suppose the demand curve for a product is given by Q=10-2P+Ps1,where P is the price of the product and Ps is the price of a substitute good. the price of the substitute good is $2.00.

a)suppose P=$1.00, what is the price elasticity of demand?what is the cross- price elasticity of demand?

b)suppose the price of the good, P, increases to $2.00. Now what is the price elasticity of demand, and what is the cross-prices elasticity of demand?

Let us say the price of widgets is $1.00. At this price, consumers demand 10 widgets. Now the widget seller increases the price to $1.50. At this new higher price, quantity demanded falls to 9 widgets. Are widgets elastic or inelastic? Please show your work.

To calculate the price elasticity of demand, you need to use the following formula:

E = (% change in quantity demanded) / (% change in price)

a) Let's start with the first part of the question. Suppose P = $1.00 and Ps = $2.00.

To find the quantity demanded, we substitute P and Ps in the demand equation:

Q = 10 - 2P + Ps
Q = 10 - 2(1) + 2
Q = 10 - 2 + 2
Q = 10

Now, let's calculate the price elasticity of demand. To do this, we need to find the percentage change in quantity demanded and the percentage change in price.

First, we need to find the initial quantity demanded and the new quantity demanded.

Initial quantity demanded: Q1 = 10 units
New quantity demanded: Q2 = 10 - 2(1.01) + 2

Now, let's calculate the percentage change in quantity demanded:

% change in quantity demanded = (Q2 - Q1) / Q1 * 100
% change in quantity demanded = (Q2 - 10) / 10 * 100

Next, we calculate the percentage change in price:

% change in price = (P2 - P1) / P1 * 100
% change in price = ($1.01 - $1.00) / $1.00 * 100

Now, we can plug these values into the formula for price elasticity of demand to find the answer.

Price elasticity of demand = (% change in quantity demanded) / (% change in price)

b) For the second part of the question, suppose the price of the good, P, increases to $2.00. Now we need to calculate the new price elasticity of demand and the new cross-price elasticity of demand.

Again, we need to find the initial quantity demanded and the new quantity demanded.

Initial quantity demanded: Q1 = 10 units
New quantity demanded: Q2 = 10 - 2(2.01) + 2

Calculate the percentage change in quantity demanded:

% change in quantity demanded = (Q2 - Q1) / Q1 * 100
% change in quantity demanded = (Q2 - 10) / 10 * 100

Calculate the percentage change in price:

% change in price = (P2 - P1) / P1 * 100
% change in price = ($2.01 - $2.00) / $2.00 * 100

Finally, plug these values into the formula to calculate the new price elasticity of demand and the new cross-price elasticity of demand.

a) To calculate the price elasticity of demand, we need to use the following formula:

Elasticity = (% change in quantity demanded) / (% change in price)

Let's start with the first question:
If P = $1.00, we can substitute it into the demand equation and calculate the quantity demanded:
Q = 10 - 2P + Ps
Q = 10 - 2(1) + 2
Q = 10 - 2 + 2
Q = 10

Now, let's calculate the quantity demanded when P increases by 1%:
Q_new = 10 - 2(1 + 0.01) + 2
Q_new = 10 - 2.02 + 2
Q_new = 9.98

Next, let's calculate the percentage change in quantity demanded:
% change in quantity demanded = (Q_new - Q) / Q * 100
% change in quantity demanded = (9.98 - 10) / 10 * 100
% change in quantity demanded = -0.02%

Now, let's calculate the percentage change in price:
% change in price = (P_new - P) / P * 100
% change in price = (1.01 - 1) / 1 * 100
% change in price = 1%

Finally, we can calculate the price elasticity of demand:
Price elasticity of demand = (% change in quantity demanded) / (% change in price)
Price elasticity of demand = (-0.02% / 1%)

To calculate the cross-price elasticity of demand, we use the same formula but substitute the price of the substitute good instead of the own price of the product. In this case, the price of the substitute good is fixed at $2.00.

Cross-price elasticity of demand = (% change in quantity demanded) / (% change in price of substitute good)

As the price of the substitute good is fixed, the cross-price elasticity of demand would be zero.

b) Now, if the price of the good increases to $2.00, we can repeat the calculations.

Q_new = 10 - 2(2) + 2
Q_new = 10 - 4 + 2
Q_new = 8

% change in quantity demanded = (Q_new - Q) / Q * 100
% change in quantity demanded = (8 - 10) / 10 * 100
% change in quantity demanded = -20%

% change in price = (P_new - P) / P * 100
% change in price = (2 - 1) / 1 * 100
% change in price = 100%

Price elasticity of demand = (% change in quantity demanded) / (% change in price)
Price elasticity of demand = (-20% / 100%)