital is 5. What is the marginal rate of technical substitution (MRTS)?

3.)Suppose the production function for the automotive and parts industry is q = L^0.31K^0.20M^0.41, where M is energy and materials. What kind of returns to scale does this production function exhibit? What is the marginal product of materials?

4.) Within the United States, the simplified supply function, in terms of quantity | tonnes per annum, is 14Q+3. The demand function for the domestic United States steel industry is 113-8Q. Based on those equations, perform/find the following:

a). Calculate the equilibrium price & quantity.

b).. Calculate consumer and producer surplus for the United States.

5.) Suppose it takes Boeing 10 machine hours to produce an airline door and 50 worker hours to produce another airline door. Now suppose, that you have 15 units of capital and 100 units of labour.

a). Complete the linear production function formula for the production function, based on the information above. b). Define and draw a Leontief production function where quantity is increasing. c). Show the formulation of a Leontief production function. d). Complete the Leontief production function formula for the production function, based on the information above. Explain its shape and why that is the case.

6.) Assume a perfectly competitive firm has the following cost function: C(Q) = 216 + Q³ and the industry price is $300 per unit.

1. What level of output should be produced to maximize profits?
2. How much profit will be earned?
3. Should this firm stay in the sector or exit?