Mathematics, Relation between supply, demand, and price.?

Question

This is similar to the other question I asked, but it involves a price as well.

Question reads:

At $1.90 each item, the supply was 410 million items and the demand was 455 million items.

When the price rises to $2.70 per item, the supply increases to 430 million and demand decreases to 415 million.

Assume the price-supply and price-demand equations are linear and find the equation that relates price and supply, another equation that relates price and demand, and then find the equilibrium point.

-end question.

Again, any help will be appreciated

Answer 1

You are given two points on the Supply curve and two points on the Demand curve.

If you have two points, you can find the equation of the line that goes through them: The equation of the line that goes through points (X1, Y1) and (X2, Y2) is:

Y = m*(X-X1) +Y1

or

Y = m*X + (-m*X1+Y1)

where m = (Y2-Y1)/(X2-X1)

Use this equation to find the line for the demand curve. Then use it to find the line for the supply curve.

You will have then in the form of:

Q(demand) = a*P+b
Q(supply) = c*P+d

When the system is in equilibriam, the quantity demanded will equal the quantity supplied, so you get:

a*P+b = x*P+d

Now, solve for the price P

Answer 2

In theory, Supply and Demand in a given country determine how much a society should produce at what price; equilibirium - demand and supply intersection. They are inversely related. The variables are always price and quantity. If price increases for a given supply output (say radios), there will be less demand as people are faced with higher prices; new equilibirium. However, if producers produce more, because lets say they offered tax incentives, then they will increase their supply and prices drop again...and so demand increases - reaching the original equilibirium. Now if supply increases (higher quantity), say because producers have better technology which save cost, prices drop, and demand increases (as people can buy more at a lower price); new equilibirium. Ok? Hope this helps. Try to graph it, it helps a lot in understanding further.