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ECS2731 2019 S2 Tutorial 5 Questions

ECS2731_2019_Tutorial 5_Questions
1. A firm has determined that its variable costs are given by the following relationship:
VC =0.05Q3-5Q2 + 500Q; where Q is the quantity of output produced.
a. Determine the output level where average variable costs are minimized.
b. Derive an equation for the firm’s marginal cost function
c. Determine the output level where marginal costs are minimized.
2. The St. Thomas Winery plans to open a new production facility in the Napa Valley of
California. Based on information provided by the accounting department, the company
estimates fixed costs of $250,000 per year and average variable costs of
𝐴𝑉𝐶 = $10 + $0.01𝑄
where AVC is average variable cost (in dollars) and Q is output measured in cases of
output per year. Estimate total cost and average total cost for the coming year at a
projected volume of 4,000 cases.
3. Suppose Mining Company uses two inputs, capital and labour to mine ore. Various-sized
pieces of capital equipment, as measured by their brake horsepower rating K, are
available to mine ore. Assume that the rental cost of using the mining equipment per
period is $0.20 per brake horsepower; and that the wage rate plus fringe benefit cost of
each work (labour) employed per period is $50. Suppose the company signed a oneyear lease to rent a 750-brake –horsepower piece of mining equipment (capital).
a. What is the total cost function equation for any given combination of labour (L) and
Capital (K)?
b. What is the total cost function in the short run?
Tutorial Assignment (to be submitted for marking during Tutorial in Week 7)
Question P8.5 in your Prescribed Textbook