McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 9: Production and Cost in the Long Run

Managerial Economics 9-2 Optimal Combination of Inputs Implies marginal product per dollar spent on last unit of each input is the same Dr. Chen’s notes: It is similar to “Consumer Equilibrium” in CH 5. The marginal product per dollar denotes the extra output generated by the input which is purchased by one dollar. For example, given MP L =10 and w=$5, if the firm spends $1 on hiring labor, the additional labor can provide MP L /w=10/5=2 extra units of output.

Managerial Economics 9-3 Optimization & Cost Expansion path gives the efficient (least-cost) input combinations for every level of output Derived for a specific set of input prices Along expansion path, input-price ratio is constant Dr. Chen’s notes: If MP L /w > MP K /r, it implies that the labor is relatively productive compared with capital; that is, your $1 should be spent on labor rather than capital to get more units of output. When the firm keeps doing so, the law of diminishing returns will work (i.e. MP L declines with more hired labor). Finally, MP L /w =MP K /r is achieved.

Managerial Economics 9-4 Returns to Scale If all inputs are increased by a factor of c & output goes up by a factor of z then, in general, a producer experiences: Increasing returns to scale if z > c; output goes up proportionately more than the increase in input usage Decreasing returns to scale if z < c; output goes up proportionately less than the increase in input usage Constant returns to scale if z = c; output goes up by the same proportion as the increase in input usage f(cL, cK) = zQ Dr. Chen’s notes: Examples on the next slide will help you to understand returns to scale. Firms prefer increasing returns to scale because the unit cost will decline with a greater output rate.

Managerial Economics 9-5 Returns to Scale Increasing returns to scale: f(L, K)=L*K  When L=1, K=1, f(1,1)=1*1=1  When L=2, K=2, f(2,2)=2*2=4 Output goes up proportionately more than the increase in input usage Decreasing returns to scale: f(L,K)=L 0.2 K 0.2  When L=1, K=1, f(1,1)=1  When L=2, K=2, f(2,2)=1.32 Output goes up proportionately less than the increase in input usage Constant returns to scale: f(L, K)=L+K  When L=1, K=1, f(1,1)=1+1=2  When L=2, K=2, f(2,2)=2+2=4 Output goes up by the same proportion as the increase in input usage

Managerial Economics 9-6 Long-Run Costs Long-run average cost (LAC) measures the cost per unit of output when production can be adjusted so that the optimal amount of each input is employed LAC is U-shaped Falling LAC indicates economies of scale Rising LAC indicates diseconomies of scale Dr. Chen’s notes: Please check Figure 9.16 (on the last slide). A falling LAC (economies of scale) implies increasing returns to scale. The unit cost declines with output rate. When a firm is at this stage, production expansion will be profitable by lowering the unit costs. When a firm enters the stage of diseconomies of scale, it might cut the scale (downsize) to maintain the lower unit costs.

Managerial Economics 9-7 Long-Run Costs Long-run marginal cost (LMC) measures the rate of change in long-run total cost as output changes along expansion path LMC is U-shaped LMC lies below LAC when LAC is falling LMC lies above LAC when LAC is rising LMC = LAC at the minimum value of LAC Dr. Chen’s notes: The relationship is similar to SMC vs. ATC in CH 8.

Managerial Economics 9-8 Derivation of a Long-Run Cost Schedule (Table 9.1) Least-cost combination of OutputLabor (units) Capital (units) Total cost (w = $5, r = $10) LAC LMC LMC $ $ $

Managerial Economics 9-9 Long-Run Total, Average, & Marginal Cost (Figure 9.8)

Managerial Economics 9-10 Long-Run Average & Marginal Cost Curves (Figure 9.9)

Managerial Economics 9-11 Various Shapes of LAC (Figure 9.13)

Managerial Economics 9-12 Economies of Scope Exist for a multi-product firm when the joint cost of producing two or more goods is less than the sum of the separate costs of producing the two goods For two goods, X & Y, economies of scope exist when: C(X, Y) < C(X) + C(Y) Diseconomies of scope exist when: C(X, Y) > C(X) + C(Y) Dr. Chen’s notes: The best example to illustrate the economies of scope is electric power cogeneration. Many oil refinery plants apply the exhausted heat to generate power. The total costs of both refinery products and power generation are less than the sum of the separate costs.

Managerial Economics 9-13 Relations Between Short-Run & Long-Run Costs LMC intersects LAC when the latter is at its minimum point At each output where a particular ATC is tangent to LAC, the relevant SMC = LMC For all ATC curves, point of tangency with LAC is at an output less (greater) than the output of minimum ATC if the tangency is at an output less (greater) than that associated with minimum LAC Dr. Chen’s notes: Remember, all LR results come from SR experiments. The LAC curve consists of the lower boundary or envelope of all the SR average total cost curves. In other words, given the output level, the firm will choose the optimal plant size to produce the product at the lowest unit cost in SR. The LAC is the combination of SR decisions at different output levels.

Managerial Economics 9-14 Long-Run Average Cost as the Planning Horizon (Figure 9.16)