Statistics Solutions

(Step-by-Step) Market Equilibrium The daily demand for beef can be modeled by D(p)=(40.007)/(1+0.033 e^0.35382 p) million pounds where the price for beef

Question: Market Equilibrium The daily demand for beef can be modeled by

\(D(p)=\frac{40.007}{1+0.033 e^{0.35382 p}}\) million pounds

where the price for beef is \(p\) dollars per pound. Likewise, the supply for beef can be modeled by

\[S(p)=\left\{ \begin{array}{*{35}{l}} 0\text{million pounds} & p<0.5 \\ \frac{51}{1+53.98{{e}^{-0.3949p}}}\text{ million pounds} & p\ge 0.5 \\ \end{array} \right.\]

where the price for beef is \(p\) dollars per pound.

  1. How much beef is supplied when the price is $\$ 1.50$ per pound? Will supply exceed demand at this quantity?
  2. Find the point of market equilibrium.

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