answer key for problem
KEY
PROBLEM 1
Suppose a candy company roaster producing generic suckers (measured by Q) has the following cost function:
C(q) =
1 3 1 2 q − q + 3q + 180
1500
15
A i) Using the cost function, set-up functions to demonstrate the following costs:
a) Fixed costs
b) Variable costs
c) Average fixed costs
d) Average variable costs
e) Average total costs
e) Marginal cost of production
Fixed Costs = FC(q) = 180
Variable Costs -
VC(q) =
1 3 1 2 q − q + 3q
1500
15
AFC(q) =
Average Fixed Costs -
180 q 1 3 1 2 q − q + 3q
1 2 1 1
15
AVC(q) = 1500
=
q − q +3 q 1500
15
Average Variable Costs 1 3 1 2 q − q + 3q + 180
1 2 1 1
180
1500
15
ATC(q) =
=
q − q + 3+ q 1500
15
q
Average Total Costs -
MC(q) =
Marginal Cost of Production –
∂
1 3 1 2
1 2 2
(
q − q + 3q + 20) = q − q+ 3
∂q 1500
15
500
15
(MC in black, AVC in blue, ATC in red, AFC in yellow – ignore scaling on graph, as it is in multiples of .1) ii) Verify that the marginal cost of production intersects (d) at that curve’s minimum point. AVC is concave up, therefore the vertex is the minimum point of the AVC.
1
b
− = 15 = 50
2
2a
1500
Vertex =
Another way of verifying this information – the intersection point of MC(q) and AVC(q)
AVC(q) = MC(q)
1 2 1 1
1 2 2 1 q − q + 3= q − q +3
1500
15
500
15
2 2 1 1
−
q + q =0
1500
15
2
1 q(− q+ )
1500
15 q = 50
AVC = $1.33 iii) Graph (a) and (b) together with the total cost function.
iv) Graph (c), (d), (e) and (f) together, and label the intersection point obtained in (ii)
(Don’t worry about drawing to scale).
B i) Write down the company’s individual supply curve, along with information about where production will shut down in the short-run.
Individual firm supply curve (in short run) given by marginal cost curve for production above AVC line.
PShort− run =
1 2 2 q − q+ 3
500
15
ii) Suppose the firm is a price-taker, and the market price it faces
PROBLEM 1
Suppose a candy company roaster producing generic suckers (measured by Q) has the following cost function:
C(q) =
1 3 1 2 q − q + 3q + 180
1500
15
A i) Using the cost function, set-up functions to demonstrate the following costs:
a) Fixed costs
b) Variable costs
c) Average fixed costs
d) Average variable costs
e) Average total costs
e) Marginal cost of production
Fixed Costs = FC(q) = 180
Variable Costs -
VC(q) =
1 3 1 2 q − q + 3q
1500
15
AFC(q) =
Average Fixed Costs -
180 q 1 3 1 2 q − q + 3q
1 2 1 1
15
AVC(q) = 1500
=
q − q +3 q 1500
15
Average Variable Costs 1 3 1 2 q − q + 3q + 180
1 2 1 1
180
1500
15
ATC(q) =
=
q − q + 3+ q 1500
15
q
Average Total Costs -
MC(q) =
Marginal Cost of Production –
∂
1 3 1 2
1 2 2
(
q − q + 3q + 20) = q − q+ 3
∂q 1500
15
500
15
(MC in black, AVC in blue, ATC in red, AFC in yellow – ignore scaling on graph, as it is in multiples of .1) ii) Verify that the marginal cost of production intersects (d) at that curve’s minimum point. AVC is concave up, therefore the vertex is the minimum point of the AVC.
1
b
− = 15 = 50
2
2a
1500
Vertex =
Another way of verifying this information – the intersection point of MC(q) and AVC(q)
AVC(q) = MC(q)
1 2 1 1
1 2 2 1 q − q + 3= q − q +3
1500
15
500
15
2 2 1 1
−
q + q =0
1500
15
2
1 q(− q+ )
1500
15 q = 50
AVC = $1.33 iii) Graph (a) and (b) together with the total cost function.
iv) Graph (c), (d), (e) and (f) together, and label the intersection point obtained in (ii)
(Don’t worry about drawing to scale).
B i) Write down the company’s individual supply curve, along with information about where production will shut down in the short-run.
Individual firm supply curve (in short run) given by marginal cost curve for production above AVC line.
PShort− run =
1 2 2 q − q+ 3
500
15
ii) Suppose the firm is a price-taker, and the market price it faces