Q=-5200 - 42P+20Px+5.21+0.20A+0.25M
(2.002) (17.5) (6.2) (0.09) (0.21)
R2 = 0.55 n=26 F=4.88
P = Price of Product = 500
Px = Price of leading competitor product=600
I = Price per capita = 5,500
A = monthly ependitures = 5000
a = Compute elasticities for each varilable
To compute the elasticities for each variable, we need to use the following formula:
Elasticity = (% change in quantity) / (% change in price)
For each variable, we will substitute the given values and compute the elasticities:
1. Price of Product (P):
Elasticity of P = (% change in quantity) / (% change in price)
Since we are not given any information about the quantity, we cannot compute the elasticity of P.
2. Price of leading competitor product (Px):
Elasticity of Px = (% change in quantity) / (% change in price)
Substituting the given values, Px = 600
3. Disposable income per capita (I):
Elasticity of I = (% change in quantity) / (% change in income)
We are not given any information about the change in income, so we cannot compute the elasticity of I.
4. Monthly expenditures (A):
Elasticity of A = (% change in quantity) / (% change in expenditures)
Substituting the given value, A = 5000
Calculating the elasticity values for each variable requires information about the change in quantity, price, income, or expenditures. Since we do not have this information, we cannot compute the elasticities.
To compute the elasticities for each variable, we need to calculate the partial derivatives of the equation with respect to each variable and then multiply it by the variable's value. Let's go through the process step-by-step:
To calculate the price elasticity of demand (PED), we need to differentiate the equation with respect to P and multiply it by P/Q (where Q is the quantity demanded):
PED = (∂Q/∂P) * (P/Q)
Here, the coefficient of P in the equation is -42. So, the price elasticity of demand is:
PED = (-42) * (P/Q)
Next, let's calculate the cross-price elasticity of demand (CPED) with respect to Px. Here, the coefficient of Px in the equation is 20. So, the cross-price elasticity of demand is:
CPED = (20) * (P/Q)
Now, let's compute the income elasticity of demand (IED). The coefficient of A in the equation is 0.20. So, the income elasticity of demand is:
IED = (0.20) * (P/Q)
To calculate the price elasticity of supply (PES), we need to differentiate the equation with respect to P and multiply it by P/Q:
PES = (∂Q/∂P) * (P/Q)
Since there is no term in the equation that directly represents the supply of the product, we cannot calculate PES.
Lastly, let's compute the price elasticity of supply with respect to the price of the leading competitor's product (CPES). The coefficient of Px in the equation is 20. So, the cross-price elasticity of supply is:
CPES = (20) * (P/Q)
Note: To calculate the exact values of these elasticities, we need the quantity demanded (Q). Without the quantity information, we can only express these elasticities in terms of their coefficients and variables.