Chapter 2, Problem 91RE

Equilibrium point. A company is planning to introduce a 10-piece set of nonstick cookware. A marketing company established price-demand and price-supply tables for selected prices (Tables $1$ and $2$ ), where $x$ is the number of cookware sets people are willing to buy and the company is willing to sell each month at a price of $p$ dollars per set.

(A) Find a quadratic regression model for the data in Table $1$. Estimate the demand at a price level of $\text{\$180}$.

(B) Find a linear regression model for the data in Table $2$. Estimate the supply at a price level of $\text{\$180}$.

(C) Does a price level of $\text{\$180}$ represent a stable condition, or is the price likely to increase or decrease? Explain.

(D) Use the models in parts (A) and (B) to find the equilibrium point. Write the equilibrium price to the nearest cent and the equilibrium quantity to the nearest unit.