Question

Suppose the demand for down pillows is given by QD pillows is given by QS

a) Solve for the equilibrium price.
b) Plug the equilibrium price back into the demand equation and solve for the equilibrium quantity
c) Double-check your work by plugging the equilibrium price back into the supply equation and solving for the equilibrium quantity. Does your answer agree with what you got in (b)?
d) Solve for the elasticities of demand and supply at the equilibrium point. Which is more elastic, demand or supply?
e) Invert the demand and supply functions (in other words, solve each for P) and graph them. Do the equilibrium point and relative elasticities shown in the graph appear to coincide with your 100 p, and that the supply of down =-20 2P. answers?

Answer 1

To solve for the equilibrium price, set the demand and supply equations equal to each other and solve for P. Plug the equilibrium price back into the demand equation to find the equilibrium quantity. Double-check the work by plugging the equilibrium price back into the supply equation. Answer: Equilibrium price is $2 and equilibrium quantity is 7.

Step-by-step explanation:

To solve for the equilibrium price, we need to set the demand and supply equations equal to each other and solve for P. The demand equation is given by QD = 8 - 0.5P and the supply equation is given by QS = -0.4 +0.2P. Setting these two equal to each other, we have 8 - 0.5P = -0.4 +0.2P. Solving for P, we find that P = $2.

To find the equilibrium quantity, we can plug the equilibrium price back into the demand equation. Substituting P = $2 into QD = 8 - 0.5P, we get QD = 8 - 0.5(2) = 7.

To double-check our work, we can plug the equilibrium price back into the supply equation. Substituting P = $2 into QS = -0.4 +0.2P, we get QS = -0.4 +0.2(2) = -0.4 + 0.4 = 0.

Therefore, our answers for the equilibrium price and quantity are $2 and 7, respectively.