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MBA Math Sample Exercise

Economics: Supply and Demand 

Moving well beyond generic GMAT aptitude questions, the MBA Math sample exercises allow prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

MBA focused, time efficient, and convenient, the MBA Math online course builds your quantitative skills. Furthermore, the MBA Math transcript provides a concise summary for admissions officers that you are up to speed.

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Exercise

Assume that the demand curve D(p) given below is the market demand for apples:

Q = D(p) = 270 - 15p, p > 0

Let the market supply of apples by given by:

Q = S(p) = 42 + 15p, p > 0

where p is the price (in dollars) and Q is the quantity. The functions D(p) and S(p) give the number of bushels (in thousands) demanded and supplied.

What is the consumer surplus at the equilibrium price and quantity?

Round the equilibrium price to the nearest cent and round the equilibrium quantity DOWN to its integer part.

Solution

Solution Commentary

(2:16)

Manual Solution

The equilibrium point is the point where the demand and supply curves intersect.

Calculate the equilibrium point algebraically by setting D(p) = S(p) and solving for p.

270 - 15p = 42 + 15p

228 = 30p

Solving for p and rounding to the nearest cent yields an equilibrium price of $7.60

Plug the value for p into either the supply or demand curve, solve, and round down to the nearest integer to obtain an equilibrium quantity of 156

Consumer surplus refers to the area of the triangle above the equilibrium price and below the demand curve.

The vertical side of the triangle is the distance between the equilibrium price and the p-intercept,

which is the demand curve price at a quantity of zero. The horizontal side of the triangle is the equilibrium quantity.

The consumer surplus is thus [(18 - 7.6)*156]/2 = $811.20.


Excel Solution

No Excel solution provided. The solution is based on simple arithmetic.

Peter Regan teaches decision science courses at Dartmouthís Tuck School and Dukeís Fuqua School. He also teaches pre-term quantitative skills courses at Tuck and Cornellís Johnson School. He created the MBA Math self-paced, online pre-MBA quantitative skills course covering finance, accounting, economics, statistics, and spreadsheets.

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