1: Assume that demand for a commodity is represented by the equation P = 10 – 0.

Question

1: Assume that demand for a commodity is represented by the equation P = 10 – 0.2 Q d, and supply by the equation P = 2 + 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd ,

A. Solve the equations to determine equilibrium price.

B. Now determine equilibrium quantity.

Explanation / Answer

First because both equations are equal to P, you can set them equal to each other: p=10-.2Qd p=2+.2Qs both become 10-.2Qd=2+.2Qs which because Qd=Qs, we can say 10-0.2Qd=2+0.2Qd So what you do now, is use algebra to solve for Qd. 1) Moved Variables to one side --> 10=2+0.4Qd 2) Get Variable by itself ---> 8=0.4Qd 3) Solve for Variable (8/0.4) = Qd 4) simplify ---> 20=Qd=Qs, so the equilibrium qty is 20. NOw use this amount and plug it back into one of the equations to solve for price (using the first equation) P=10-0.2Qd P=10-0.2(20) P=10-4 P=6 Thus the equilibrium qty is 20 and equilibrium price is 6

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