Answer to Question #163748 in Microeconomics for Gbemisola

Question

In 2008 a car manufacturer sold 10,000 units of its leading model at N10,000. After deducting operating  costs, dealers’ costs and all other variable cost this produced a surplus of N4,000 on each unit sold. Due to  the recession, sales slump in early 2009 and the marketing director advises a price cut of N2000, arguing  that this makes sense because the Own Price Elasticity of demand is –1.5. Calculate the amount of surplus  that would be generated by the manufacturer in 2009 if the marketing director is correct and her  recommendation is accepted.

Answer 1

Using the demand and supply curve, the producers' surplus is the area shaded below the equilibrium price as shown in the picture below.

To calculate the producers' surplus, we use the formula of triangle, taking the quantity (Q1) as the base (b) and price (P) as the height (h).

Initial quantity = 10,000

Initial price = N10,000

Initial surplus = N4,000

New price = N8,000 (cut of N2,000 from N10,000)

New Price elasticity demand (PED)= -1.5

But PED = change in price/change in quantity

               -1.5= (8,000-10,000)/(x-10,000)

-1.5(x-10,000) =-2,000

-1.5x+15,000 = -2,000

-1.5x=-17,000

X=11,333

New demand is 11,333 units

Producer surplus = 1/2bh

We will use new demand as b and new price as h

               = (1/2)X 11,333 X 8,000

=45,333,333

Unit surplus = total surplus/number of units sold

=45,333,333/10,000

= 4,533 units

Note: we divide the total surplus by 10,000 units to obtain the surplus on each unit sold (total units sold were 10,000)