The demand curve for a product is given by p = f(q) = 10 e^-0.008q and the suppl
ID: 2892257 • Letter: T
Question
The demand curve for a product is given by p = f(q) = 10 e^-0.008q and the supply curve is given by p = g(q) = 4 Squareroot q + 10 for 0 lessthanorequalto q lessthanorequalto 500, where p is in dollars per unit. At a price of $50, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push prices up or down? Find the equilibrium price and equilibrium quantity. Does your answer to part (a) support the observation that market forces tend to push prices closer to the equilibrium price? If the price is equal to the equilibrium price, calculate and interpret the consumer surplus and the producer surplus.Explanation / Answer
16)demand p=f(q)=100e-0.008q, supply p=g(q)=4q +10 , 0q500
a)at p=50
f(q)=50
100e-0.008q=50
=>e0.008q=2
=>0.008q=ln2
=>q=(1/0.008)ln2
=>q=86.64
consumers are willing to buy 86.64 units
at p=50
g(q)=50
=>4q +10=50
=>q =10
=>q=100
producers willing to supply 100 units
market push prices down as supply is more than demand
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b)for equilibium , f(q)=g(q)
100e-0.008q=4q +10
by calculator q =91.22
p=f(91.22)=100e-0.008*91.22=48.2
equilibrium price =48.2 dollars
equilibrium quantity=91.22 units
yes answer in part (a) support the observation that market tends to push prices closer to the equilibrium price
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c)
consumer surplus =[0 to 91.22](100e-0.008q-48.2) dq
consumer surplus =[0 to 91.22](-12500e-0.008q-48.2q)
consumer surplus =(-12500e-0.008*91.22-48.2*91.22) -(-12500e-0.008*0-48.2*0)
consumer surplus =2078 dollars
producer surplus =[0 to 91.22](48.2-(4q +10)) dq
producer surplus =[0 to 91.22](38.2q-(8/3)q3/2)
producer surplus =(38.2*91.22-(8/3)91.223/2) -(38.2*0-(8/3)03/2)
producer surplus =1161.3 dollars
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