Question 3 Martin’s Enterprise has been experiencing difficulties with respect t

Question

Question 3

Martin’s Enterprise has been experiencing difficulties with respect to the competitiveness of the price that it charges to consumers. In January 2017, a market research team used demand and supply information to arrive at the following demand and cost functions:

P= 200- 4Q; where P is the unit selling price and Q is the quantity of units in thousands.

TC= 6Q2 + 30Q + 350; where TC is total costs in thousands of dollars.

Required:

Determine the output level that would maximize profits for Martin’s Enterprise. (6 marks)

Compute the optimal price that Martin’s Enterprise should charge. (3 marks)

Calculate the revenue that would maximize profits. (3 marks)

How much profit would Martin’s Enterprise make in January 2017? (7 marks)

Advise Martin’s Enterprise on four (4) factors to be considered when setting selling price. (6 marks)

Explanation / Answer

MArginal Revenue = dTR/dQ = 200- 8Q

Marginal cost (MC) = dTC/dQ = 12Q + 30

Profit maximises at th epoint where MR = MC
200- 8Q = 12Q + 30

200 - 30 = 12Q + 8Q

1. Q = 170 / 20 = 8.5 units

2. P = 200- 4 x 8.5 = 166

3. TR = 166 x 8.5 = 1411

TC = 6 x 8.52 + 30 x 8.5 + 350 = 1038.5

4. Profit = TR - TC = 1411 - 1038.5 = 372.5

5. Selling price should be same as average revenue.

It should be at the optimal output where MR = MC.

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