Question

Graphic Tees is a design company that sells custom printed t-shirts. The firm sells printed t-shirts under a block pricing scheme that charges $16 per t-shirt if the customer buys up to 10 t-shirts and $13 if they buy 11 to 20 t-shirts. The demand curve is Q = 1200 - 50P, and the marginal cost of a t-shirt is $7. What are the profits for Graphic Tees under this block pricing scheme?

Answer 1

Let Block 1 be where P1 = 16, Q1 is the quantity sold, Π1 be the profit and TC1 be the total cost.

Let Block 2 be where P2 = 13, Q1 is the quantity sold, Π2 be the profit and TC2 be the total cost.

Quantity sold in block 1 is, Q1 = 1200 - 50P and in block 2: Q2 = 1200 - 50P

Substituting values of P, we get quantity in the two blocks.

Q1 = 1200 - 50 * 16 =1200 - 800 =400 Q2 = 1200 - 50 * 13 = 1200 - 650 = 550

Total revenue (TR) = Price * quantity. Therefore,

TR1 = P1 * Q1 = 16 * 400 = 6400 TR2 = 13 * 550 = 7150

Profit (Π) = Total revenue - Total cost (we know the marginalcost (MC). Total cost = MC * Q TC1 = 7*400 = 2800; TC2 = 7*550 = 3850)

Π1 = 6400 - 2800 = 3600   Π2 = 7150 - 3850 = 3300

So, in block 1 (where price = 16), firm will sell 400 units of t-shirts and make $ 3600 profits.

In block 2, (where price= $13) firm will sell 550 units of t-shirts and make a profit of $3300