Answer to Question #163074 in Math for Ajay

Question #163074

A short run cost function for an entrepreneur is

q3 − 8q2 + 30q + 60 Determine the

price at which the entrepreneur cases production in an ideal market. Also, derive the

supply function.


1
Expert's answer
2021-03-02T04:50:08-0500
MC=3q216q+30MC=3q^2-16q+30

MR=MC=>p=3q216q+30MR=MC=>p=3q^2-16q+30

p=3(q22(83)q+649)643+30p=3(q^2-2(\dfrac{8}{3})q+\dfrac{64}{9})-\dfrac{64}{3}+30

p3=(q83)2+269\dfrac{p}{3}=(q-\dfrac{8}{3})^2+\dfrac{26}{9}

(q83)2=p3269(q-\dfrac{8}{3})^2=\dfrac{p}{3}-\dfrac{26}{9}

q83=p3269q-\dfrac{8}{3}=\sqrt{\dfrac{p}{3}-\dfrac{26}{9}}

Supply function

q=p3269+83q=\sqrt{\dfrac{p}{3}-\dfrac{26}{9}}+\dfrac{8}{3}


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