ch2_example2

ch2_example2 - 80 = a O + -0.064(500) 80 = b O + 0.24(500)...

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Midcontinent Plastics makes 80 fiberglass truck hoods per day for large truck manufacturers. Each hood sells for $500.00. Midcontinent sells all of its product to the large truck manufacturers. If the own price elasticity of demand for hoods is -0.4 and the price elasticity of supply is 1.5. a. Compute the supply and demand for truck hoods. b. If the local county government imposed a per unit tax of $25.00 per hood manufactured, what would be the new equilibrium price of hoods to the truck manufacturer? c. Would a per unit tax on hoods change the revenue received by Midcontinent? Solution: Given: P* = $500 Q* = 80 hoods per day E d = -0.40 E s = 1.5 a. Demand: Q d = a O + a 1 P Supply: Q s = b O + b 1 P Use: P Q Q P E × = to compute a 1 and b 1 . 1 a 80 500 4 . 0 = - 1 b 80 500 5 . 1 = a 1 = -0.064 b 1 = 0.24 Solve for a 0 and b 0 Q d = a O + a 1 P Q s = b O + b 1 P
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Unformatted text preview: 80 = a O + -0.064(500) 80 = b O + 0.24(500) a o = 112 b o = -40 Q d = 112 - 0.064P Q s = -40 + 0.24P b. The tax represents a price increase to the purchaser regardless of the current price. Thus, the supply curve will be adjusted vertically upward by $25. Q s = -40 + 0.24P or P = 166.67 + 4.17 Q s , then P t = P + $25 = 166.67 + 25 + 4.17Q s P t = 191.67 + 4.17Q s or Q s = -45.96 + 0.24P The new equilibrium price will be: New Supply = Demand Q s = -45.96 + 0.24P = 112 - 0.064P = Q d Solving yields P = $519.60 per truck hood c. Since the new selling price in (c) is $519.60 and the tax is $25 per hood, Midcontinent would receive only $494.6 per hood. As quantity sold has fallen too, revenues would fall....
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