Assume that the firm Pandemic Lid has a production technology of the form: 4= K L MPL = 2LK MPK = 2KZ where q is the amount of vaccines produced, & is the amount of labour used to produce the vaccines and K is the amount of capital used to produce the vaccines. (a) What is the marginal rate of technical substitution for production of vaccines using labour and capital for Pandemic Lid? Show your working for your answer. Briefly interpret your result. (2 marks) (b) Derive the optimal input demand functions for labour and capital for Pandemic Lid Are they economically sensible? Explain your answer. (5 marks) (e) Derive the total and average cost functions for Pandemic Ltd. How does total and average cost change as output produced by Pandemic Lid increases? Explain your answer. (4 marks) (d) Is the production technology used to produce vaccines by Pandemic Lid of the constant returns, increasing returns, or decreasing returns form? Use the cost structure of Pandemic Led to explain your