Costs PDF

Costs  Chapter Preview nIn this chapter we will focus on: nHow firm chooses inputs it uses to produce a given output at lowest possible cost nHow firm’s production costs change as it changes the number and mix of inputs  Overview 1. Basic Cost Conc...

Costs  Chapter Preview nIn this chapter we will focus on: nHow firm chooses inputs it uses to produce a given output at lowest possible cost nHow firm’s production costs change as it changes the number and mix of inputs  Overview 1. Basic Cost Concepts 2. Economic Profits and Cost Minimization 3. Firm’s Expansion Path 4. Cost Curves 5. Short Run and Long Run  1. Basic Cost Concepts n Accounting cost: actual cost paid for inputs (out-of-pocket expenses, depreciation, and other bookkeeping entries) n Economic cost: amount required to keep an input in its present use or amount that input would be worth in its next best alternative use  1. Basic Cost Concepts n Labor costs ¨ Economists and accountants treat labor the same way ¨ Wage payments are explicit costs (current expenses) n Capital costs ¨ Accountant would use the historical cost of capital and some depreciation rule ¨ Economist treats cost of capital as a sunk cost ¨ Sunk cost is expenditure that once made can’t be recovered ¨ Implicit cost of capital is equal to its rental rate 2. Economic Profits and Cost Minimization n Two assumptions we will make: ¨ Two inputs: labor (L) and capital (K) ¨ Inputs are hired in perfectly competitive market n Total costs = TC = wL + rK n Economic profit = π = Total Revenues – Total Costs ¨ π = Pq – wL – rK ¨ π = Pf(K,L) – wL – rK n Firm’s economic profit depend only on the amount of labor and capital it hires  2. Cost Minimizing Input Choice n How does a firm produce a given output at the lowest possible cost? n We’ll look at this three ways: ¨ MRTS = w/r (2.1) ¨ Graphically, point where isoquant is tangent to total cost line (2.2) ¨ MPL/w = MPK/r (2.3) 2.1 Cost Minimizing Input Choice: MRTS = w/r n Suppose that to produce q units of output the firm uses 10 K and 10 L n Assume that MRTS = 2, w = $1 and r = $1 n What’s wrong? ¨ Total costs = $20 = 10 x $1 + 10 x $1 ¨ But MRTS = 2 ≠ w/v = 1 ¨ Since the MRTS = 2, the firm could replace two units of capital with one worker n So as long as MRTS ≠ w/r the firm can substitute one input for the other and reduce its costs 2.2 Cost Minimizing Input Choice: Graphical Approach Capital per week K* q TC1 TC2 TC3 L* Labor per week  2.3 Cost Minimizing Input Choice: MPL/w = MPK/r n From previous chapters we know that: ¨ MRTSL,K = MPL/MPK n We also know to minimize costs: ¨ MRTSL,K = w/r n Therefore: ¨ MPL/MPK = w/r ¨ MPL/w = MPK/r n To minimize costs the firm should get the same marginal contribution from each input  2.3 Cost Minimizing Input Choice: MPL/w = MPK/r n Suppose that the MPL/w > MPK/r. Why is the firm not minimizing costs? Should the firm hire more or less labor? more or less capital? n Firm is not minimizing costs since it is getting more output per dollar from labor than from capital n Therefore, it should use less capital and more labor  3. Firm’s Expansion Path n In order to expand output, the firm will want to hire more capital and more labor n Each time it increases output, it wants to use cost minimizing combination of K and L  3. Firm’s Expansion Path Capital n Expansion path is the set of cost- per week minimizing input combinations a firm will use to produce different levels of output n As output expands, input use and total costs rise q3 K1 q2 q1 L1 Labor per week  4. Cost Curves n What is the relationship between output and total costs? n Depends on the nature of production: constant, decreasing, increasing returns to scale  4. Constant Returns to Scale Total Cost TC As output expands, costs expand proportionally. Quantity per week  4. Decreasing Returns to Scale Total Cost TC Costs expand more rapidly than output Quantity per week  4. Increasing Returns to Scale Total Cost TC Costs expand less rapidly than output Quantity per week  4. Optimal Scale Total Cost TC Over lower levels of output there are increasing returns As output expands decreasing returns kicks in Quantity per week  4. Average and Marginal Costs n Average Cost is total cost divided by output "# %)*+,-*A#C'(A=A%#A=A ! n Marginal Cost is additional cost of producing one more unit ΔTC Marginal Cost = MC = Δq  4. Average and Marginal Costs n Imagine that we measure the average height of students in the classroom. Say there are three students in the room, and their heights are 165cm, 170cm, and 175 cm, for an average of 170. Now, a new student enters the classroom: this is the “marginal”, or additional student. If this student’s height is below the average (less than 170), the new average of all the students in the classroom will fall. For example, if the new student’s height is 166cm, the new average is 168cm. If the student’s height is above average, it pulls the average up. If she is exactly average (her height is 170) the average neither goes up nor goes down. n Hence, there is a general relation between average and marginal “anything” (product or cost)  4. Average and Marginal Costs n When the marginal is above the average, the average rises. n When the marginal is below the average, the average falls. n When the marginal equals the average, the average does not change. n If the average is falling, the marginal curve must lie somewhere below. n If the average is rising, the marginal must lie somewhere above. n ONLY place where the marginal can equal the average is where the average is neither rising nor falling: minimum point on a U-shaped curve. 4. Average and Marginal Cost Curves: Constant Returns AC, MC As output expands, MC and AC remain the same AC, MC Quantity per week 4. Average and Marginal Cost Curves: Decreasing Returns AC, MC MC AC As output expands, both MC and AC increase Quantity per week 4. Average and Marginal Cost Curves: Increasing Returns AC, MC As output expands, both MC and AC decrease MC AC Quantity per week 4. Average and Marginal Cost Curves: Optimal Scale AC, MC MC AC q* Quantity per week Also True for Average and Marginal Products!  5. The Short Run and the Long Run n Short run: period in which a firm must consider some inputs to be fixed n Long run: period in which a firm may consider all inputs to be variable n Fixed Costs: associated with inputs that are fixed in short run n Variable Costs: associated with inputs that can be varied in short run  5. Input Inflexibility and Cost Minimization n Will a firm always be able to use the cost minimizing combination of inputs in short run? n No. Capital is fixed in the short run so the firm may have to use non-optimal amounts of labor to produce some given output  5. Input Inflexibility and Cost Minimization Capital Suppose the amount of capital is fixed at K1 per week To produce q0 the firm would use L0 and face costs STC0 STC0 STC1 To produce q1 the firm would use L1 and face costs STC1 K1 q1 q0 L0 L1 Labor per week  Input Inflexibility and Cost Minimization Capital To produce q2 firm would use L2 and face per week costs STC2 STC0 STC1 STC2 K1 q2 q1 q0 L0 L1 L2 Labor per week  Input Inflexibility and Cost Minimization Capital For which output level is firm minimizing costs? per week q1: only at this point is MRTS equal to STC0 ratio of input prices STC1 STC2 K1 q2 q1 q0 L0 L1 L2 Labor per week  Shifts in Cost Curves n Three changes will affect the shape and position of a firm’s cost curves n Changes in input prices such as wages n Increase/decrease in input prices will cause the cost curves to shift up/down n Will depend on ability of the firm to substitute inputs  Shifts in Cost Curves n Three changes will affect the shape and position of a firm’s cost curves 1. Changes in input price 2. Technological innovation n Cost curves will shift down n Technological change may be “biased” 3. Economies of scope n Relates to multiproduct firms n Expansion of one product may improve the ability to produce another product  A Numerical Example n Back at Burger Queen ¨ TC = $5K + $5L ¨ q = 40 !"#$"#%C'(% )G+,-+K%CL(% 0+1OOK%C3(% 4G#5O%6GK#%C46(% !"# ##$# $%&"# '()&""# !"# ##*# ##(&"# ##)"&""# !"# ##+# ##)&+# ##!$&)"# !"# ##!# ##!&"# ##!"&""# !"# ##)# ##+&*# ##!$&""# !"# ##%# ##*&,# ##!+&)"# !"# ##,# ##*&+# ##!%&)"# !"# ##(# ##*&"# ##)"&""# !"# ##-# ##$&(# ##)!&""# !"# $"# ##$&%# ##)(&""# #  A Numerical Example Capital per hour E 4 40 hamburgers per hour Total Cost = $40 4 Labor per hour  A Numerical Example Total Cost TC 80 60 40 20 20 40 60 80 Quantity per week  A Numerical Example n Suppose we now fix the number of grills to 4 )G+,-+K% M+1OOK% 4G#5O%SGK#% 89-+5W-% ;5+W1