Question

If Individual A's demand was Q=10-2P and Individual B's demand was P=10-2Q, what is the market demand?

Answer 1

To determine the market demand, we need to sum up the individual demands of Individual A and Individual B.

Individual A's demand function is given as Q = 10 - 2P, where Q is the quantity demanded and P is the price.

Individual B's demand function is given in terms of P, as P = 10 - 2Q. To make them compatible, we need to express Individual B's demand as Q in terms of P like Individual A's. To do that, we solve for Q:

P = 10 - 2Q
Q = (10 - P)/2

Now let's align the definitions of Q. Multiply both sides of Individual B's adjusted equation by 2 to get rid of the fraction:

2Q = 10 - P

Now we can solve for Q (the quantity demanded by Individual B) in terms of P:

Q = 5 - 0.5P

Now that we have both demands expressed in terms of P, we can sum them to get the market demand:

Individual A's demand: Q = 10 - 2P
Individual B's demand: Q = 5 - 0.5P

Market demand (Q_market) is the sum of Individual A's and Individual B's demands:

Q_market = (10 - 2P) + (5 - 0.5P)
Q_market = 10 - 2P + 5 - 0.5P
Q_market = 15 - 2.5P

Thus, the market demand is Q_market = 15 - 2.5P, which represents the total quantity demanded for both individuals at any given price level P.