Question #200473

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
2021-06-07T14:41:29-0400
C(q)=q38q2+30q+60C(q)=q^3-8q^2+30q+60


MC=3q216q+30MC=3q^2-16q+30MR=MC=>p=3q216q+30MR=MC=>p=3q^2-16q+30p=3(q22(83)q+649)643+30p=3(q^2-2(\dfrac{8}{3})q+\dfrac{64}{9})-\dfrac{64}{3}+30p3=(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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