This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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=32.94.7P. 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 marketclearing 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....
View
Full Document
 Spring '11
 adam
 Economics, Microeconomics, Supply And Demand, producer

Click to edit the document details