a) Show that a business operating in an industry of perfect competition has a supply curve which is identical to its marginal cost curve above its average variable cost.
Perfect competition is a market which consists of many firms selling identical products to many buyers, at a price set by the market. There are no restrictions on entry or exit and buyers are assumed to have perfect knowledge about price. Industries such as fishing and dry cleaning could be considered as close examples to perfect competition.
The firms in a perfectly competitive industry are price takers, which means that they adopt the price set by the market. The firms being profit maximizers would always produce at the profit maximizing output, where Marginal cost equals Marginal revenue. Marginal revenue being the additional revenue firms earn by selling an extra unit of output, is equal to the price while marginal cost is the additional cost incurred due to production of an additional unit of output.
While the demand curve of a firm in a perfectly competitive industry is the same as its average revenue (price), it will have a supply curve which is identical to the marginal cost curve above the average variable cost curve. This could be explained with the use of a diagram.
Figure 1 shows the cost and revenue curves of David who produces wheat in a perfectly competitive market. The U-shaped curves on the graph shows the costs. The horizontal lines show the market price adopted by David, which is the same as his marginal revenue. As we can see from the above diagram the initial price is 30 pounds. Being a profit-maximizing firm he produces where marginal cost equals marginal revenue. Thus at a price of 30 pounds, he produces 10 units.
Let us consider a lower price. As with the previous case, the interaction of market demand and supply leads to a lower price at 20, which is adopted by David. At the price of 20 pounds, David's Marginal revenue is equal to the Average variable cost and is lower than Average total cost, resulting in an economic loss equal to his total Fixed cost. This point of intersection is known as the shutdown point. David could either continue producing 8 units at 20 pounds or temporarily shutdown his business. However if the price falls below 20 pounds David would stop producing.
Therefore, since the intersection of Marginal cost and Average variable cost (shutdown point) shows the lowest price at which a firm will produce and since firms will produce at any point above this given that MC=MR, we can say that the supply curve of a firm operating in a perfect competition is identical to the Marginal cost curve above Average variable cost.
b) Show that in the long run, the price of the good supplied by a perfectly competitive industry is wholly determined by the cost structure of the business and not by demand conditions at all.
The long run in a perfect competition refers to a condition where no firm in the industry is earning economic profit and all firms produce at the minimum of Long run average cost. This means that in the long run the price of a good supplied by a firm in perfect competition is wholly determined by the cost structure.
Figure 2. Industry Firm
As we can see from figure 2, initial price of the industry is at P where the quantity is Q. The firm adopts the market price and produces at the profit maximizing output where quantity is Q units, earning an economic profit per unit equal to the difference between its MR0 and LRATC. However this profit attracts others to enter the market resulting in an increase in supply. The supply curve shifts to the right from S to S1 which results in a fall in a the market price from P to P1 and an increase in quantity from Q to Q1. The firm again adopts the new price P1 and produces at the profit