Managerial Economics and Strategy 3rd Edition by Jeffrey M Perloff Solution manual

Q = 50 + 15p
Q = 50 + 15(2.0)
Q = 50 + 30
Q = 80 units.
         If a $0.55 tax is imposed, the demand curve can be rewritten to account for the tax. First, the demand curve can be rewritten as inverse demand by solving for p
Q = 160 − 40p
p = 4 − 0.025Q.
 
         The tax is subtracted from inverse demand to give
p = 3.45 − 0.025Q
and then this inverse demand curve can be turned back into a demand curve
Q = 138 − 40p.
 
Setting supply equal to demand, the new equilibrium (pretax) price is
D = S
138 − 40p = 50 + 15p
88 = 55p
p = $1.60.
         The after-tax price is $2.15. 
 
Using the supply function, the equilibrium quantity is
Q = 50 + 15p
Q = 50 + 15(1.60)
Q = 50 + 24
Q = 74 units.
5.7    a. If demand is vertical and supply is upward sloping, then all the tax burden is paid      by consumers because they are not price sensitive.
If demand is horizontal and supply is upward sloping, then all the tax burden is paid by producers because consumers are infinitely price sensitive.
If demand is downward sloping and supply is horizontal, then all the tax burden is paid by consumers because producers are infinitely price sensitive.
5.8    If instead of the tax being levied on producers it is collected from consumers, then the effect will be a decrease in demand. The demand curve will shift left until the vertical distance between the original demand curve and the new one is equal to the tax of $2.40. This new demand curve, call it D2, will intersect the original supply curve (S1) at a price of $5.60 and a quantity of 11.6. In addition to the price of $5.60 per bushel, buyers will also have to pay the $2.40 tax for a total, after-tax price of $8.00. The seller will receive the $5.60 per bushel, and the government will collect $27.84 billion in tax revenue (the $2.40 tax multiplied by the 11.6 billion bushels of corn traded in the new equilibrium).
 
This equilibrium is not the same as the case in Q&A 2.3 because in that problem the supply curve is perfectly elastic, while in this case it is not. In Q&A 2.3, the seller passes on the entire tax to consumers, while here, the tax is split with $0.80 being paid by consumers and $1.60 paid by producers.
5.9 A tax on consumers will undoubtedly shift the demand curve down by an amount equal to the size of the tax. The new equilibrium price and quantity with the tax will be where the new demand curve intersects the original supply curve. The decrease in quantity will be larger (and tax revenue smaller) the more horizontal the supply curve is. Just the opposite is true if the supply curve is more vertical—quantity effects will be small, and revenue generation from the tax will be large.
When to Use the Supply-and-Demand Model
6.1    The supply-and-demand model is accurate in perfectly competitive markets, which are markets in which all firms and consumers are price takers: no market participant can affect the market price. If there is only one seller of a good or service—a monopoly—that seller is a price taker and can affect the market price. Firms are also price setters in an oligopoly—a market with only a small number of firms. Experience has shown that the supply-and-demand model is reliable in a wide range of markets, such as those for agriculture, financial products, labor, construction, many services, real estate, wholesale trade, and retail trade.
 

 
Managerial Problem
7.1    A tax paid by consumers shifts the demand curve down by an amount equal to the size of the tax. Just the opposite, suspending a tax on consumers should raise the demand curve by an amount equal to the size of the suspended tax. Although fuel supply is more likely to be vertical in the short run than in the long run, equilibrium fuel prices will increase when the demand curve shifts up whether the supply curve is vertical or upward sloping.
 

 
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