1. Production Grid, Isoquants, Short-Run Production and Costs
The following production grid shows the relationship between capital and labor inputs and the output that can be produced by a firm.
Capital
Labor
0
1
2
3
4
5
6
7
8
0
0
1
3
6
8
10
12
13
13
1
1
10
30
60
85
105
120
130
135
2
3
30
85
105
120
150
180
210
230
3
6
60
105
130
210
280
340
380
410
4
8
85
120
210
410
500
570
620
660
5
10
105
150
280
500
700
850
950
1000
6
12
120
180
340
570
850
1100
1300
1400
7
13
130
210
380
620
950
1300
1500
1600
8
13
135
230
410
660
1000
1400
1600
1700
Based on this information use Excel Charts to do the following:
(a) Set up an isoquant map with isoquants representing output levels of 10, 105, and 410 units of output.
(b) Set up a diagram showing the firm’s short run production function assuming that the firm has only one unit of capital.
(c) Set up a diagram showing the firm’s marginal product schedule assuming that the firm has only one unit of capital.
(d) Assume that capital is fixed at one unit in the short run and that the costs associated with the use of fixed inputs are $30 per period, while the wage rate is $10 per unit of labor per period. Use this information to perform the calculations necessary to set up a diagram showing total cost (TC) and total variable cost (TVC) of the firm per period in the short run.
(e) Also, use the information in part c to then set up a another diagram showing the firm’s short run marginal cost (MC), average total cost (ATC), and average variable cost (AVC) in the range from 10 to 135 units of output.
2. Price Discriminating Monopoly Part I
Consider a monopolistic firm selling the same product in two completely separate markets with the following demand schedules:
Quantity (Q1)
0
1
2
3
4
5
6
7
8
Price (P1)
24
21
18
15
12
9
6
3
0
Quantity (Q2)
0
1
2
3
4
5
6
7
8
Price (P2)
8
7
6
5
4
3
2
1
0
The marginal cost of this firm is equal to its average total cost and is constant at $3 per unit produced (note that this also means that there are no fixed costs). Based on this information use excel to calculate marginal revenues and set up a diagram that shows the demand and the marginal revenue curves of this firm as well as the quantities and prices it should charge in each market in order to maximize overall profits from the two markets.
3. Price Discriminating Monopoly Part II
Consider a monopolistic firm selling the same product in two separate markets, A and B, which have different demand curves. The demand in market A is defined by PA = 18 – 2QA for positive prices and quantities (i.e., for all PA, QA > 0) and the demand in market B is defined by PB = 9 – QB for positive prices and quantities (i.e., for all PB, QB > 0). Assume that the marginal cost of this firm is equal to its average total cost and is constant at $4 per unit produced.
Based on this information, your task is to use excel to set up diagrams that show the demand and the marginal revenue curves of this firm, as well as the quantities and prices it charges in each market, and also calculate the firm’s total profit from selling in the two markets.