Question

1. (a) A micro-entrepreneur produces caps and hats for women. The output-cost data of the business is reproduced below:

Output	Total Cost
50	870
100	920
150	990
200	1240
250	1440
300	1940
350	2330

TC = 944.29 - 2.24Q + 0.02Q²

Using the above estimated total cost equation determine the average and marginal cost functions. Determine the output rate that will minimize average cost and the per-unit cost at that rate of output. The current market price of caps and hats per unit is Tk. 6.00 and is expected to remain at that level for the foreseeable future. Should the firm continue its production?

(b) Using the following cost data how would you estimate your short run supply curve. If there are 100 firms in the industry, would be the industry supply? [ Hint. Think about the relationship between MC and AVC and find the output supply of a single a firm]

OUTPUT	FC	VC	TC	ATC	AVC	MC
0			100
1			125
2			145
3			157
4			177
5			202
6			236
7			270
8			326
9			398
10			490

Answer 1

1)

Output	Total Cost
50	870
100	920
150	990
200	1240
250	1440
300	1940
350	2330

Total Cost = 944.29 - 2.24 * Q + 0.02Q2

Average Cost = (Total Cost / Q) = (944.29 / Q) - 2.24 + 0.02Q

Marginal Cost (Derivative of Total Cost with Respect to Q) = -2.24 + 0.04Q

Point at which average cost is minimized when first derivative of average cost is equal to zero which is (-944.29 / Q2) + 0.02 = 0

Q = 217.29

Output	Total Cost	Price	Total Revenue	Marginal Revenue	Marginal Cost	Profit	Average Variable Cost
50	870	6	300	-	-	-570	17.4
100	920	6	600	300	50	-320	9.2
150	990	6	900	300	70	-90	6.6
200	1240	6	1200	300	250	-40	6.2
250	1440	6	1500	300	200	60	5.8
300	1940	6	1800	300	500	-140	6.5
350	2330	6	2100	300	390	-230	6.7

There is only one point when the firm is making profit which is 250 units of production. At all other level of production,. marginal revenue is less than average variable cost which induce firm to shut down.

2) TC at output level of 0 is fixed cost

FC + VC = TC

ATC = TC / Outpt

AVC = VC / Output

MC = TC from current unit - TC from previous unit

Output	FC	VC	TC	ATC	AVC	AFC	MC
0	100	0	100	-	-	-	-
1	100	25	125	125.00	25.00	100.00	25
2	100	45	145	72.50	22.50	50.00	20
3	100	57	157	52.33	19.00	33.33	12
4	100	77	177	44.25	19.25	25.00	20
5	100	102	202	40.40	20.40	20.00	25
6	100	136	236	39.33	22.67	16.67	34
7	100	170	270	38.57	24.29	14.29	34
8	100	226	326	40.75	28.25	12.50	56
9	100	298	398	44.22	33.11	11.11	72
10	100	390	490	49.00	39.00	10.00	92