Question

competitive firm is the . 4. the vert Mive is atroduction. The short-run supply curve of ortion of its short-tun marginal cost curve that is competitive firm in the above its average variable cost curve, The o ward sloping an u petitive firm is the portion of its short-run marginal cost curve that supply curve of a Leuward-sloping and lies above its long-run average cost curve. Example: A firm has the long-run cost function cy) = 2y + 200 for > 0 and c(0) = 0. Let us find its long-run supply curve. The firm's arginal cost when its output is y is MC() = 4y. If we graph output on he horizontal axis and dollars on the vertical axis, then we find that the tong-run marginal cost curve is an upward-sloping straight line through the origin with slope 4. The long-run supply curve is the portion of this surve that lies above the long-run average cost curve. When output is Jong-run average costs of this firm are AC(y) = 2y + 200/y. This is a U- shaped curve. As y gets close to zero, AC() becomes very large because 200/y becomes very large. When y is very large, AC(y) becomes very large because 2y is very large. When is it true that AC(y) < MC()? This happens when 2y + 200/y <4y. Simplify this inequality to find that AC ) < MC(y) when y> 10. Therefore the long-run supply curveis >10. So the the piece of the long-run marginal cost curve for which for v > 10. If we want to long-run supply curve has the equation find quantity supplied as a function of price, we just solve this expression for y as a function of p. Then we have y=p/4 whenever p > 40. / Suppose that p < 40. For example, what if p =20, how much will the firm supply? At a price of 20, if the firm produces where price equals long-run marginal cost, it will produce 5 = 20/4 units of output. When the firm produces only 5 units, its average costs are 2 x 5 + 200/5 = 50. Therefore when the price is 20, the best the firm can do if it produces a positive amount is to produce 5 units. But then it will have total costs of 5 x 50 = 250 and total revenue of 5 x 20 = 100. It will be losing money. It would be better off producing nothing at all. In fact, for any price p < 40, the firm will choose to produce zero output. 23.1/0) Remember Otto's brother Dent Carr, who is in the auto repair Bulness? Dent found that the total cost of repairing s cars is c(s) = 282 + 100. (a) This implies that Dent's average cost is equal to his average variable cost is equal to - -, and his marginal cost is equal On the graph below, plot the above curves, and also plot Dent's supply curve.

Answer 1

Answer 23.1

a. C(s)= 2s^2+100

Average total cost=C(s)/s=2s+100/s

Average variable cost=Total variable cost/s=2s

Marginal cost=dC(s)/s=4s

b. P=$20, MC=P

4s=20

Number of cars s=5

when P=$40

40=4s

Number of cars=10

c. When P$40, s=10 and

Total cost=ATC*Q

Total revenue Price* Quantity

Profit= TR-TC

Note-According to HOMEWORKLIB RULES first question can be answered