Suppose Ford currently sells $250,000$ Ford Tauruses annually. The unit cost of a Taurus, including the delivery cost to a dealer, is $$16,000.$ The current Taurus price is $$20,000,$ and the current elasticity of demand for the Taurus is $-1\mathrm{.}5.$

a$.$ Determine a profit$-$maximizing price for a Taurus.

Do this when the demand function is of the con$-$

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stant elasticity type. Do it when the demand function is linear.

b$.$ Suppose Ford makes an average profit of $$800$ from servicing a Taurus purchased from a Ford dealer. $($This is an average over the lifetime of the

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car.$)$ How do your answers to part a change?