Question

According to one economic model, the demand for gasoline is a linear function of price. If the price of gasoline is p # $3.10 per gallon, the quantity demanded in a fixed period of time is q - 65 gallons. If the price is $3.50 per gallon, the quantity of gasoline demanded is 45 gallons for that period.

a) Find a formula for q (demand) in terms of p (price).




b) According to this model, at what price is the gas so expensive that there is no demand.

Answer 1

Your first line calculation is already true but reversed. The demand will decrease (that mean the formula would be minus) by 20 gallons for every $0.4 price increase, which means 50 gallons/$. To find the formula you need to insert one sample of either the first equation (65gallon and $3.1) or 2nd equation (45 gallons and $3.5). The formula for demand should be:

q= C - 50p
65 gallon= C- 3.1 * 50
C= 65 gallon + 155 gallon= 220 gallon

The formula would be:
q= 220- 50p

So the second question can be solved by putting 0 on the Q. It would be:
q= 220- 50p
0=220-50p
50p=220
p= $4.4