Well the answer is Ed=-7/5 i.e(-)1.4 by applying the formula (Ed=-bp/a-bp) hence,the elasticity of demand at price 7/5 is highly elastic.. as u are asking about a and b in the formula so 'a' suggest that all factors other than price that affect demand hence if there is any change in income or price it will be represented by a change in the value of 'a' and 'b' is the slope of the demand curve as u already know that the linear demand curve has an equation i.e Qd=a-b(p)....

Introduction:

In economics, elasticity measures the responsiveness of quantity demanded or supplied to a change in price. It helps us understand the degree to which consumers react to price changes. In this case, we are given a demand curve represented by D(p) = 12 - 5p. We need to calculate the elasticity of demand at a price of 7/5.

Understanding Elasticity:

Elasticity is calculated using the formula:

E = (%ΔQd) / (%ΔP)

Where:
E = Elasticity of demand
%ΔQd = Percentage change in quantity demanded
%ΔP = Percentage change in price

Calculating Elasticity:

To calculate the elasticity of demand at a price of 7/5, we need to determine the percentage change in quantity demanded and the percentage change in price.

Step 1: Calculate the initial quantity demanded:

To find the initial quantity demanded, we substitute the given price (7/5) into the demand curve equation:

D(7/5) = 12 - 5(7/5)
D(7/5) = 12 - 7
D(7/5) = 5

The initial quantity demanded is 5.

Step 2: Calculate the new quantity demanded:

Now, let's assume the price changes to a new value, say p'.

To find the new quantity demanded, we substitute the new price (p') into the demand curve equation:

D(p') = 12 - 5p'

Step 3: Calculate the percentage change in quantity demanded:

The percentage change in quantity demanded is given by the formula:

%ΔQd = ((Qd' - Qd) / Qd) * 100

Where:
Qd' = New quantity demanded
Qd = Initial quantity demanded

In this case, Qd' is the quantity demanded at price p' and Qd is the initial quantity demanded at price 7/5.

%ΔQd = ((D(p') - D(7/5)) / D(7/5)) * 100

Step 4: Calculate the percentage change in price:

The percentage change in price is given by the formula:

%ΔP = ((p' - p) / p) * 100

Where:
p' = New price
p = Initial price (in this case, 7/5)

Step 5: Calculate the elasticity:

Now, we can substitute the calculated percentage changes into the elasticity formula:

E = (%ΔQd) / (%ΔP)

E = (((D(p') - D(7/5)) / D(7/5)) * 100) / (((p' - p) / p) * 100)

Simplifying the equation, we get:

E = ((D(p') - D(7/5)) / D(7/5)) / ((p' - p) / p)

E = (D(p') - D(7/5)) / (D(7/5) * (p' - p))

Conclusion:

By following the above steps and substituting the values, we can calculate the elasticity of demand at the given price of 7/5. The calculated