BASIC CONCEPTS FROM ECONOMICS
Chapter 2
2.1 A manufacturer estimates that its variable cost for manufacturing a given product
is given by the following expression: C ( q ) = 25q 2 + 2000q [$] where C is the total
cost and q is the quantity produced.
a. Derive an expression for the marginal cost of production.
The marginal cost of production is the rate of change of the cost with respect of the quantity
produced; therefore:
d C (q)
MC (q ) = = 50q + 2000
dq
b. Derive expressions for the revenue and the profit when the widgets are sold at
marginal cost.
Since the widgets are sold at marginal cost, p = MC ( q )
The revenue is then given by:
revenue = p q = ( 50q + 2000 ) q = 50q 2 + 2000q
Since the profit is the difference between the revenue and the production cost, we have:
profit = ( 50q 2 + 2000q ) - ( 25q 2 + 2000q ) = 25q 2
2.2 The inverse demand function of a group of consumers for a given type of widgets is
given by the following expression: p = -10q + 2000 [$/unit] where q is the demand
and p is the unit price for this product.
a. Determine the maximum consumption of these consumers
The inverse demand function can be represented by a straight line with a negative slope, as
shown below:
, BASIC CONCEPTS FROM ECONOMICS
2200
2000
1800
1600
1400
1200
p
1000
800
600
400 q
max
200
0
0 20 40 60 80 100 120 140 160 180 200 220
q, [units]
Figure P2.2-a: Price as a function of the quantity produced
The maximum consumption qmax is achieved when p = 0 [$/unit]. From the inverse demand
function, we get:
0 = -10q + 2000 $
-2000
qmax = = 200 units
-10
b. Determine the price that no consumer is prepared to pay for this product
The price that no consumer is prepared to pay is such that no widget is sold:
p = -10 ´ 0 + 2000 = 2000 $/unit
c. Determine the maximum consumers’ surplus. Explain why the consumers will
not be able to realize this surplus
Since the area under the inverse demand function represents the consumers’ surplus, this
surplus will maximum when the area is maximized. This occurs when the number of
widgets sold is at its maximum (q = qmax and p = 0). Thus, we have:
qmax p max 200 ´ 2000
surplus = = = 200, 000 $
2 2
This surplus is not achievable because no rational producer would be willing to “sell” its
production at a price of 0 $/unit.
d. For a price p = 1000 $/unit, calculate the consumption, the consumers’ gross
surplus, the revenue collected by the producers and the consumers’ net surplus.
, BASIC CONCEPTS FROM ECONOMICS
For a price of 1,000 $/unit the number of widgets sold would be:
p 1000
q= + 200 = - + 200 = 100 units
-10 10
2200
2000
1800
1600
1400
1200
A
p
1000
800
600
400
B q
max
200
0
0 20 40 60 80 100 120 140 160 180 200 220
q, [units]
Figure P2.2-b: Price as a function of the number of widgets produced for a price of 1,000
$/unit
Therefore, the consumers’ gross surplus would be given by the sum of areas A and B:
100 ´1000
A+ B = + 100 ´ 1000 = 150, 000 $
2
The revenue collected by the producers is given by area B, which is 100,000 $
The consumers’ net surplus is given by area A, which is 50,000 $
e. If the price p increases 20%, calculate the change in consumption and the
change in the revenue collected by the producers.
A 20% increases means that p would be 1,200 $/unit. The new number of widgets
consumed would therefore be:
p 1, 200
q= + 200 = - + 200 = 80 units
-10 10
The revenue collected by the producers would then be 80 ´ 1,200 = 96,000 $. Therefore,
the change in consumption is 80 – 100 = –20 units and the change on the revenue collected
is 96,000 – 10,0000 = – 4,000 $.
, BASIC CONCEPTS FROM ECONOMICS
f. What is the price elasticity of demand for this product and this group of
consumers when the price p is 1000 $/unit?
The elasticity of demand is given by:
p dq
e=
q dp
From the inverse demand function, we know that the amount of widgets consumed is given
by:
p
q= + 200
-10
Therefore, the rate of change of the amount of widgets consumed with respect of the price
change is given by:
dq 1
=-
dp 10
Since the price is 1000 $/unit for 100 units, the price elasticity of demand is:
1000 æ 1 ö
e= ç - ÷ = -1
100 è 10 ø
g. Derive and expression for the gross consumers’ surplus and the net consumers’
surplus as a function of the demand. Check these expressions using the results
of part d.
The gross consumer surplus is given by the sum of the areas A and B; therefore:
q (p max - p )
gcs = A + B = +qp
2
Where pmax = 2000 $/unit. Since the price is related to the demand by p = -10q + 2000 ,
we have:
( ) ( )
gcs = 5q 2 + −10q 2 + 2000q = −5q 2 + 2000q
Evaluating the previous equation for an amount of 100 widgets we obtain a gross
consumers’ surplus of 150000 $, which is equal to the result obtained in part d.
Chapter 2
2.1 A manufacturer estimates that its variable cost for manufacturing a given product
is given by the following expression: C ( q ) = 25q 2 + 2000q [$] where C is the total
cost and q is the quantity produced.
a. Derive an expression for the marginal cost of production.
The marginal cost of production is the rate of change of the cost with respect of the quantity
produced; therefore:
d C (q)
MC (q ) = = 50q + 2000
dq
b. Derive expressions for the revenue and the profit when the widgets are sold at
marginal cost.
Since the widgets are sold at marginal cost, p = MC ( q )
The revenue is then given by:
revenue = p q = ( 50q + 2000 ) q = 50q 2 + 2000q
Since the profit is the difference between the revenue and the production cost, we have:
profit = ( 50q 2 + 2000q ) - ( 25q 2 + 2000q ) = 25q 2
2.2 The inverse demand function of a group of consumers for a given type of widgets is
given by the following expression: p = -10q + 2000 [$/unit] where q is the demand
and p is the unit price for this product.
a. Determine the maximum consumption of these consumers
The inverse demand function can be represented by a straight line with a negative slope, as
shown below:
, BASIC CONCEPTS FROM ECONOMICS
2200
2000
1800
1600
1400
1200
p
1000
800
600
400 q
max
200
0
0 20 40 60 80 100 120 140 160 180 200 220
q, [units]
Figure P2.2-a: Price as a function of the quantity produced
The maximum consumption qmax is achieved when p = 0 [$/unit]. From the inverse demand
function, we get:
0 = -10q + 2000 $
-2000
qmax = = 200 units
-10
b. Determine the price that no consumer is prepared to pay for this product
The price that no consumer is prepared to pay is such that no widget is sold:
p = -10 ´ 0 + 2000 = 2000 $/unit
c. Determine the maximum consumers’ surplus. Explain why the consumers will
not be able to realize this surplus
Since the area under the inverse demand function represents the consumers’ surplus, this
surplus will maximum when the area is maximized. This occurs when the number of
widgets sold is at its maximum (q = qmax and p = 0). Thus, we have:
qmax p max 200 ´ 2000
surplus = = = 200, 000 $
2 2
This surplus is not achievable because no rational producer would be willing to “sell” its
production at a price of 0 $/unit.
d. For a price p = 1000 $/unit, calculate the consumption, the consumers’ gross
surplus, the revenue collected by the producers and the consumers’ net surplus.
, BASIC CONCEPTS FROM ECONOMICS
For a price of 1,000 $/unit the number of widgets sold would be:
p 1000
q= + 200 = - + 200 = 100 units
-10 10
2200
2000
1800
1600
1400
1200
A
p
1000
800
600
400
B q
max
200
0
0 20 40 60 80 100 120 140 160 180 200 220
q, [units]
Figure P2.2-b: Price as a function of the number of widgets produced for a price of 1,000
$/unit
Therefore, the consumers’ gross surplus would be given by the sum of areas A and B:
100 ´1000
A+ B = + 100 ´ 1000 = 150, 000 $
2
The revenue collected by the producers is given by area B, which is 100,000 $
The consumers’ net surplus is given by area A, which is 50,000 $
e. If the price p increases 20%, calculate the change in consumption and the
change in the revenue collected by the producers.
A 20% increases means that p would be 1,200 $/unit. The new number of widgets
consumed would therefore be:
p 1, 200
q= + 200 = - + 200 = 80 units
-10 10
The revenue collected by the producers would then be 80 ´ 1,200 = 96,000 $. Therefore,
the change in consumption is 80 – 100 = –20 units and the change on the revenue collected
is 96,000 – 10,0000 = – 4,000 $.
, BASIC CONCEPTS FROM ECONOMICS
f. What is the price elasticity of demand for this product and this group of
consumers when the price p is 1000 $/unit?
The elasticity of demand is given by:
p dq
e=
q dp
From the inverse demand function, we know that the amount of widgets consumed is given
by:
p
q= + 200
-10
Therefore, the rate of change of the amount of widgets consumed with respect of the price
change is given by:
dq 1
=-
dp 10
Since the price is 1000 $/unit for 100 units, the price elasticity of demand is:
1000 æ 1 ö
e= ç - ÷ = -1
100 è 10 ø
g. Derive and expression for the gross consumers’ surplus and the net consumers’
surplus as a function of the demand. Check these expressions using the results
of part d.
The gross consumer surplus is given by the sum of the areas A and B; therefore:
q (p max - p )
gcs = A + B = +qp
2
Where pmax = 2000 $/unit. Since the price is related to the demand by p = -10q + 2000 ,
we have:
( ) ( )
gcs = 5q 2 + −10q 2 + 2000q = −5q 2 + 2000q
Evaluating the previous equation for an amount of 100 widgets we obtain a gross
consumers’ surplus of 150000 $, which is equal to the result obtained in part d.
