Microeconomics II_PS 1_2011-1

Microeconomics II_PS 1_2011-1 - Microeconomics II Spring...

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Unformatted text preview: Microeconomics II Spring 2011 Problem Set 1 Suggested Solutions: Any queries can be emailed or discussed in the discussion session on Tuesday 1. In 1998, Americans smoked 23.5 billion packs of cigarettes. They paid an average retail price of $2 per pack. (Assume the market is perfectly competitive) a. Given that the elasticity of supply is 0.5 and the elasticity of demand is -0.4, derive linear demand and supply curves for cigarettes. Let the demand curve be of the general form Q=a+bP and the supply curve be of the general form Q=c+dP, where a, b, c, and d are the constants that you have to find from the information given above. To begin, recall the formula for the price elasticity of demand E P D = P Q ∆ Q ∆ P . You are given information about the value of the elasticity, P, and Q, which means that you can solve for the slope, which is b in the above formula for the demand curve. - 0.4 = 2 23.5 ∆ Q ∆ P ∆ Q ∆ P = - 0.4 23.5 2 = - 4.7 = b . To find the constant a, substitute for Q, P, and b into the above formula so that 23.5=a- 4.7*2 and a=32.9. The equation for demand is therefore Q=32.9-4.7P. To find the supply curve, recall the formula for the elasticity of supply and follow the same method as above: E P S = P Q ∆ Q ∆ P 0.5 = 2 23.5 ∆ Q ∆ P ∆ Q ∆ P = 0.5 23.5 2 = 5.875 = d . To find the constant c, substitute for Q, P, and d into the above formula so that 23.5=c+5.875*2 and c=11.75. The equation for supply is therefore Q=11.75+5.875P. b. A new tax was added of $0.15 in 2002. What will this increase do to the market-clearing price and quantity? First rewrite the equation for the supply curve as a function of Q instead of P: Q S = 11.75 + 5.875 P ⇒ P = Q S 5.875- 11.75 5.875 . The new supply curve is now P = Q S 5.875- 11.75 5.875 + .15 = 0.17 Q S- 1.85. To equate the new supply with the equation for demand, first rewrite demand as a function of Q instead of P: Q D = 32.9- 4.7 P ⇒ P = 7- .21 Q D . Now equate supply and demand and solve for the equilibrium quantity: 0.17 Q- 1.85 = 7- .21 Q ⇒ Q = 23.29. Plugging the equilibrium quantity into the equation for demand gives a market price of $2.11. c. How much of the tax will consumers pay? What part will producers pay? Since the price went up by, change in ‘P’ = 11 cents, consumers pay 11 of the 15 cents or (11/15) = 73% of the tax, and producers will pay the remaining 27% or 4 cents....
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Microeconomics II_PS 1_2011-1 - Microeconomics II Spring...

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