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# 2 - Todays Outline Short-Run Costs Implications of...

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Today’s Outline: Short-Run Costs Implications of diminishing marginal returns to labor = MC wMPL = AVC wAPL Effects of per-unit taxes Slope of TC is ATC Short Run Costs: = + TC FC VC FC are capital costs and VC are labor costs = = MC dTCdq dVCdq = wdLdq o Because FC is constant o = FC rK and = VC wL o As q increases, the firm needs to hire more labor = MPL dqdL = 1MPL dqdL So = × = MC w dLdq wMPL At some point, diminishing marginal returns kicks in and L and q move in the same direction so MC is increasing If < dMPLdL 0 , this means we have diminishing marginal returns Some production functions do not have diminishing marginal returns = = = AVC VCq wLq wAPL o Use = APL qL and = 1APL Lq Costs are tied to production functions Effects of Per-Unit Taxes: Per-unit taxes can be written tq where t is per-unit tax and q is quantity Example: Before tax, the cost function is = Cq q2 and after the tax, the function is + = + Cq tq q2 tq . Write the cost function in terms of q. Before tax: = MC 2q After tax: = + MC 2q t Since = + TC FC VC , then = = MC dTCdq dVCdq since the only component in TC that is changing is VC Per-unit tax shifts MC up by an amount of the per-unit tax

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Long Run: Cost Minimization: Isocosts are like budget constraints Along isocosts, costs are fixed = + C wL rK Graph isocost by writing equation of K in terms of L o Rearrange to = + y mx b form o = - rK C wL o = - K Cr wrL Isocost lines are a set of straight parallel downward sloping lines with a slope of - wr (always linear) Same total cost along an isocost The closer to the origin, the lower the cost o o Cost Minimization: Graphically choosing lowest isocost Finding tangency point (only works with well-behaved production functions) Bang-for-the-buck condition/last dollar equivalence o o Like in utility, budget constraints, and indifference curves, best way to produce quantity is lowest cost, which is the tangency point o o Choose highest indifference curve Slope of isocost = - wr Slope of isoquant = - = MPLMPK MRTS o o At tangency point: - = wr - MPLMPK = MPLMPK wr
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