*GOOD LUCK ON YOUR FINAL!*

Many products are subject to indirect taxation imposed by the government. Good examples include the excise duty on cigarettes (cigarette taxes in the UK are among the highest in Europe) alcohol and fuels. Here we consider the effects of indirect taxes on a producers costs and the importance of price elasticity of demand in determining the effects of a tax on market price and quantity.

A tax increases the costs of a business causing an inward shift in the supply curve. The vertical distance between the pre-tax and the post-tax supply curve shows the tax per unit. With an indirect tax, the supplier may be able to pass on some or all of this tax onto the consumer through a higher price. This is known as **shifting the burden of the tax** and the ability of businesses to do this depends on the price elasticity of demand and supply.

Consider the two charts above. In the left hand diagram, the demand curve is drawn as price elastic. The producer must absorb the majority of the tax itself (i.e. accept a lower profit margin on each unit sold). When demand is elastic, the effect of a tax is still to raise the price – but we see a bigger fall in equilibrium quantity. Output has fallen from Q to Q1 due to a contraction in demand. In the right hand diagram, demand is drawn as price inelastic (i.e. Ped <1 over most of the range of this demand curve) and therefore the producer is able to pass on most of the tax to the consumer through a higher price without losing too much in the way of sales. The price rises from P1 to P2 – but a large rise in price leads only to a small contraction in demand from Q1 to Q2.

**Graphical Analysis of Tax Incidence:**

Because the consumer is inelastic, he will demand the same quantity no matter what the price. Because the producer is elastic, the producer is very sensitive to price. A small drop in price leads to a large drop in the quantity produced. The imposition of the tax causes the market price to increase from *P without tax* to *P with tax* and the quantity demanded to fall from *Q without tax* to *Q with tax*. Because the consumer is inelastic, the quantity doesn’t change much. Because the consumer is inelastic and the producer is elastic, the price changes dramatically. The change in price is very large. The producer is able to pass (in the short run) almost the entire value of the tax onto the consumer. Even though the tax is being collected from the producer the consumer is bearing the tax burden. The tax incidence is falling on the consumer, known as *forward shifting*.

Most markets fall between these two extremes, and ultimately the incidence of tax is shared between producers and consumers in varying proportions. In this example, the consumers pay more than the producers, but not all of the tax. The area paid by consumers is obvious as the change in equilibrium price (between *P without tax* to*P with tax*); the remainder, being the difference between the new price and the cost of production at that quantity, is paid by the producers.

Price of input1(Price of substitute) | SE vs OE | Demand for input2 |

increase | SE > OE | increase |

increase | SE < OE | decrease |

decrease | SE > OE | decrease |

decrease | SE < OE | increase |

where SE is substitution effect, OE is output effect.

Let’s show the given conclusions graphically.

Isocost curves 1 and 3 represent all combinations of factors of production (input 1 and input 2) which in a sum cost C1 and C2 (not depicted on the graph) respectively. Isoquant curves 2 and 4 depict technological limits of the firm – all combinations of input 1 and input 2 that give equal total output Y1 and Y2 (not depicted on the graph) respectively.

An increase in the price of input 1 shifts isocost 1 into isocost 3. The dotted isocost is parallel to isocost 3 and tangent to the isoquant 2. There is new resource allocation and substitution effect in this case equals SE, where “substitution” is movement along isoquant 2 from the point (I1_1,I2_1) to the point x. Output effect OE depends on tangency point of new isoquant 4 to isocost 3. Thus in the upper graph (img 1) we can see that if OE > SE then demand for input 2 decreases from I2_1 to I2_2. Similarly if OE < SE (img 2) then demand for input 2 increases.

]]>Click the link above to access an explanation of cost minimization.

Let y – firm’s output, TC(y) – total cost, ATC(y)= TC(y)/y – average total cost. Given TC = VC+FC – the sum of fixed and variable cost. And, it must be borne in mind – the short run differs from the long run by the presence of the fixed cost, because all inputs are variable in the long run.

MC(y) = dTC(y)/dy .

The reason that MC intersects ATC and AVC in their minimums is that whatever MC curve below ATC and AVC curves, the latter will decrease (because MC – T additional cost and if MC is less then prior average cost so AC decrease), and vice versa, as long as MC curve exceeds ATC and AVC, the latter will increase.

Formal derivation:

MC(y) = dTC(y)/dy, ATC(y) = TC(y)/y – let’s find a minimum point. We equate the derivative to zero.

(ATC(y))’ = d(ATC(y))/dy = d(TC(y)/y)/dy = (y* MC(y) – TC(y) )/y^2 = 0

y^2 > 0, hence, y* MC(y) – TC(y) = 0, therefore

MC(y) = ATC(y) in the ATC minimum point (minimum, because in this point (ATC)’ < 0 under the condition MC < ATC, and under MC > ATC (ATC)’ > 0).

The case with AVC is similar, because d(TC(y)-FC)/dy = MC(y) too.

]]>Click the link above to access an explanation of Firms and Technology, including information on Special Isoquants.

*Isoquants show the locus of input combinations for which output is constant.*

*Isoquants cannot cross.*

*Marginal rate of substitution which measures the slope of an isoquant.*

*The isoquants for perfect substitutes are parallel straight lines.*

*The isoquants for perfect complements are in the form of an L.*

*The technology has increasing, constant or decreasing returns to scale depending upon whether, when we increase the scale of inputs by s, the output goes up by more, the same or less than this scale factor s.*

The expression for the *marginal rate of substitution, *that is, the slope of an isoquant, is given by:

*f(q**1**, q**2**) = constant*

If we take the total derivative of this expression we get:

*[∂f(q**1**, q**2**)/∂q**1**]dq**1 **+ [∂f(q**1**, q**2**)/∂q**2**]dq**2 **= 0*

**The Firm’s Supply Curve from Marginal Cost:**

**Industry Supply Curves and the Role of Entry and Exit:**

**Relating Short Run and Long Run Cost curves:**

**Consumer and Producer Supply:**

Be sure to check out Professor Dunz’s notes on **Uncertainty** posted on Blackboard!!

Click the link above to access a Powerpoint on the **Choice Under Uncertainty Theory**

The following link include notes on **Uncertainty**

Provided by the University of New York

Uncertainty (Page 106)

**Expected Utility Model:**

Click the Link above to access a Powerpoint on the **Two-Period Consumption Model**

The following links include additional notes and outlines on **Intertemporal Budget Constraints** and the **Consumption-Savings Models:**

**Choice Over Time**; (Page 85)

]]>

Click the link above to access examples on the **Labor Supply Model**

**Labor Supply Theory:**

**Substitution and Income Effects on the Backward Bending Supply Curve of Labour:**

**Quasilinear Utility and Demand:**

Click the link above to access an outline on Consumer Welfare.

Includes Effects of Government Policy on Consumer Welfare!

**Deriving Demand from Utility:**

**Income and Substitution Effects:**

**Demand Derived from Substituion Effect:**

**The Slutsky Equation and Demand Curves:**

**Compensating Variation and Equivalent Variation:**

]]>