This is Section 5.1 Problem 50: The demand and supply curves of a certain brand

Question

This is Section 5.1 Problem 50: The demand and supply curves of a certain brand of running shoes are given by p=D(x)= 112-0.04x, and p=S(x)=0.06x+42, where p is the price in dollars and x is the quantity sold. Answer the following: (a) The equlbrium quantity is xE700 (b) The producer's surplus at that demand is $14700 (c) The consumers' surplus at that demand is $9800 (d) The total surpluses at that demand is $ 24500 Hint: Follow Example 6 and the equilibrium price is pE84 Submit Answer Save Progress +2 points This is Section 5.1 Problem 52: Refer to Exercise #50: A tax of $2.00 will be imposed on the producer for each pair of the running shoes sold. Answer the following: (a) The new supply function is p S(x) The new equilibrium quantity is (b) The producer's surplus at that demand is $ (c) The consumers' surplus at that demand is $ (d) The total surpluses at that demand is s$ ,and the new equilibrium price is pPE- (Round to 1 decimal place.)

Explanation / Answer

original demand function p =D(x) = 112- 0.04 x

supply function p = S(x) = 42 + 0.06x

Let p = the new price, including the tax. The consumer pays p dollars for the product, but the supplier receives only

p –2 dollars, since $2 goes to the government. The demand function remains the same p = 112- 0.04 x ......(1)

But the supply function changes (replace p with p – 2):

p - 2 = 42 + 0.06x => p = 44 + 0.06 x

a) new supply function p = S(x) = 44 + 0.06 x ......(1)

for equilibrium equating p from (1) and (2)

112- 0.04 x = 44 + 0.06 x

=> 112 - 44 = 0.04 x +0.06 x

=> 68 = 0.1 x

=> x = 680  

equilibrium quantity 680

equilibrium price = 44 +(0.06 ) . 680 = 84.8 $

b)

producer surplus  

=1/2 ( difference of price between equilibrium and the price when quantity of supply equal zero ) x ( quantity at equilibrium point )

now from demand function when x = 0 => p =44 + (0.06 )0 = 44

difference of price between equilibrium and the price when quantity of demand equal zero = (84.8-44) $= 40.8$

quantity at equilibrium point = 680

so consumer surplus = 1/2 ( 40.8).( 680) = 27744 $

c)

consumer surplus

=1/2 ( difference of price between equilibrium and the price when quantity of demand equal zero ) x ( quantity at equilibrium point )

now from demand function when x = 0 => p =112-( 0.04). 0 = 112

difference of price between equilibrium and the price when quantity of demand equal zero = (112 - 84.8) $= 27.2 $

quantity at equilibrium point = 680

so consumer surplus = 1/2 ( 27.2 ).( 680) = 9248 $

d) total surplus = consumer surplus + producer surplus = 27744+ 9248 = 36992 $

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