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Unformatted text preview: S. Nageeb Ali April 15, 2008 Long Run
Develop concept of isocost line Similar to budget line from consumer theory
Tangency of indiff curve and budget line = optimal for consumer Tangency of isoquant and isocost line = optimal for producer Important conditions: L and K are interior
MRTS is decreasing in L: May be easiest to check MPL is decreasing in L MPK is decreasing in K Today
Do some more examples Finish Chapter 7 Midterm
April 22, in class Relevant Material from Chapter 6
6.1 6.5, except p. 188-9 (Elasticity of Substitution) Relevant Material from Chapter 7
7.1 7.4 (except p. 212-213, 229, 236-237). Problem Sets
PS#1 and solutions posted PS#2 posted Very important for midterm Special Review: Friday, CENT 105 from 6:00pm-7:50pm ! " f(L,K) = 3K1/3L2/3, w = 1, r = 32
Does the production function have diminishing MRTS? What is the relationship between optimal choices of L and K? To produce q units, how much capital and labor are required (what is the expansion path)? What is C(q)?
How much does it cost to produce 100 units? Suppose r decreases from 32 to 4: how does this affect input choices, and what is C(q) now? # $ $ %& & ' & & (!) * Suppose f(L,K) = (L2 + K2)1/2, w = 1, r = 2 Could look at tangency, but this will give exactly the wrong answer. +! " , + Recall that a production function is CRS if f( L, K) = f(L,K) Let q = 1 and C(q) = C(1) = C* = wL* + rK*. Then for every q, C(q) = qC*.
If you figure out cost for 1 unit, easy to figure out costs for more Costs are linear; MC(q) = AC(q) = C* for all q Main idea: one just scales up and down as necessary. +!
C(q) = wL + rK where L and K solve minL,K wL + rK subject to f(L,K) = q C(1) = C* = wL* + rK* means that for all other L, K where f(L,K) = 1, wL + rK C* +- / . . 0 +1
Pick q > 1: 1. Suppose C(q) > qC* 2. Suppose C(q) < qC* & $+ + & ! AC is U-shaped as one increases output
AC is downward sloping initially because AC is upward sloping eventually because
Hint: MC is going up because !+ $ $ # ' ! ! !+
AC in long-run different from AC in short-run
No fixed costs in long-run Not diminishing marginal returns since both inputs can be increased Action is from economies of scale
C(q) has economies of scale if AC(q) decreases as q increases C(q) has no economies of scale if AC(q) is constant as q increases C(q) has diseconomies of scale if AC(q) increases as q increases !
Returns to Scale Economies of Scale $ Returns to scale is about production, economies of scale about costs However, Returns to scale equivalent to economies of scale (book is WRONG!)
Increasing returns to scale Economies of Scale Constant returns to scale No Economies of Scale (shown earlier) Decreasing returns to scale Diseconomies of Scale Factors that drive scale effects ...
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- Spring '07