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14 Pages

ARE 100A4

Course: ARE 100A, Spring 2008
School: UC Davis
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Word Count: 1108

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TC a. 2. 3. = TVC+TFC aka TC= VC+FC a. TC=wL+rK b. Q= f(L,K) i. AVC=TVC/Q ii. AFC= TFC/Q iii. ATC= AVC+AFC c. MC= dTVC/dQ = dTC/dQ d are deltas i. TC= TVC+TFC ii. DTFC/dQ= 0 d. Ex. rent an apartment for \$500/month e. Rent a hotel for \$100/night. 4. Consider: AFC = TFC/Q a. ATC AVC+AFC i. As Q increase AFC goes to ii. As Q increase AVC goes to ATC iii. b. 5. Now some special cases a. 6. Review: we just...

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TC a. 2. 3. = TVC+TFC aka TC= VC+FC a. TC=wL+rK b. Q= f(L,K) i. AVC=TVC/Q ii. AFC= TFC/Q iii. ATC= AVC+AFC c. MC= dTVC/dQ = dTC/dQ d are deltas i. TC= TVC+TFC ii. DTFC/dQ= 0 d. Ex. rent an apartment for \$500/month e. Rent a hotel for \$100/night. 4. Consider: AFC = TFC/Q a. ATC AVC+AFC i. As Q increase AFC goes to ii. As Q increase AVC goes to ATC iii. b. 5. Now some special cases a. 6. Review: we just completes SR production and costs w/general 3 stage a. 7. Next, Long run costs and long run production a. We introduce and isocost is the same cost at any point on the line, marginal benefit of MRT vs marginal cost on the market b. c. TC = wL+rK d. Draw the line by isolating K i. rK= tc- wL ii. K = TC/r W/r *L 1. w/r *L is the slope or the relative labor price iii. Examine w/r = \$/unit of labor / \$/unit capital = units K /units L 1. if the firm purchases 1 unit of labor, then it must forego some units of capital. iv. e. Isocost example i. Suppose W = 10, r= 2 ii. TC = 10L + 2K iii. K = TC/2 5L iv. f. in the market, w/r = Pl/PK g. MRTSlk = w/r i. h. recall that MRTSlk = MPL/MPK this is a definition i. MRTSlk = w/r only at equilibrium, not a definition ii. Restate: MPL/MPK = w/r WPL/w = MPK/r 1. MPL/w how productive last unit of labor you hired is 2. MPK/r is how productive the last unit of capital you bought is Per dollar a. When these two are equal, product is maximized. b. If one is less than the other, you spend more on the other to get more productivity. 8. Midterm 2 is on: a. Ch 6 all b. Ch 7 not econ of scale, not scope, not learning curve i. Long run equilibrium ii. Consumer problem iii. Same format of MT1 9. Numeric example aobout LR equilibrium about isocost and isoquants a. Change in demand b. Change in price of inputs c. SR adjustments d. Back to LR 10. Ex. can do legrange but in general: a. We assume: the firm wants to minimize input costs to meet a fixed demand for product b. Must product 100, we have input costs lamda 11. Change of thought: note: a. Compare i. Max Utility U = f(q1, q2) ii. So P1q1 +p2q2 = I iii. This is not on the exam iv. I is the contraint 1. but you choose values of q1 and q2 to maximize your utility 2. v. Min LK TC = wL+ rk vi. Subject to q = f(LK) = q fixed 1. note, we want to push the isocost to the origin, unlike the budjet line 2. the constraint is q fixed, the curly line, and the iso costs straight lines are moved to meet Q 3. b. Suppose firm want sot minimize TC = 5L + 10K i. ST q = 6LK= 100 ii. We need 2 things 1. need MRTSlk = w/r a. Be careful if you have a linear production function it will be a corner solution 2. must satisfy constraint: that q= 100 iii. the rest of the problem is simply algebra 1. MRTSlk = MPL/MPK 2. MPL = 6K 3. MPK = 6L a. MRTSlk = K/L b. Is it diminishing: yes because as L gets bigger, K gets smaller and MRTS diminishes 4. W/R = 5/10 = 5. THEN PUT IT ALL TOGETHER: = MRTS w/r a. K/L = b. L= 2K iv. From above we know L = 2K KNOW THIS PROBLEM W/EXPONENTS, remember to distribute it to everything in the parenthasis 1. q = 100 = 6(2K)K 2. K^2 = 8.33 3. K* = 2.9 L* = 5.8 4. v. From MRTSlk = W/r 1. we can also write MPl / w = MPK /r a. MPL = 6K b. MPK = 6L c. So: i. 6K/w = 6L/r ii. 6(2.9)/ \$5 = 6 (5.8) / \$10 iii. = 3.48 iv. this means that the last dollar you spent on labor and capital yielded 3.48. 1. capital is more productive but its more expensive, if you didnt have to pay, youd use more capital, but the highest return per dollar spent is here at 3. 48 d. Suppose MPL/ w < MPk/ r i. You would use CAPITAL bc it has a bigger return per dollar. ii. But as you use more capital, you have diminishing marginal productivity iii. As you use more capital, itll equal out to MPL. 12. Midterm 2 on Friday a. Ch 6 all b. Ch 7 through Mondays lecture, todays lecture is not exam material c. Hw 5 and 6 only. No hw 4. d. SR LR production, SR LR costs. 13. non MT 2 material : a. Long run Average total costs concepts where all inputs are variable i. Economies of scale ii. learning curve iii. economies of scope b. recall i. SR average costs and marginal costs ii. 14. Economies of scale a. As Q increases then ATC decreases but here we are also assuming that the scale of operations increases Ie K increases (bigger factory) b. In the SR in stage one, you can increases q and ATC will fall, but thats just increase in productivity due to specialization, this is not what were looking at. c. d. If you build a Costco in a town if 3 people, even though it is a bigger more efficient store, there is a demand issue, even though its less efficient. i. There is a huge waste of money bc of the capital investment is not met by demand. ii. Build a plant sized to meet demand e. If the population of riverside increases to 100 people, you can increase labor initially, then you can move (but dont forget that moving also is costly) f. In davis i. There is a regulation to limit grocery stores to 35k sq ft. ii. That regulation adds to the cost of buying groceries, so you go somewhere else aka Costco in woodland. If there was a Costco in davis, shopping would be cheaper bc Costco is more efficient. iii. 15. Learning curve. a. Aka learning by doing. i. Dynamic learning b. NOTE: Q is the amount q produced at a single point in time. i. Cq is cumulative Q aka the running total of all Q that the firm has produced. 1. there is a time component ii. ex. pharmaceuticals and high tech 1. often times, increasing production from the lab mass production can be tricky 2. vs making bread, there is no learning curve, weve been doing forever 3. for a drug, the recipe, there is a trial and error, early unit costs can be very high bc sometimes the drugs dont work every time. c. Two ways to examine the learning curve. i. ii. Another way to look at this: 1.
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UC Davis - ARE - 100B
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UC Davis - ARE - 157
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UC Davis - ARE - 157
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