2-(a) Sue has a monopoly over the production of strawberry shortcake. Her cost f

Question

2-(a) Sue has a monopoly over the production of strawberry shortcake. Her cost function is C(y) y+10y. The market demand curve for strawbeny shortcake is p (y) = 1 00- y Sue's profit maximising level of output is as the profit. and the price is She obtains Because the consumers surplus is the total welfare is QUESTION5 2-(b) Suppose the dictator decides to force Sue to price at marginal cost. Her new level of output is and the new price is Her profit is Now the consumer surplus is thus the total welfare is

Explanation / Answer

C(y) = y2 + 10y

Marginal cost (MC) = dC(y) / dy = 2y + 10

p = 100 - (y/2) = 100 - 0.5y

Profit is maximized by equating MR with MC.

Total revenue (TR) = p x y = 100y - 0.5y2

MR = dTR / dy = 100 - y

Equating with MC,

100 - y = 2y + 10

3y = 90

y = 30

p = 100 - (30 x 0.5) = 100 - 15 = 85

From demand function, when y = 0, p = 100 (Reservation price)

Consumer surplus = Area between demand curve and market price = (1/2) x (100 - 85) x 30 = 15 x 15 = 225

(Part b)

When p = MC,

100 - 0.5y = 2y + 10

2.5y = 90

(i) y = 36 [New output]

(ii) p = MC = (2 x 36) + 10 = 72 + 10 = 82 [New price]

(iii) Profit TR - C(y)

TR = 82 x 36 = 2,952

C(y) = (36 x 36) + (10 x 36) = 1,296 + 360 = 1,656

Profit = 2,952 - 1,656 = 1,296

(iv) New Consumer surplus = (1/2) x (100 - 82) x 36 = 18 x 18 = 324

Now the Consumer surplus is higher (324 > 225), thus total welfare is higher.

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