The local coffee shop serves 400 customers per day with 8 employees, 420 with 9 employees, 450 with 10 employees while it keeps its size same, such as a number of seats.
Producer Behavior
1. (Recall the assumptions of production) Following each part, determine which basic assumption of production is violated
a. The local coffee shop serves 400 customers per day with 8 employees, 420 with 9 employees, 450 with 10 employees while it keeps its size same, such as a number of seats.
b. The government makes the law very difficult for employers to hire new workers or fire existing workers. On the other hand, employers can instantly change the quantity of big, heavy equipment in each factory.
c. You have own bicycle factory which has a booming market. When you increase the number of employees from 40 to 45, your production falls from 500 bikes per month to 480.
2. Consider the production function given below: ???????? = 4???????? 0.5 ????????0.5
a. Find marginal product of labor and capital
b. From each marginal product, discuss whether it shows diminishing marginal product
c. Find Marginal rate of technical substitution of labor and capital (???????????????????????????????????????????????? )
3. (Cost minimization problem) Firm A produces video contents using digital editing equipment (????????) and employed editors (????????). The firm has the production function ???????? = 30???????? 0.67 ????????0.33, where ???????? is the hours of edited video. The wage for editor is $25, and the rental rate on editing equipment is %50. The firm wants to produce 3,000 units of output at the lowest possible cost.
a. Write out the firm’s constrained optimization problem.
b. Write the cost-minimization problem as a Lagrangian.
c. Use the Lagrangian to find the cost-minimizing quantities of capital and labor used to produce 3,000 units of output. d. What is the total cost of producing 3,000 units?
e. How will total costs change if the firm produces an additional unit of output?
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