Question

1. (10 pts) A firm has the following short run total costs, where Q is output and TC is total cost:

Q	TC
0	$ 100
1	110
2	130
3	160
4	200
5	250
6	310
7	380
8	460
9	550
10	650
11	760

1. What is total fixed cost equal to? $100

2. What is average total cost at Q = 4? $50

3. What is average variable cost at Q = 7? $40

4. What is marginal cost at Q = 8?

5. At Q=8, is the firm operating under increasing or decreasing returns? Why?

2. (6 pts) An economy has the following total transactions (or total requirements) input-output matrix:

                                             Agriculture    Manufact.   Energy    Services

Agriculture                               1.40                0.30         0.40         0.40

Manufacturing                         0.40                1.50         0.50          0.60

Energy                                      0.30                0.60        1.20           0.40

Services                                    0.40                0.50        0.40           1.30

1. If final demand for manufacturing increases by $ 50 billion, what will be the increase in total production in each industry? In the economy as a whole?

2. Calculate the industry multiplier for services.  

3. (2 pts) A firm is producing a product using only labor and physical capital. The price of labor (wage rate) is $ 20/hour, and the cost of capital is $ 60/hour. If the marginal product of labor is 300 units an hour, what must be the marginal product of capital if the firm is a profit maximizer?      

4. (2 pts) A firm has the following production function, where Q is output, K is capital and L is labor:

Q = 400K^0.5L^0.7

Does this firm operate under increasing, decreasing or constant returns to scale, and why?

Answer 1

Q	TC
0	$ 100
1	110
2	130
3	160
4	200
5	250
6	310
7	380
8	460
9	550
10	650
11	760

a. Total Fixed Cost is equal to the Total Cost at zero output. TC = $100 at Quantity = 0. Therefore TFC = $100

b. At Q = 4, Total Cost = $200

Average Total COst = Total Cost/Quantity of Output = $200/4 = $50

c. At Q = 7, TC = $380

From (a), we obtain that the TFC = $100

Therefore, Total Variable Cost, TVC = TC - TFC = $380 - $100 = $280

Average Variable Cost = TVC/Quantity of Output = $280/7 = $40

d. At Q = 8, TC = $460

At Q = 9, TC = $550

At Q = 8, MC = TC of 9 units - TC of 8 units = $550 - $460 = $90

e.

Quantity	TC	MC
0	100	-
1	110	10
2	130	20
3	160	30
4	200	40
5	250	50
6	310	60
7	380	70
8	460	80
9	550	90
10	650	100
11	760	110

It can be observed from the above table that the marginal cost is continuously increasing from Q= 0 to Q=11. Therefore, as the quantity of output increases, the average total cost increases and hence, the firm is operating under decreasing returns to scale i.e., each additional unit of output production costs higher than the previous unit.

Ans: Decreasing returns to scale