Chapter 2.6, Problem 85E

Supply and demand. A cordless screwdriver is sold through a national chain of discount stores. A marketing company established price-demand and price-supply tables (Tables $2$ and $3$ ), where $x$ is the number of screwdrivers people are willing to buy and the store is willing to sell each month at a price of $p$ dollars per screwdriver.

(A) Find a logarithmic regression model $\left(y=a+b\ln x\right)$ for the data in Table $2$. Estimate the demand (to the nearest unit) at a price level of $\$50$.

(B) Find a logarithmic regression model $\left(y=a+b\ln x\right)$ for the data in Table $3$. Estimate the supply (to the nearest unit) at a price level of $\text{\$50}$.

(C) Does a price level of $\text{\$50}$ represent a stable condition, or is the price likely to increase or decrease? Explain.