Question

In: Economics

QD=8000-2PX+0.4I+2PY-4PZ Where QD = quantity demanded of good X PX = price of good X I...

Q_D=8000-2P_X+0.4I+2P_Y-4P_Z

Where

Q_D = quantity demanded of good X

P_X = price of good X

I = consumer income, in thousands

P_Y = price of good Y

P_Z = price of good Z

a. Based on the demand curve above, is X a normal or an inferior good?

b. Based on the demand curve above, what is the relationship between good X and good Y?

c. Based on the demand curve above, what is the relationship between good X and good Z?

d. What is the equation of the demand curve if consumer incomes are $75,000, the price of good Y is $105, and the price of good Z is $80? Be careful - remember that the income in the equation is in "thousands".

e. What are the intercepts and slope of your demand curve? You do not need to draw the demand curve. Just indicate the price intercept and the quantity intercept and the slope, but show your calculations!!

f. If the price of good X is $100, what is the quantity demanded? Show your calculations!

g. Now suppose the price of good Y rises to $150. What would happen to your demand curve? What are the price intercept, quantity intercept and slope? Show your calculations!

Expert Solution

Ans QD = 8000-2PX+0.4I+2PY-4PZ

a) In the above demand function for good X is positively related with income as shown by the positive sign with income which shows that increase in income, increases demand for good X. This means that Good X is a normal good.

b) As we can see that demand for good X is positively related with price of good Y. This shows that increase in price of good Y increase demand for good X. This means that good X and good Y are substitutes goods

c) As demand for good x and price of good z is negatively related, so, increase in price of good Z decreases demand for good X which means that good X and Z are complementary goods

d) Qd = 8000 - 2Px + 0.1*75 + 2*105 - 4*80

=> Equation of demand curve for good X,

Qd = 7897.5 - 2Px

*As I have to bind by some guidelines, so, I am doing first four parts only. For the rest please reupload the them on the portal.

Rahul Sunny answered 2 years ago

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