Exam 7: Demand Estimation and Forecasting

A forecaster used the regression equation $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$ and quarterly sales data for 2004I-2021IV (t = 1,...,64)for an appliance manufacturer to obtain the results shown below.Q is quarterly sales,and $D _ { 1 } , D _ { 2 }$ and $D _ { 3 }$ are dummy variables for quarters I,II,and III. What is the estimated intercept of the trend line in the second quarter?

problem with consumer interviews is that

The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively. The estimated QUARTERLY increase in price is ______,and the estimated ANNUAL increase in price is ______ .

The estimated demand for a good is $\hat { Q } = 4,800 - 16 P - 0.65 M - 1.5 P _ { R }$ where Q is the quantity demanded of the good,P is the price of the good,M is income,and $P _ { R }$ is the price of related good R.If the price of the good rises by $10,all else constant,the quantity demanded will ________ by ________ units.

Build-Right Concrete Products produces specialty cement used in construction of highways.Build-Right is a price-setting firm and estimates the demand for its cement by the State Highway Department using a demand function in the nonlinear form: $Q = a P ^ { b } M ^ { c } P _ { R } ^ { d }$ where Q = yards of cement demanded monthly,P = the price of Build-Right's cement per yard,M = state tax revenues per capita,and $P _ { R }$ = the price of asphalt per yard.The manager at Build-Right transforms the nonlinear relation into a linear relation for estimation.The estimation results are presented below: Given the above,if Build-Right decides to charge the State Highway Department $55 per yard for its cement when tax revenues per capita are $3,200 and the price of asphalt is $35 per yard,the expected quantity demanded is

The estimated demand for a good is $\hat { Q } = 4,800 - 16 P - 0.65 M - 1.5 P _ { R }$ where Q is the quantity demanded of the good,P is the price of the good,M is income,and $P _ { R }$ is the price of related good R.If income decreases by $2,000,all else constant,quantity demanded will ________ by _________ units.

The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively. At the 2 percent level of statistical significance,the results indicate that price in the ________ quarter is significantly lower than in any other quarter.

A forecaster used the regression equation $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$ and quarterly sales data for 2004I-2021IV (t = 1,...,64)for an appliance manufacturer to obtain the results shown below.Q is quarterly sales,and $D _ { 1 } , D _ { 2 }$ and $D _ { 3 }$ are dummy variables for quarters I,II,and III. What is the estimated intercept of the trend line in the fourth quarter?

If demand is estimated using the empirical specification $\ln Q = \ln a + b \ln P + c \ln M + d \ln P _ { R }$ ,then an equivalent expression for demand is

The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively. What is the estimated intercept of the trend line in the 1st quarter?

Build-Right Concrete Products produces specialty cement used in construction of highways.Build-Right is a price-setting firm and estimates the demand for its cement by the State Highway Department using a demand function in the nonlinear form: $Q = a P ^ { b } M ^ { c } P _ { R } ^ { d }$ where Q = yards of cement demanded monthly,P = the price of Build-Right's cement per yard,M = state tax revenues per capita,and $P _ { R }$ = the price of asphalt per yard.The manager at Build-Right transforms the nonlinear relation into a linear relation for estimation.The estimation results are presented below: Given the above,the estimated cross-price elasticity of demand for cement relative to the price of asphalt is

Possible problems with consumer interviews include:

Demand equations derived from actual market data are

The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively. At the 2 percent level of statistical significance,the estimation results indicate that price in the ________ quarter is significantly higher than in any other quarter.

Seasonal or cyclical variation in a time series model

Build-Right Concrete Products produces specialty cement used in construction of highways.Build-Right is a price-setting firm and estimates the demand for its cement by the State Highway Department using a demand function in the nonlinear form: $Q = a P ^ { b } M ^ { c } P _ { R } ^ { d }$ where Q = yards of cement demanded monthly,P = the price of Build-Right's cement per yard,M = state tax revenues per capita,and $P _ { R }$ = the price of asphalt per yard.The manager at Build-Right transforms the nonlinear relation into a linear relation for estimation.The estimation results are presented below: Given the above,if tax revenue per capita (M)increases 5%,the estimated quantity of cement demanded will

estimated demand for a good is $\hat { Q } = 4,800 - 16 P - 0.65 M - 1.5 P _ { R }$ where Q is the quantity demanded of the good,P is the price of the good,M is income,and $P _ { R }$ is the price of related good R.The coefficient on P

The estimated demand for a good is $\hat { Q } = 4,800 - 16 P - 0.65 M - 1.5 P _ { R }$ where Q is the quantity demanded of the good,P is the price of the good,M is income,and $P _ { R }$ is the price of related good R.This good and good R are

Build-Right Concrete Products produces specialty cement used in construction of highways.Build-Right is a price-setting firm and estimates the demand for its cement by the State Highway Department using a demand function in the nonlinear form: $Q = a P ^ { b } M ^ { c } P _ { R } ^ { d }$ where Q = yards of cement demanded monthly,P = the price of Build-Right's cement per yard,M = state tax revenues per capita,and $P _ { R }$ = the price of asphalt per yard.The manager at Build-Right transforms the nonlinear relation into a linear relation for estimation.The estimation results are presented below: Given the above,the estimated demand for cement is

Manager-determined prices are