Lecture12 - Lecture #12 Short Run Cost Curves and Taxes...

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Lecture #12 Short Run Cost Curves and Taxes Let’s consider the effect of taxes on our short run cost curves. We will investigate two types of taxes in this analysis, a specific tax per unit on output and a lump sum tax. How do these two types of taxes enter our short run cost structure? 1. A specific tax per unit of output will enter our short run cost structure as a variable cost per unit. This will affect the ATC, AVC, and MC curves. To see this, let’s consider a specific unit tax of $11 per unit on good Y (levied on producers). Remember, the Average Total Cost (ATC) is the Average Variable Cost (AVC) PLUS the Average Fixed Cost (AFC). ATC a = AVC a + AFC b where a = ATC after tax AVC a = AVC after tax AFC b = AFC before tax
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Short Run Cost Curves and Taxes (continues) We need to notice the definitions of each of these measures We need to notice the definitions of each of these measures… ATC a = TVC b + 11 Y + TFC b YY and with some minor algebraic simplifications… a = TVC b + 11+ TFC b which is simply, a = AVC b + AFC b + 11 Now, remember that ATC b = AVC b + AFC b so… a = ATC b + 11 Marginal cost is simply the change in Total Variable Cost divided by the change in the quantity of Y or the slope of the TC curve quantity of Y, or the slope of the TC curve. MC a = ! TC a = ! TVC a + ! TFC a ! Y ! Y ! Y MFC (always = 0) Sinse Marginal Fixed cost does not change due to a specific tax per unit of output (i.e. MFC = 0 by definition) , we have…
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MC a = ! TVC a = ! (TVC b + 11 Y) ! Y ! Y and with some minor algebraic simplifications… MC a = ! TVC b + 11 ! Y ! Y ! Y Now, remember that MC b = ! TVC b so… ! Y MC a = MC b + 11 Graphically, we can now show how a specific tax of $11 per unit of Y affects the optimal quantity of Y that is produced. We can see that this type of tax displaces (shifts) the ATC curve and displaces (shifts) the ATC curve and the MC curve up (vertically) by the amount of the tax, for all output levels.
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Recall that the lowest point on the ATC curve is the point where the MC curve crosses it. Originally, this occurred at point e where the quantity was Q Y. After the tax was imposed, the point of intersection of the ATC and MC curves occurs at point f where the quantity is still Q This makes sense because the specific tax per unit of output has been shown to simply displace both the ATC curve and the MC curve parallel vertically by $11. This implies that a specific tax per unit of output does not influence the firm’s optimal quantity decisions. It does, however, affect their TC, ATC, AVC, and MC curves. This may have an adverse effect on the firm’s profits if they are unable to pass the cost of such a tax on to consumers through a price increase. 2. A lump sum tax will enter our short run cost structure as a fixed cost (one time expense). Let’s see how this affects our ATC, AFC, and MC curves.
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Lecture12 - Lecture #12 Short Run Cost Curves and Taxes...

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