# Equilibrium Quantity

Question

Suppose the demand for guitars in State College is given by Qd = 5,000 – 5P where Qd is the quantity demanded, and P is the price of guitars. Also, suppose the supply of guitars is given by Qs = 20P – 2000, where Qs is the quantity supplied of guitars.

a) Calculate the equilibrium price of guitars and the equilibrium quantity of guitars in State College. Show your work.

b) Suppose the actual price of guitars is \$300. Determine if there is a shortage, a surplus, or if the market is in equilibrium at a price of \$300. If there is a shortage or surplus, calculate how much the shortage or surplus is.

c) Given your answer to b), is the price of guitars likely to rise, fall, or stay the same?

d) Suppose guitars and guitar strings are complements. On the back, draw a graph indicating what will happen in the market for guitar strings if the price of guitars decreases. Be sure to label your graph carefully, putting Price on the vertical axis and Quantity on the horizontal axis. You do not need to have actual numbers on this graph, but you should clearly indicate how the decrease in the price of guitars will affect the market for guitar strings, and what will happen to the equilibrium price and quantity of guitar strings.

Question

Can someone please explain how summing quantities of x^2 equals (1/3)x^3?
This summation process can be eliminated by using (1/3)x^3. Can you please show me the process in detail that one would use to prove this? Could you give me a geometrical example?

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