Chapter 7 (7.1 – 7.4)

1. Chapter 7(7.1 – 7.4) • Firm’s costs of production: • Accounting costs: actual dollars spent on labor, rental price of bldg, etc. • Economic costs: includes accounting costs plus opportunity costs. • Opportunity costs include value of land already owned.

2. Costs of Production • Sunk costs: costs that have already been incurred and cannot be undone  should not be considered in current decision-making; cannot be recovered even if firm goes out of business. • Fixed costs = FC: costs that do not vary with output level; only way to avoid FC is to go out of business.

3. More on Costs • Total Cost = TC: • Total economic costs of production. • TC = FC + VC • FC = fixed costs: • Costs that do not vary as output changes. • VC = variable costs: • costs that do vary with output: • VC  as Q. • In the long run, all costs are VC.

4. Cost in the Short Run • Marginal cost = MC: extra costs from Q by one unit. = TC/Q = VC/Q • ATC (=AC) = average total cost AC = TC/Q : per-unit cost of production. = AFC + AVC where: AFC = avg fixed cost = FC/Q. AVC = avg variable cost = VC/Q. Note: since FC no  with Q, then as Q, AFC.

5. SR Cost • Remember: VC and TC  with Q  Rate at which these costs rise depends on nature of production process. I.e., how much diminishing returns to variable factors. • Diminishing Returns to Labor: occurs because in SR, L is only variable input so the MPL  as L at some point. • So: if MPL  as L, then must hire even more labor to keep Q by one unit. So VC and TC  with Q.

6. Further Details • Firm in competitive market: can hire all L it wants at going market wage = W. • Recall: MC = VC/Q ; but VC = W * L. • MC = (W*L)/Q • Recall that MPL = Q/L so: • MC = W/MPL. • MC = price of input divided by its marginal product: whenever MPL , MC  with  Q. • See Table 7.1 again: MC  for Q = 0 to 4; MC  for Q = 5 to 11. • Latter reflects diminishing marginal returns.

7. Shapes of Cost Curves • A) FC is flat: no  as Q es. • B) TC and VC have same shape; vertical distance between the two = FC. • C) AFC  as Q . • D) ATC and AVC get closer as Q because the distance between the two is AFC and it  as Q goes up. • E) MC is u-shaped. • MC = ATC at its minimum point. • MC = AVC at its minimum point. Recall: when marginal > average, the average is rising.

8. Exercise • Given SR cost function: • C = 190 + 53Q. • 1) What is FC? • 2) If Q = 10, what is AVC? • 3) What is its MC per unit produced? • 4) If Q=10, what is its AFC?

9. Costs in Long Run • User cost of capital: annual cost of owning and using a K asset • User cost of K = economic depreciation plus foregone interest. • Foregone interest = (interest rate)*(value of K) • Reflects financial return that could have been earned had the money been invested elsewhere. • Express user cost of K as a rate per dollar of K = r • where r = depreciation rate + interest rate. • This r is same whether K is purchased or rented.

10. Selecting K and L in Long Run • Firm’s cost-minimizing choice of K and L to produce a given output level. • Assumes firm has already chosen profit-maximizing level of output. • Assume two variable inputs are K and L and their prices are r and w. • Will need isocost line and isoquant curve.

11. Isocost Line • Isocost line: shows all possible K/L combos that can be purchased for a given TC. • TC = C = w*L + r*K ; • Rewrite as equation of a line: K = C/r – (w/r)*L Slope = K/L = -(w/r). • Interpret slope: * shows rate at which K and L can be traded off, keeping TC the same. • Relate to consumer’s budget constraint: * slope = ratio of prices with price from horizontal axis in numerator. Vertical intercept = C/r. Horizontal intercept = C/w.

12. Exercise • Draw and label each of the three following isocost lines, giving numbers for the slope and both intercepts in each case. Also write out the equation for each isocost line using the expression: k = c/r – (w/r)*L • (Note: all costs and factor prices are measured in dollars.) 1. C = 200, w = 20, and r = 40. 2. C = 300, w = 20, and r = 40. 3. C = 300, w = 30, and r = 40.

13. Tangency Point • Tangency point is cost-minimizing point to produce a given Q. • At tangency: isocost line slope = isoquant curve slope • Recall slope of isoquant: = MRTS = -K/L = MPL/MPK • So at tangency: MPL/MPK = w/r • Rewrite: MPL/w = MPK/r. • Interpret: • additional Q from spending extra 1$ on L is equal to the foregone Q from spending 1$ less on K. • Choose cost min K/L combo so that last $ worth of any input added to production process yields the same amount of extra output.

14. Example: Effluent Fee • Effect of effluent fee on input choice when Q does not change. • Effluent:a by-product of the production process (pollution). • Goal of fee: to “internalize” an external cost. • Simplistic example: two inputs are K and water used for dumping the waste. • Start: K=2000 and r = $40; • Water = 10,000 gallons; p = $10

15. More on Example • TC = $180,000 • Add up costs for K and water. • Slope of isocost = -Pwater/PK = 10/40 = -0.25. • Effluent fee = $10 per g water • So p water  $20 per g. • KEY: holding Q constant so stay on same isoquant. • See es in TC, K, and water. • See TC if had not responded to fee.

16. Two factors in result: • The more easily the firm can deal with the effluent without dumping it in the water (I.e., more ease of substitution between K and water): • 1) the more effective the fee will be in reducing effluent. • 2) the less the firm will have to pay.

17. Cost-Minimization when Output Can Change • See Figure 7.6: three different tangency points, coming from three different K/L combos for producing three different levels of output. • Connect cost-min points to get expansion path: describes K/L combos that firm will choose to minimize costs at each Q level. • If both K and L  as Q, expansion path will slope up. • Use expansion path to derive LR TC curve (straight due to constant RTS).

18. LR versus SR Costs • SR versus LR expansion path. • Shape of LAC and LMC: depends on relationship between scale of the firm’s operation and the inputs required for cost-minimization. • Constant RTS LAC is flat. And so LMC is flat too at same $ amount (if double inputs  double Q but also double costs).

19. Returns to Scale • Remember: term applies when input proportions do not change as output changes. • Constant RTS: double inputs (so double costs)  double output. • So AC is flat. • Increasing RTS: as double inputs (and so double costs)  more than double output. • This is special case of Economies of Scale. • So AC slopes downward.

20. Economies and Diseconomies of Scale • Term used when input proportions change as output changes. • Economies of Scale: Firm can double its output for less than double the cost. • Increasing RTS is special case. • Diseconomies of Scale: to double output requires more than double the cost. • U-shaped LAC: economies of scale at low q and diseconomies of scale at high q. • See Figure 7.8.

21. Exercise • Textbook Exercise #5, pg. 244. • Chair manufacturer: • W = 22; r = 110. • One chair can be produced with any combination of L and K that totals to 4 units. • Currently, firm is using L=3 with K=1. • Is this a cost-minimizing combination of K and L? • If not, what would be the cost-min combination?