Suppose that in reality the number of cars demanded, Q, depends on the real interest rate, r,

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Suppose that in reality the number of cars demanded, Q, depends on the real interest rate, r, according to an equation of the form
Q = Ar + B
Where A and B are constants. An econometrician believes that the number of cars demanded depends on the nominal interest rate, i, and uses data to estimate the coefficients C and D in the equation
Q = Ci + B
a. Express the estimated coefficients C and D in terms of the “true” coefficients A and B and the inflation rate, π.
b. Explain why this model will make good predictions as long as the inflation rate is constant.
c. Suppose that it is considered desirable to raise the demand for cars and that the government can affect i by adopting policies that lead to a change in π. What will the econometrician advise?
d. When the new policy is adopted, what happens to C and D? Explain why the recommended policy won’t work.

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