ECON111 Tutorial 9 Week 10

Question 1.a Two firms have exactly the same MC curve, but their AFC is not the same. Will their AVC cost curve be the same or different? Their AVC cost will be the same because if they have the same MC curve, then they must have the same TC curve, with intercept zero and slope equals MC. Will their ATC curve be the same or different? Their ATC will be different because ATC = AFC + AVC and we don’t know whether their AFC is not the same.

Question 1.b What shape does the AFC curve take? Cost TFC TVC TC AFC AVC ATC MC $200 $0   - 2 200 100 300 50 150 $50.00 5 400 40 80 33.33 9 500 22.222 33.333 55.556 25 12 600 16.667 14 700 14.286 35.714 15 800 13.333 53.333 Cost TFCs do not vary with Q Hence, as Q increases AFC = TFC/Q falls continuously and approaches the horizontal axis as Q expands. Q

Question 1.b Why do the AVC and MC curves maintain a set relationship to each other? AVC = TVC/Q MC = ∆TC/∆Q = ∆TVC/∆Q MC and AVC are both derive from TVC, hence they are related to each other.

Question 1.c Explain why the MC curve must intersect the ATC and the AVC curves at their minimum point?

ATC, AVC and MC When MC is above AVC and ATC, AVC and ATC is increasing When MC is below AVC (ATC), the AVC and ATC is falling When MC = AVC (ATC), AVC (ATC) is at its minimum. $150 125 100 75 50 25 Cost ($) MC ATC AVC 5 10 15 Q

Question 2.a How is the law of diminishing marginal returns related to the shape of the short-run marginal cost curve? According to that law, beyond some point the MP decreases as more of a variable factor is added to a fixed factor of production. As production increases, diminishing marginal returns for the variable production factors mean that each additional unit of output will require more of the variable factors, so marginal costs go up when diminishing returns set in.

Suppose capital is fixed and labour is the variable factor of production. Assuming the wage rate remains constant (new employees earn the same wage as existing employees), as marginal product increases, marginal cost falls. When the marginal product curve is at its maximum, the marginal cost curve is at a minimum. As diminishing returns set in and the marginal product curve falls, the marginal cost curve rises. Hence, the marginal cost curve is a u shape, which is inversely related to the marginal product curve.

Diminishing and Negative Units of the variable factor (Labor or L) TP (tons moved per day) MPL Return 1 2 3 4 5 6 7 8 9 12 14 15 - -1 ------ Increasing “ Diminishing Diminishing and Negative

TP and MPL 5 10 15 TP Total product 5 7 Labor 7 10 1 3 5 MPL 2 4 7 10 1 3 5 MPL 2 4 Increasing marginal returns Diminishing but positive marginal returns Marginal product Negative marginal returns Labor 5 10

MP = ∆Q/∆L MC = ∆ATC/ ∆Q = w.∆L/∆Q ∆Q = MP. ∆L ∆Q = w. ∆L/MC So, MP. ∆L = w. ∆L/MC There is an inverse relationship b/w MP and ML As MP increases, MC decreases As MP decreases, MC increases

MP and MC are mirror images of each other. Costs (dollars) Average product and marginal product When marginal product is increasing, marginal cost falls. When marginal product falls, marginal costs increase. MP and MC are mirror images of each other. MP Quantity of labor Quantity of output MC 12

Question 2.b Much discussion of productivity focuses on “output per worker”. Is this an average or a marginal productivity notion? Which of these concepts do you think is most relevant to a firm’s hiring decisions? Output per worker is an average notion. APP = Q/L Marginal productivity (ΔQ/ΔL) is most relevant to a firm’s hiring decisions because firms weigh up the additional benefits against the additional costs when deciding whether or not to hire an extra worker.

Question 3.c At a management luncheon, two managers were overheard arguing about the following statement: “A manager should never hire an extra worker if the new person causes diminishing returns”. Is this statement correct? If so, why? If not, explain why not. No – just because an extra worker may have lower marginal product that the last unit of labour hired, does not mean that the worker should not be hired. The decision to hire depends on marginal benefits and marginal costs. The value of marginal product is the marginal product (ΔQ/ΔL) multiplied by the price of output. A competitive profit maximising firm hires workers up to the point where the value of marginal product of labour equals the wage rate. Below this level of employment, the value of marginal product exceeds the wage, so hiring another worker would increase profit. Above this level of employment, the value of marginal product is less than the wage, so the marginal worker is

Question 3.a TC = TFC + TVC MC = ∆TC/∆Q ATC = TC/Q = AFC + AVC 20   1 21 1.00 2 24.00 4.00 12 10 3.00 3 32.00 12.00 10.667 6.667 4 8.00 48.00 28.00 5 7 16.00 75.00 55.00 15 11 27.00 6 116.00 96.00 19.33 3.33 16 41.00 174.02 154.02 24.86 2.86 22.00 58.02 8 260.02 240.02 32.50 2.50 30.0025 86.00 9 380.00 360.00 42.22 2.22 40 119.98 540.00 520.00 54 52 160.00 TC = TFC + TVC ATC = TC/Q = AFC + AVC AFC = TFC/Q AVC = TVC/Q MC = ∆TC/∆Q MC = ∆TFC/∆Q + ∆TVC/ ∆Q MC = ∆TVC/ ∆Q Note: ∆TFC/ ∆Q = 0

Question 3.b Explain the difference between MC and AC. MC vs. ATC ATC = TC/Q = TFC/Q + TVC/Q MC = ∆TC/∆Q = ∆TFC/∆Q + ∆TVC/∆Q Since ∆TFC = 0 MC = ∆TC/∆Q = ∆TVC/∆Q

Question 3.c Explain why short-run marginal cost is equal to the slope of both the total cost and total variable cost curves, and why can marginal cost be computed from either total variable cost or from total cost? Because fixed costs do not vary as output varies (ΔTFC/ΔQ = 0), MC can be calculated from either TC or TVC. The slope of the TC curve gives MC. Since TC = TVC+TFC where TFC is the constant fixed costs, the TVC curve is parallel to the TC curve and hence has the same slope. So MC can be calculated from either TC or TVC curve.

Question 3.c