Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Student Number: QUIZ 4 Econ 212-Section B Question 1. [4 marks] Consider the short-run production function Q 50L 100K a) [2 mark] Derive the cost-minimizing quantity of labor as a function of output and capital. How does the cost-minimizing quantity of labor vary with Q ? with K ? Answer: Q 100K 50 It increases with Q and decreases with K bar. Q 50L 100K L b) [2 marks] Assume the price of labor is w and the rental rate of capital is r . Assume that K is variable now. Derive the long-run total cost function. Answer: Note that we have a production function in which inputs are perfect substitutes. Thus, given w and r , we can compare marginal product of Labour per dollar spent on labor 50 100 1 2 , with marginal product of capital per dollar spent on capital. So if w r w r then we use only labor to produce Q and the Labor demand function is Q wQ L , and K=0. Thus the total cost function is 50 50 If 50 100 1 2 Q rQ K and L 0 . And the total cost function is w r w r 100 100 Thus, in general we have a corner solution for choice of K or L. If we have interior 50 100 1 2 , we can use any combination of solution, it is indeterminate i.e. if w r w r Labour and capital that produces Q, including just using either capital or labor. 1 w =Price ratio. If this 2 r inequality holds, then use K to produce Q. If the inequality is in the other direction, only use L to produce Q . Alternatively, Absolute value of slope of isoquant 1 Question 2. [4 marks] Dave and Carolyn run a landscaping company. They employ people and rent equipment to dig holes for tree planting. They rent power auger machines, which need two people to run each machine. The production function can be written as Q min 10K ,5L . Dave and Carolyn pay their workers $10 per hour. The machines rent for $20 per hour. Dave and Carolyn need to dig 500 holes by the end of the week. a) [2 marks] In order to minimize their costs for this level of output, how many labor hours should they hire? How many machine hours should they rent? Answer: 500 min 10 K ,5 L 10 K 500 K 50 5 L 500 L 100 b) [2 marks] What is the total cost of digging the 500 holes? Answer: Total cost = 100 w + 50 r = 2000 Question 3. [2 marks] Identify the returns to scale (increasing, constant, or decreasing) for the following production functions. a) [1 mark] Q 2 * min K ,2L Answer: It is constant returns to scale. b) [1 mark] Q 5 K 0.25L0.5 Answer: It is decreasing returns to scale. 2