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.
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.
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.
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?