Scenario 4.4:
The demand curve for the new computer game, Rock and Roll Trivia, is given as follows:
Q = 200 - 5P - .1Pc - .5Pd + .2A - I
where P is the price of the game
Pc is the price of a computer
Pd is the price of a diskette
A is the level of advertising
Q is the level of income
-See the information in Scenario 4.4. Suppose P = 10, Pc = 100, Pd = 2, A = 5, and I = 50. What is the price elasticity of demand?

Question

Quizplus · Accepted Answer

To determine the price elasticity of demand, we need to use the formula:
E = (% change in quantity demanded)/(% change in price)
We are given P = 10 and Pc, Pd, A, and I are constants. So we only need to consider the impact of a change in the price of the game on the quantity demanded. 
At P = 10, the demand equation is:
Q = 200 - 5(10) - 0.1(100) - 0.5(2) + 0.2(5) - 50
Q = 85
If the price of the game were to increase from $10 to $11, the new level of quantity demanded would be:
Q' = 200 - 5(11) - 0.1(100) - 0.5(2) + 0.2(5) - 50
Q' = 80
% change in quantity demanded = (Q' - Q)/Q = (80 - 85)/85 = -0.0588 or -5.88%
% change in price = (11 - 10)/10 = 0.1 or 10%
Using the formula for price elasticity of demand, we get:
E = (-0.0588/-0.1) = 0.588 or approximately -5/9. 
Therefore, the answer is B, and the price elasticity of demand is -5/9. 
Since the absolute value of this elasticity is less than 1, demand is inelastic in this range, meaning that an increase in price would result in a smaller percentage decrease in quantity demanded.

Scenario 4.4: the Demand Curve for the New Computer Game, Rock and Rock