Question

The Paradise Shoes Company has estimated its weekly TVC function from data collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC represents the total variable cost and Q represents pairs of shoes produced per week. And its demand equation is Q = 4100 – 25P. The company is currently producing 1,000 pairs of shoes weekly and is considering expanding its output to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2,000 per week fixed payment until the lease period ends).

1. What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
2. Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation.

Answer 1

2. From the previous estimate it was found that the maximum profit for the Paradise shoes is 1500 units produced and sold. This is why production should be increased with 1200 pairs of shoes a week.

" Perofit maximising output MR a me Mez 20+ 0.016Q MR Need to be de 1 den and function Q2 4100-259 *P2 164-2/25TR = QxP = 164Q-QYes MR 2 STR = 164-29/25 on MR= MC * 169 -20/25 : 20 +0.016Q > 2.4Q = 3600 Q 1500 Putting value of a in demand function 1500 2 4100-25p a) / P =$104 |

Assumptions are that the fixed cost increase would be less than marginal revenue generated from increasing from 1200 units to 1500.