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. Describe and derive an expression for the marginal cost (MC) curve.
2. Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).

Answer 1

TVC = 3450 + 20Q + 0.008Q2

Then, MC = 20 + 0.016Q : This is the expression for the marginal cost curve.

b) To lease the new machine, a weekly fixed payment of $2000 is required till the end of the lease period. Let's see how the cost curve (TC) changes

TC = FC + TVC (FC: fixed cost)

TC= 2000 + 3450 + 20Q + 0.008Q2

To calculate the incremental cost, we need the marginal cost of an extra pair of shoes. However, the marginal cost is not affected by any additional fixed costs. Hence the incremental cost of the extra 200 pair of shoes remains the same as before.