DSC1520 - Quantitative Modelling Questions & Answers

1. 4
Point A is the intercept for the demand function since the demand function slopes
downwards.
Using the demand function when Q = 0
P = 952 + 8(0) = 952

Point B is the intercept for the supply function




P = 400 + 4(0) = 400

Point C use the demand function when P = 0
0 = 952 -8Q
Q = 119




2. 2
Point D is the equilibrium point and it is calculated as
dd function = ss function
952 – 8Q = 400 + 4Q
Solve for Q
Q = 46
Solve for P using the demand function
P = 952 – 8(46) = 584

,3. 1




= -1/5


When Q=8 P = 60


Price elasticity of demand = -1/5 x 60/8 = - 1.5




4. 4
At breakeven point Total revenue = total cost
P = 100 – 20Q
Total revenue equals price, P, times quantity, Q, or TR = P×Q
Total revenue = Q(100 – 20Q)


Total cost = Total variable cost + fixed costs = 10Q + 40


At BEP
Q(100 – 20Q) = 10Q +40
100Q -20Q^2 =10Q +40
20Q^2 -90Q +40 = 0
Solve for Q using quadratic formula and get 0.5 or 4

,5. 1

= (-3)/5


Using this as the slope we can derive the equation as below
(80 – Q)/(40 – P) = -3/5
80 –Q = -24 + 3/5P
Making Q the subject and simplifying we get
Q = 104 - 3/5P = 104 -0.6P

, 6. 3
Marginal Cost function is a derivative of the total cost function. So to get the total cost
from the marginal cost we have to find the integral of the MC and the fixed cost will be
the constant.




C = 100