Econ100B Lecture2 - 4-03

Econ100B Lecture2 - 4-03 - S. Nageeb Ali April 3, 2008...

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Unformatted text preview: S. Nageeb Ali April 3, 2008 Production function: Maximum that can be produced given inputs Short-run: Capital Fixed Marginal Product of Labor: Incremental change in production with additional unit of labor Slope of Production Function (wrt Labor) Relationship between MPL and APL Diminishing Marginal Returns: MPL <0 L Today Talk about long-run where capital and labor are both adjusted Develop concept of isoquant: similar to indifference curve Discuss Marginal Rate of Technical Substitution ! "# Now suppose that K and L are variable Provides greater flexibility Production function q = f(L, K) e.g., q = L0.5 K0.5 " $ Specifies possible combinations of inputs that will produce a fixed level of output q = f(L,K) Suppose q = L0.5K0.5; what are pts on the isoquant? " $ # %" $ Similar concept to indifference curves Indifference curves hold utility constant Isoquants hold production constant Farther isoquant is from origin, greater level of production Isoquants do not cross Isoquants slope downwards Isoquants are thin lines % # ! & % ' q = min {L, K} % At efficient point, # ! L= & K % ' q = min { L, K } K= L So slope of efficient line is / % ( K q= K+ L L Does this technology have diminishing marginal returns? ( !) * + ! & * ( ' % ! ( Slope of isoquant indicates how one input can be substituted for another MRTS indicates while holding output constant how many units of capital can be substituted by additional unit of labor * ( * ( Intuition Suppose MPL = 1, MPK = 1/4, and you were producing 6 units If you hire additional worker, Increases production by MPL = 1 So output goes up by 1 Have to decrease capital to keep output same Decrease one unit of capital, output goes down by MPK = 1/4 So have to decrease _ units of capital * (, )* * (% K % ( q= K+ L=1 L Can calculate slope using standard ways * (% K % ( q= K+ L=1 L MPK = , MPL = MRTS = / * (, -. + ! q = ALa Kb . +* ( Typically assume that |MRTS| is diminishing i.e., | MRTS |< 0 L This is equivalent to isoquants being convex * ( ( ! MP tells us what happens when one input is increased holding others fixed What if all inputs are increased in a proportional way? E.g., if you double the # of inputs, do you increase output by more than 2? (Increasing Returns to Scale) increase output by exactly 2? (Constant Returns to Scale) increase output by less than 2? (Decreasing Returns to Scale) ) + ( ! ( ! Suppose >1 Decreasing Returns to Scale: f( L, K) < f(L,K) Increasing Returns to Scale: f( L, K) > f(L,K) Constant Returns to Scale: f( L, K) > f(L,K) / # ! Suppose f( L, K) = a) x f(L,K), for all > 1. When would f have CRS? b) When would f have Decreasing RS? c) When would f have Incr. RS? . + ! / # ! Theory of Production Isoquants: Combination of inputs necessary to make a fixed level of output Slope of isoquant = Assume Diminishing MRTS Economies of Scale 0 / 1 Think about Costs (Perloff, Ch. 7) Profit maximization involves using right combo of inputs given their cost Problem Set 1 will be posted on WebCT tomorrow Monday and Wednesday sections begin next week ...
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This note was uploaded on 07/22/2008 for the course ECON 100B taught by Professor Rauch during the Spring '07 term at UCSD.

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