production process

Q1. Cally uses labour (L) and capital (K) in her production process. The wage rate for one unit of labour is $10, while units of capital cost $20 per unit.

a. Graphically depict the isocost line for Cally’s firm for a $12,000 expenditure by Cally on inputs. Draw a typical Cobb-Douglas isoquant for an output level to depict the optimal levels of L and K for quantity Qo and TCo = $12,000. Make sure all relevant points on your diagram are identified. [4 marks]

b. The provincial government has decided that a minimum hourly wage for labour should be of $12 per hour. In the short-run, with capital fixed at K, show graphically what happens to total cost when Cally continues to produce Qo and explain why. [6 marks]

c. Show the optimal factor mix the Cally will use in the long-run to produce Qo given the change in the wage rate, also explain your answer. [6 marks]



Q.2 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. [4 marks]

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? [6 marks]

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)? [4 marks]

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? [4 marks]