Question #111389

Consider a competitive firm with initial profits given by π0 = 15, and total cost function c(q) = 10 + q^2. The market price is stochastically distributed as follows-

P˜ =(

8 with prob 1/2

2 with prob 1/2

)

If the firm manager’s utility function is given by-

u(π) = E(π) −1/9Var(π).

derive firm’s optimal output level and associated profit level.

P˜ =(

8 with prob 1/2

2 with prob 1/2

)

If the firm manager’s utility function is given by-

u(π) = E(π) −1/9Var(π).

derive firm’s optimal output level and associated profit level.

Expert's answer

Solution:

We find the price of the goods on the market as the mathematical expectation of a random variable described in the condition of the problem.

So, price will be

"\\pi=5+5q-q^2"

"\\pi=5+5\\times2.5-2.5^2=17.5-6.25=11.25"

Answer: q=2.5, "\\pi" =11.25

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