Question

Assume that there are 6 firms producing a good and all have the cost function C[y] = 0.5 y 2+8 (MC[y] = y), where y is the quantity of the good a single produces. Use this information to answer the following questions.

(c) If demand is given by X[p] = −10p + 80, at what price will the market clear in the short-run? How many units will be sold in the short-run?

(e) Calculate the total profit / loss each firm is making / incurring by selling the good at the price you found in (c). At that level of output, are there economies of scale or diseconomies of scale?

Answer 1

C(y) = 0.5y² + 8

Firm supply function being its MC curve,

Firm supply: p = y

Since there are 6 firms,

Market supply (Y) = 6y

y = Y/6

p = Y/6

Y = 6p (market supply)

(c)

In short run equilibrium, market demand equals market supply.

-10p + 80 = 6p

16p = 80

p = 5

Y = 6 x 5 = 30

y = 30/6 = 5

(e)

When p = y = 5,

Revenue (R) = p x y - 5 x 5 = 25

Cost (C) = (0.5 x 5 x 5) + 8 = 12.5 + 8 = 20.5

Profit per firm = R - C = 25 - 20.5 = 4.5

From cost function, Average cost (AC) = C(y)/y = 0.5y + (8/y)

Slope of AC = dAC/dy = 0.5 - (8/y²)

When y = 5, dAC/dy = 0.5 - [8 / (5 x 5)] = 0.5 - (8/25) = 0.5 - 0.32 = 0.18

Since dAC/dy > 0, the AC function is increasing with increase in output. This signifies diseconomies of scale.