Question

The demand for farmed salmon from your firm is random. Assume that the market is perfectly competitive and that on any given day the price of a pound is either $4.40 or $4.80, with a probability of 1/2 for either possibility. The marginal cost of producing a pound of salmon is MC = 0.02Q.

(a) What is your firm’s expected price and expected marginal revenue?

(b) If you produce so that expected marginal revenue equals marginal cost, E[MR]= MC, how much profit is lost if the price turns out to be $4.80? How much is lost if the price turns out to be $4.40?

(c) Presuming that each day you can change the price of your salmon, what is the value of a perfect forecast of the demand?

Answer 1

Ans)- Price on a day is either $4.40 or $4.80 with a probability of 1/2.

MC = 0.02Q,

TC = integration of MC w.r.t. Q

TC = 0.02Q²/2 = 0.01Q²

a) Expected price level E(P) = 1/2(4.80) +1/2(4.40)

= $4.60

In a competitive market , P=MR

so, E(P) = E(MR)= $4.60

Because, Marginal revenue is a incremental increase in total revenue from a one unit increase in output. and in competitive market because the firms are the price taker due to the perfect competition in market hence the Price will be constant at each level of output, so the Marginal revenue will also be constant and will be equal to price level.

b) Equilibrium condition

E(MR) = MC

4.60 = 0.02Q

[Q= 230 units] -------------we wil produce 230 units At E(P)=$4.60

Now, equilibrium condition when P = $4.80

P = MC

4.80 = 0.02Q

[Q = 240] ----------------We should produce 240 at P=4.80

Actual profit when P=4.80 = TR - TC

= 230*4.80 - 0.01(230)²

= 1104 - 529 = $575

Profit at Q=240 = 240*4.80 - 0.01(240)²

= $576

Loss of profit when p=4.8 will be = 576-575 =$1

Now, equilibrium condition when P = $4.40

P = MC

4.40 = 0.02Q

[Q = 220] ----------------We should produce 220 at P=4.40

Actual profit when P=4.40 = TR - TC

= 230*4.40 - 0.01(230)²

= 1012 - 529 = $483

Profit at Q=220 = 220*4.40 - 0.01(220)²

= $484

Loss when p=4.8 will be = 484 -483  =$1

c) Perfect forecast of demand

demand at P=4.80 will be-

P = MC

4.80 = 0.02Q

[Q = 240]

Similarly demand at P = 4.40

P=MC

4.40 = 0.02Q

[Q = 220]

Probability of happening P=4.80 and P=4.40 is 1/2.

So, perfect forecast of demand will be = 240*1/2 + 220*1/2

= 230 units