Question

With such a demand schedule you could calculate four elasticities of demand for the intervals between price 5 and 4, 4 and 3, 3 and 2, as well as 2 and 1. Calculate all four showing all work.

Also, imagine a market demand with a schedule of prices from 1-5 associated with quantities demanded from 5-1, thus a price of 5 is coordinated with a quantity of 1 all the way down to a price of 1 associated with a quantity of 5. What would the slope of this line be and would that be appropriate for a demand curve (explain why)?

Please show work

Answer 1

Given the information the demand schedule is given below.

So, here as the “P” decreases from “5” to “4” the quantity demand increases to “2” from “1”, => dQ/dP = (1/-1) = (-1), => the elasticity is given by, => e=(dQ/dP)*(P/Q) = (-1)*(4/2) = (-2).

So, the above table shows the elasticity for the “4 possible” prices.

Now, given the information the slope of the demand curve is given by “dP/dQ=(-1)”.

=> the equation of the demand curve is given by.

=> P=A-Q, => one point on the demand curve is given by “P=5, Q=1”.

=> P=A-Q, => 5=A-1, => A=6, => the equation of the demand curve is given by, => P=6-Q. So, the demand curve is the negatively sloped linear demand curve in appropriate form.