Chunzheng's production function is given by:
Q = K^2L
a. What are the returns to scale associated with Chunzheng's production function? Prove your answer.
b. Derive Chunzheng's input demand curves for labour and capital when w is the wage for labour and r is the rental cost of capital?
c. The wage rate is w = 10 and the rental rate of capital is r = 20. Suppose the firm wants to produce 27,000 units of output. What is the most efficient combination of labour and capital (L, K)?
d. Given your results from above, what is the equation for the Chunzheng's long-run total cost curve as a function of quantity Q. How much does it cost to produce 27,000 units?