ECON 1B03 Lecture Notes - Lecture 6: Average Cost, Average Variable Cost, Fixed Cost

Q1) Soundscape Enterprises manufactures Sonoblast, a device that produces a high-pitched reminder to telemarketers that they have once again disturbed you just when you were sitting 1⁄2 down to dinner. The production function for Sonoblasts is given by the formula Q = 2KL where Q is in units of output per period, K is in machine-weeks per period, and L is in labour- weeks per period. The machine rental rate r is $512 per machine-week and the wage rate w is $128 per labour-week. In the short run, K is fixed at 4 machine-weeks per period.

a. Give the formulas for the short-run production function and the marginal product of labour (MPL) function.

b. Express variable cost (VC), total cost (TC), and marginal cost (MC) as functions of L and as functions of Q; and average variable cost (AVC), average fixed cost (AFC) and average total cost (ATC) as functions of Q.

c. At what level of Q is ATC minimized? What are the values of ATC and of MC at this level of output?

d. If K is increased to a fixed 16 units, at what level of Q is ATC minimized, and what are the values of ATC and of MC at this level of output?

e. In the long run, with all inputs variable, what is the optimal K/L ration with input prices unchanged? How many units of L and of K would be required to produce the levels of output in 1c and in 1d and what is the average cost of producing Sonoblasts in each case? Explain the relation between your results here and those for 1c and 1d.

Q1. Average total cost is equal to
a. AFC + AVC
b. AFC/total output
c. AFC/AVC
d. AVC/AFC

Q2. As output increases, the ATC
a. increases
b. decreases
c. remains constant
d. falls and then rises

Q3. Total profit is equal to
a. total revenue minus total cost
b. total revenue minus explicit cost
c. total revenue minus variable cost
d. total revenue minus marginal cost

Q4. Marginal cost crosses the
a. AVC curve at the highest point of the AVC curve
b. ATC curve at the lowest point of the ATC curve
c. AFC curve at the lowest point of the AFC curve
d. ATC curve at the highest point of the ATC curve

Q5. Wages paid are an example of an explicit cost of doing business.
a. true
b. false

Q6. Any revenue over and above total cost is labeled economic profit.
a. true
b. false

Q7. If the selling price of a product is $10, the average total cost is $8, and total sales are 5,000 units, the total profit will be
a. $5,000
b. $8,000
c. $10,000
d. $20,000

Q8. Whenever marginal revenue exceeds marginal cost,
a. profit declines if output increases
b. profit increases if output increases
c. losses increase if output increases
d. marginal revenue must be rising

Q9. Under perfectly competitive conditions, marginal revenue is
a. greater than average revenue
b. equal to average revenue
c. less than average revenue
d. equal to the average variable

Q10. A firm's break-even point occurs where
a. marginal revenue equals marginal cost
b. marginal revenue equals average variable cost
c. total revenue equals total cost
d. total revenue equals total variable cost

Q11. The addition to total output resulting from using one more unit of a productive resource is the
a. average product
b. marginal input
c. total product
d. marginal product

Q12. Unlike a firm in pure competition, a monopolist may be able to
a. block the entry of new firms into the industry
b. continue to earn economic profits in the long run
c. earn economic profits in the short run
d. both (a) and (b)

Q13. Producer surplus is the difference between the price the firm is willing to sell its goods and the price it actually receives.
a. true
b. false

Q14. In the long run, under conditions of perfect competition, market forces come into play to
a. enhance profits
b. increase demand
c. eliminate profits
d. separate MR and AR

Q15. Consumer surplus is the area above the demand curve and below the equilibrium price.
a. true
b. false

Q16. Under perfect competition, market price is determined by market demand and supply.
a. true
b. false

Q17. The more that firms advertise, the closer they get to perfect competition.
a. true
b. false

Q18. Perfect competition assumes that a producer is interested in maximizing profit.
a. true
b. false

Q19. In the long run, under conditions of perfect competition, the buyer will eventually be able to buy the product at a
a. price equal to the lowest point on the ATC curve past the optimal scale of operation
b. price below cost
c. price equal to the lowest point on the ATC curve at the optimal scale of operation
d. discount

Q20. The lowest possible ATC curve is attained at the optimal scale of output.
a. true
b. false

3. A firm has a long-run production function:   

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run? 

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?