Question

Question 3 (35 marks – ALL CALCULATIONS MUST BE SHOWN)

The market for fidget spinners has been described by the following supply and demand functions:

Demand: P = 13 – 0.2Q

Supply: P = 4 + 0.4Q

where

P = the price in dollars

Q = the number of fidget spinners sold per month, in thousands.

a) Construct a graph of supply and demand for this market showing all intercepts. What are the equilibrium prices and quantities? Show these on your graph.

b) At the market equilibrium price, what would be the total monthly revenue?

c) Calculate consumer surplus at the market equilibrium and indicate this surplus as an area on your diagram. Interpret the meaning of the value you generate.

d) Calculate producer surplus at the market equilibrium and indicate this surplus as an area on your diagram. Interpret the meaning of this value.

e) School children (the main purchasers of fidget spinners) last year exhibited a change in tastes such that fidget spinners are much less popular. This means that at any price, the quantity demanded of fidget spinners has shrunk by 65%. The new demand equation is then

P = 4.55 – 0.2Q

Sketch it on your graph.

f) Calculate the new equilibrium price and quantity after the end of the craze and show them on your graph.

Answer 1

Solution:

Demand: P = 13 - 0.2Q

Supply: P = 4 + 0.4Q

(a)

Data table used:

Q	Demand	Supply
0	13	4
5	12	6
10	11	8
15	10	10
20	9	12
25	8	14
30	7	16
35	6	18
40	5	20
45	4	22
50	3	24
55	2	26
60	1	28
65	0	30

Graph:

In equilibrium, demand price equals supply price.

13 - 0.2Q = 4 + 0.4Q

0.6Q = 9

Q = 15

P = 13 - (0.2 x 15) = 13 - 3 = $10

It is shown by point E in graph where demand & supply curves intersect with price P0 (= $10) and quantity Q0 (= 15).

(b) Revenue = P0 x Q0 = $10 x 15 = $150

(c) From demand curve, when Q = 0, P = 13 (Reservation price/Vertical intercept)

Consumer surplus (CS) = Area between demand curve and Price = Area AEP0

= (1/2) x $(13 - 10) x 15 = (1/2) x $3 x 15

= $22.5

This represents the gain to consumers as measured by difference between maximum willingness to pay and actual price paid.

(d) From supply curve, when Q = 0, P = 4 (Minimum acceptable price/Vertical intercept)

Producer surplus (PS) = Area between supply curve and Price = Area BEP0

= (1/2) x $(10 - 4) x 15 = (1/2) x $6 x 15

= $45

This represents the gain to producers as measured by difference between actual price paid and minimum acceptable price.

(E) When new demand function is: P = 4.55 - 0.2Q,

Data table used for new demand function, original demand function and supply function are as follows.

	Original Demand	Supply	New Demand
0	13	4	4.55
5	12	6	3.55
10	11	8	2.55
15	10	10	1.55
20	9	12	0.55
25	8	14	-0.45

Graph:

(F) Initial equilibrium is at point A where original demand and supply curves intersect with price P0 and quantity Q0. New equilibrium is at point B with new demand curve intersects supply curve with price P1 and quantity Q1.

Equating new demand curve with supply curve,

4.55 - 0.2Q = 4 + 0.4Q

0.6Q = 0.55

Q (= Q1) = 0.92

P (= P1) = 4 + (0.4 x 0.92) = 4 + 0.37 = 4.37