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# Answer to Question #111389 in Microeconomics for Ansh

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.
1
2020-04-22T11:42:41-0400

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.

"M(p) =\\displaystyle\\sum_{i=1}^n price_i probability_i"

So, price will be

"P=8\\times \\frac{1}{2}+2\\times \\frac{1}{2}=5"

"MC=P"

"MC=C^\/(q)=2q"

"2q=5"

"q=2.5"

"\\pi=15+(TR-TC)"

"\\pi=15+5q-10-q^2"

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

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

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