1. Two groups of consumers live in a perfectly competitive market. The 20 consum
ID: 1123003 • Letter: 1
Question
1. Two groups of consumers live in a perfectly competitive market. The 20 consumers in Group A have identical demand curve: q- 100-20P. The 100 consumers in Group B have identical demand curve: P-5-40. The quantity demanded by a consumer in Group A isThe quantity demanded by a consumer in Group B is q, The same perfectly competitive market also has two groups of firms. The 50 firms in Group E have identical total cost function: SCE 40+24s+(1/176eThe 50 firms in Group F have identical total cost function: SC,-400 + 29, + (1/176g,. The quantity supplied by a firm in Group E is q The quantity supplied by a firm in Giroup F is g In all equations, P is the market price. (6)(4 pts, Use the market demand curve to calculate consumer surplus at the competitive equilibrium (2 pts) Calculate ga and 4, at the competitive equilibrium. (8) (3 pts) Calculate the profit of an individual firm in Group E at the competitive equilibrium. After every firm had enough time to adjust, Group E firms will[choose either exit or stay in the market] (9) (3 pts) Calculate the profit of an individual firm in Group F at the competitive equilibrium. After every firm had enough time to adjust, Group F firms will [choose either exit or stayExplanation / Answer
6. At the competitive equilibrium, the market price is $3 and the market quantity is 8,800 units. The demand curve is: Q = 22,000 – 4,400P. Inserting 0 at the place of Q in the demand curve, one knows that the vertical intercept of the demand curve is $5.
Consumer surplus = (1/2) ($5 – $3) (8,800) = $8,800.
7. The demand function of each individual firm in the market is
q = 88P – 176
Hence, qE = qF = 88(3) – 176 = 88 units.
8. Profit of an individual firm in group E
= Revenue – Cost
= (3) (88) – [40 + 2(88) + (882/176)]
= 264 – 260
= 4
The profit of an individual firm in group E is $4, which means Group E firms will stay in the market.
9. Profit of an individual firm in group F
= Revenue – Cost
= (3) (88) – [400 + 2(88) + (882/176)]
= 264 – 620
= – 356
The profit of an individual firm in group F is –$356, which is a loss. This means Group F firms will exit the market.
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