Question

Baker premium is a company producing buns in a rented factory with the rental cost of $100 per day. The wage per worker is $40 per day. The table below shows the daily amount of buns produced with a different number of workers employed in the factory

Workers	Buns
1	30
2	70
3	130
4	210
5	260
6	300
7	320
8	330

(a) Compute and explain the minimum price per bun for Baker Premium to operate in the short-run and in the long-run

(b) If the price per bun is $1.50, determine the optimal output and compute the daily profit or loss incurred by Baker Premium. Explain why this ouput is optimal

(c) Consider the utility company in a city which is the only licensed water supplier in the city. The demand for water is given by P = 10 - 0.006Q and the marginal cost of the company is given by MC = 2 + 0.004Q. Identify the optimal output, the market price, the consumer surplus, the producer surplus and the deadweight loss in the water market.

Answer 1

We need to calculate the total cost, marginal cost, average variable cost and Average cost.

In the short run the minimum price must be greater than or equal the minimum average variable cost. In the long run the price must be equal to the minimum average cost.

Refer the attached picture below

In the short run minimum price must be $ 0.76 per bun.

In the long run the minimum price must be $ 1.13 per bun.

B. When the price is $ 1.50 per bun then the Baker must hire 6 labour and the optimal output will be 300 units.

Profit = 300*1.5 - 340 = 450 - 340 = $ 110

The output is optimal since the price is greater than the marginal cost. At this output the MC is 1 and for 7 units of labor the MC is $ 2 thus the firm must not hire 7 units of labor.

C. P = 10 - 0.006Q

MC = 2 + 0.004Q

First determine the Total revenue

TR = PQ = (10 - 0.006Q)Q

Differentiate TR wrt Q

Now equate the MR to MC

P= 10 - 0.006*500 = $ 7 per unit

In case of perfect competition the profit maximization must be set equal to Marginal cost

P = MC

10 - 0.006Q = 2 + 0.004Q

0.006Q + 0.004Q = 10 - 2

0.01Q = 8

Q = 800 units

P = 10 - 0.006*800 = $ 5.2 per unit

Refer the attached picture

Consumer surplus = (1/2)*(10-7)*500 = $ 750

Dead weight loss =(1/2)*(7-4)*(800-500) = $ 450

Producer surplus =(7-4)*500 + (1/2)*(4-2)*500 = $ 2000