Competitive economy with finite firms

[Asd1995]

F(K,L) = SQRT[(K − 1)*L]

Consider the cost of capital to be r and the wage to be w. Both inputs are variable, and Sebastian
faces no fixed costs.

Consider now that r = 4, w = 1, and that the market demand for coffee is Qd = 20 − P. There are 7
other companies operating in this market, all with cost structures identical to Sebastian’s company.
(e) (6 points) What is the aggregate supply in this market?
(f) (6 points) Calculate the equilibrium price, aggregate quantity sold, quantity sold by each firm,
and economic profit of each firm.

[happy]

Ci = 4Qi + 4 (By equating MPK/MPL = r/w) (for each firm)
MCi = 4

Supply curve for firm i : P = 4

AS: P=4 (Because AS is horizontal summation of individual supply curve)

AD: P = 20 - Qd

AS intersect AD at P = 4 and Qd(Aggregate quantity sold) = 16
Because of symmetry in the cost, quantity sold by each firm = 2

Economic Profit of each firm = TR - TC = 8 - (8+4) = -4

[Algaeconomics]

Im getting the same answer but then aggregate supply will be 0? Cause of negative profits?
He would not shut down the firm but will produce 0?

[Asd1995]

Seems legit, just wanted to verify my solution.

[Abhitesh]

solution.pdf

[Asd1995]

Makes sense, price is not a given so P=MC should not necessarily be optimal.

[Algaeconomics]

Thanks.