Homework 7
Economics 503
Foundations of Economic Analysis
Assigned: Saturday, October 21st, 2006
Due: Saturday, September 28 th, 2006
1.
You are the brand manager of a new lemon flavored toothpaste. You make
the toothpaste in batches of 1000 boxes. You face the following demand and cost
schedule.
a. Calculate the profit maximizing price and output level. Calculate the
marginal revenue from moving to the next batch size. Calculate the
marginal cost of increasing to the next largest batch size. Calculate the
( P  MCt )
Lerner Markup Index t
for this market using the profit
Pt
maximizing price and this marginal cost. Calculate the elasticity of
demand (using the midpoint method) for this market by calculating the %
effect on raising the price by $2 from the profit maximizing price.
Quantity
Price
1
58
Total Cost Revenue Profit
13
58
Marginal Cost
Lerner Index
Elasticity
45
2
56
15
112
97
3
54
17
162
145
4
52
28
208
180
5
50
45
250
205
6
48
68
288
220
7
46
97
322
225
8
44
132
352
220
9
42
173
378
205
10
40
220
400
180
2
0.965517
-19
2
0.964286
-11
11
0.796296
-7.57143
17
0.673077
-5.66667
23
0.54
-4.45455
29
0.395833
-3.61538
35
0.23913
-3
41
0.068182
-2.52941
47
-0.11905
-2.15789
b. Considering that your company is the only one that produces exactly this
flavor of toothpaste but anyone can enter the toothpaste market, how
would you expect to see profits evolve over time? In the long run, will the
Lerner Index be greater than, less than or equal to zero?
As the company is making profits, more firms will enter the market with
similar brands. The price that the firm will be able to charge for a given
amount of goods will fall as will profits.
2.
You observe information describing the price elasticity of Coca-Cola and
Starbucks coffee as -2.5 and -1.5. Assuming that the marginal cost of producing
each good is $1 and each is sold in a monopolistically competitive market,
calculate the profit maximizing price using the rule of thumb.
P  MC 1
1
The rule of thumb is
. Applying this we get,

P

P
MC 1  1
P
P
Elasticity P/MC
-2.5 1.666667
1.5
3
3.
You observe a monopoly electric company operating in a market with price
schedule given by the equation
P  150  2  Q
where P is the price per Megawatt Hour and Q is the quantity of megawatt hours.
You know the electricity company must pay a fixed cost of 1050 to operate plus
50 per unit of output produced. Create a table like the one in Table 1 for quantities
in the range of 10 to 60 inclusive with increments of 5 MWH. Calculate revenue,
profits, and average cost of production at all levels. Calculate the profit
maximizing level of production. Calculate levels of production where profits are
zero (i.e. where average total cost of production is equal to the price level).
Calculate the marginal cost of increasing production by another by MWH at a
zero profit level of production. Would the firm operate if it had to price at
marginal cost?
Quantity Price
Total Cost Revenue Profit
Marginal Cost
Lerner Index
10
130
1550
1300
-250
50
0.615385
15
120
1800
1800
0
50
0.583333
20
110
2050
2200
150
50
0.545455
25
100
2300
2500
200
Monopoly Price
50
0.5
30
90
2550
2700
150
50
0.444444
35
80
2800
2800
0
Average Cost Pricing
50
0.375
40
70
3050
2800
-250
50
0.285714
45
60
3300
2700
-600
50
0.166667
50
50
3550
2500
-1050
Marginal Cost Pricing
50
0
55
40
3800
2200
-1600
50
-0.25
60
30
4050
1800
-2250
Elasticity
-5
-3.28571
-2.33333
-1.72727
-1.30769
-1
-0.76471
-0.57895
-0.42857
-0.30435