I have a concussion and would really appreciate help with these problems so I do not fall behind in my classes. Thank you for your help and please show work!
1.Cable Cars Incorporated builds cable cars using workers and robotic arms. Their production function is given by Q = K + 0.5L, where L= workers and K= robotic arms. The wage of a worker is $50. The rental rate of each robotic arm is $90.
a) Suppose Cable Cars Inc. currently has 5 large robotic arms on hand. Cable Car Inc.’s robotic arm supplier indicates it will be at least another year before they are able to supply more. Given this information, if Cable Cars Inc. wants to produce 10 cars, how much will it cost them?
b) After the year has passed and Cable Cars Inc. is able to rent additional robotic arms, if they still want to produce 10 cars, how should they adjust their input mix? How will their costs of producing 10 cable cars change?
c) Using an isoquant and isocost line with K on the y-axis and L on the x-axis, illustrate your answer on the graph in part (b) and explain.
2. Phil and Bob run a paper company. Each week they need to produce 4,000 reams of paper to ship to their customers. The paper plant’s long-run production function is Q= 2K 0.25 L 0.75, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The rental rate of capital is $5 and the price of labor is $10.
a) What ratio of capital to labor minimizes Phil and Bob’s total costs?
b) How much capital and labor will Phil and Bob need to rent and hire in order to produce 4,000 reams of paper each week?
c) How much will hiring these inputs cost them?
3. Suppose a firm’s total cost is given by TC = 180 + 5Q + 5Q2. Its marginal cost is $105. Determine the following:
a) What quantity is this firm producing?
b) At this quantity (in a), what is this firm’s average variable cost?
c) At this quantity (in a), what is this firm’s fixed cost?
d) At this quantity (in a), what is this firm’s total cost?