This problem deals with the effects of taxation. Suppose that the market demand

Question

This problem deals with the effects of taxation. Suppose that the market demand curve for a good is given by P 100 Q and that the market supply curve is given by P = 10 + Q. On a piece of paper, graph these curves. a) Set the P values equal using the above formulas, and solve for Q to find the equilibrium quantity, at which the supply and demand curves intersect. The equilibrium quantity is given by Q = 45 Substitute this value backinto the demand unction to nd the e num price, which is given by P55 b) Now suppose that a tax of $1 per unit is levied on each unit of output. As a result, the market supply curve shifts up by one unit. The curve is now given by P 11 Q. Repeating the steps of part (a), the new equilibrium quantity is Q44.5 and the equilibrium price is P 55.5 include one digit following the decimal point). Comparing the P value to that from part (a), the $1 tax has led to a price increase 5 cents. Illustrate this outcome in your diagram c) Suppose instead that the market demand curve is given by P 100-3Q. This curve is O A. flatter O B. steeper than the curve from part (a). Assuming that no tax is present, so that the supply curve is once again P 10Q, compute the equilibrium quantity and price in the market. These values are given by Q = and P = (include one digit following the decimal point) d) Now reimpose the $1 tax, so that the supply curve is P = 11 + Q. The new equilibrium quantity and price values are Q-L and P- (include two digits following the decimal point). In this case, the $1 tax has led to a price increase ofcents e) Based on the above answers, you can conclude that, when demand is less price sensitive (when the demand curve is steeper and thus more inelastic), the share of a tax passed on to consumers in the form of a higher price is O A. smaller O B. greater

Explanation / Answer

c) Steeper. Just plugging the values Q= 0,10,20 .. will give a graph through which we can know that the graph gets steeper when P = 100 - 3Q.

Calculating the equilibrium price and quantity, equate the supply and demand functions:

100 - 3Q = 10 + Q

=> 90 = 4Q  

=> Q = 22.5 the equilibrium quantity.

The equilibrium price is given by putting the value of Q in demand function, as

P = 100 - 3(22.5)

=> P = 32.5

d) The supply changes to P = 11+ Q hence the equilibrium quantity and price becomes :

100 - 3Q = 11 + Q

=> Q = 22.25 and thus P = 100 - 3(22.25) = 33.25.

Thus there is an increase of 75 cents.

e) greater as the increase in price is larger in case of steeper demand curve i.e when P = 100 - 3Q. which is 75 cents as compared to 55 cents in the other case.

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