Task: Carolina Textiles, Inc., is a small manufacturer of cotton linen that it sells in a perfectly competitive market. Given $100,000 in fixed costs per day, the daily total cost function for this product is described by:
TC = $100,000 + $2Q + $0.0625Q2
MC = dTC/dQ = $2 + $0.125Q
where Q is units of cotton linen produced per day. Assume that MC > AVC at every point along the firm's marginal cost curve, and that total costs include a normal profit.
1. Derive the firm's supply curve, expressing quantity as a function of price.
2. Derive the market supply curve if North Carolina Textiles is one of 1,000 competitors.
3. Calculate market supply per day at a market price of $47 per unit.