Please show work so i can learn how this was done. Thank you. 5. If supply incre
ID: 1173664 • Letter: P
Question
Please show work so i can learn how this was done. Thank you.
5. If supply increases and demand also increases, we can conclude that the new equilibrium:
The multivariate demand function (below) is needed for questions 6 – 12.
Setting: U.S. Auto manufacturers are trying to develop a multivariate function with which to estimate the demand for their gas-electric hybrid compact cars. Here is one that Motors General developed for its Jolt:
Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A
Where:
Qj = the number of Jolts demanded per week.
Pj = the price of each new Jolt (in $).
Pf = the price of each new Ford gas-electric hybrid (in $).
Pt = the price of each new Toyota gas-electric hybrid (in $).
Pb = the price of replacement batteries for the Jolt (in $).
Tc = the amount of tax credit incentive offered with the purchase of a new hybrid (in $).
Y = average weekly disposable income of a typical Jolt purchaser (in $).
Mg = the miles per gallon of gas rating of the Jolt (in miles per gallon).
A = average weekly Jolt advertising expenditure (in $).
6. If all variables remain unchanged except that the price of Jolts (Pj) increases by $1000, then the quantity demanded of Jolts will:
7. If all variables remain unchanged except that the average weekly disposable income (Y) increases by $350 then demand for Jolts will:
8. You can tell by looking at the sign of the price of Toyota hybrids (Pt) that they are considered:
Explanation / Answer
The multivariate function is given as: Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A. All these parameters are given in the question
6. All the variables are unaffected but the price of Pj increases by 1000. Therefore new price Pj* = 1000 + Pj. Putting this new price in the demand function to get the new quantity Qj*, we have:
Qj* = 65000 – 20Pj* + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A
Putting the value of Pj* = 1000 + Pj, we have:
Qj* = 65000 – 20(Pj + 1000) + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A
Cross multiplying the term in the bracket
=> Qj* = 65000 – 20Pj - 20000 + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A
= Putting all functional variables at one side and putting 20000 at the last we see:
=> Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A - 20000
Note that the underlined terms are actually terms of the demand function of Qj, that us:
=> Qj* = Qj - 20000
Therfore new quantity will be old quantity - 20000, or in other words when price of Jolts increases by 1000, the demand decreases by 20000.
7. If all variables remain unchanged except that the average weekly disposable income (Y) increases by $350 then demand for Jolts will change as follows:
We will do the same exercise as we did in the previous question. We will see how Quantity of jolts changes from the original equation when income increases.
So let new income Y* be equal to Y + 350, that is, old income + 350.
Now we will denote new qauntity demanded by Qj*.
(Note: The old equation is or equation giving Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A)
Now now new quantity demanded is when Y equals Y* =
Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05(Y*) + 10Mg + 0.04A
=> Putting Y* = Y + 350
=> Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05(Y + 350) + 10Mg + 0.04A
=> Simplyfying the bracket we have:
=> Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y* + 0.05*350 + 10Mg + 0.04A
=>Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y* + 17.5 + 10Mg + 0.04A
=> Putting all variable terms on one side we have:
=> Qj* = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y* + 10Mg + 0.04A + 17.5
Notice that the underlined terms are the same as that in equation Qj, that is:
=> Qj* = Qj + 17.5
Therefore new quantity is old quantity increased by 17.5. Therefore quantity of jolts demanded inreased by 17.5 when income increased by 350.
8. We see that the sign of Pt is postive. This means if the price of toyota increases, the quantity demand of jolts increases. We can show this by differentiating the Qj function with respect to Pt function:
d(Qj)/d(Pt) = 35
Therefore the differential is positive. This means if Pt increases, Qj will increase and if Pt decreases (i.e d(Pt) is negative then Qj will also decrease (d(Qj) is negative hence negative in numerator denominator cancel out each other)
Hence this tells us that Toyota and Jolts are substitute goods. This is because in substitute goods, if price of one increases, the quantity of the substitute good increases and if it decreases then quantity demanded of substitute good decreases.