pb = 70 -0.0005qb(brand name) pp = 20-0.0002qp (private label). Marginal cost is a constant $10 per tire.quantities are measured in thousands per month and price refers to the wholesale price. marginal cost is a constant $10 per tire. american currently sells brand name tires at a wholesale price of $28.50 and private label tires for a price pf $17. Are these prices optimal for the firm?
To determine if the prices are optimal for the firm, we need to compare the current prices with the marginal costs and demand equations provided.
The demand equations for the brand name (pb) and private label (pp) tires are given as:
pb = 70 - 0.0005qb (brand name)
pp = 20 - 0.0002qp (private label)
The marginal cost is a constant $10 per tire.
Given that the firm currently sells brand name tires at a wholesale price (pb) of $28.50 and private label tires for a price (pp) of $17, we can calculate the corresponding quantities demanded for each type of tire.
For brand name tires:
Plug pb = $28.50 into the brand name demand equation:
28.50 = 70 - 0.0005qb
Subtracting 70 and multiplying by -1 on both sides:
41.50 = 0.0005qb
Divide by 0.0005 on both sides:
qb ≈ 83,000
For private label tires:
Plug pp = $17 into the private label demand equation:
17 = 20 - 0.0002qp
Subtracting 20 and multiplying by -1 on both sides:
3 = 0.0002qp
Divide by 0.0002 on both sides:
qp ≈ 15,000
Now, we can calculate the total cost for each type of tire based on the quantities demanded and the marginal cost of $10 per tire.
For brand name tires:
Total cost = qb * $10
Total cost = 83,000 * $10 = $830,000
For private label tires:
Total cost = qp * $10
Total cost = 15,000 * $10 = $150,000
Finally, we compare the total cost for each type of tire with the revenue generated from selling them at the current prices.
For brand name tires:
Revenue = qb * pb
Revenue = 83,000 * $28.50 ≈ $2,365,500
For private label tires:
Revenue = qp * pp
Revenue = 15,000 * $17 ≈ $255,000
Based on these calculations, we can see that the revenue generated from selling brand name and private label tires at the current prices is significantly higher than the corresponding total costs. Therefore, the current prices of $28.50 for brand name tires and $17 for private label tires are optimal for the firm.