Answer to Question #262862 in Microeconomics for neoyame

Question

Suppose the absolute values of the intercept and slope of the demand function

are approximated to be ten (10) and three (3) respectively. If the absolute

values of the intercept and slope of the supply function are assessed to be six (6),

and five (5) respectively, calculate equilibrium price and quantity (4 Marks)

- Suppose the intercept of the demand function increases by two (2), while the

slope remains the same. If the supply function remains the same, estimate the

new equilibrium price and quantity (4 Marks)

- Demonstrate graphically, the effect of the increase in the intercept of the

demand function in (b) above on the equilibrium quantity and price. What

generalization can you come up with from the resulting graphical analysis?

(7 Marks)

Answer 1

a) Given, the absolute value of the demand curve slope is 3, and the intercept value is 10. then, the equation will be D=-3P +10 or D=10−3P

Similarly, given the absolute values, the equation of the supply curve will be S=6+5P

$10-3p=6+5P\\10-6=5P+3P\\4=8P\\p=\frac{4}{8}\\=0.5$

and

$D=10−3×0.5\\=10−1.5\\=8.5$

The equilibrium price is 0.5, and the equilibrium quantity is 8.5.

b) The intercept of the demand curve increases by 2 without a change in slope, which means the new demand equation will be D=12−3P. The supply curve is unchanged. Then the new equilibrium will be achieved where the new demand curve intersects the supply curve. Thus,

$12−3P=6+5P\\12-6=5P+3P\\6=8P\\p=\frac{6}{8}\\=0.75$

and

$D=12−3×0.75\\=12−2.25\\=9.75$

The new equilibrium price is 0.75, and the quantity is 9.75.

c) An increase in the intercept of the demand curve will shift the demand curve upwards by the intercept parallel as the slope is unchanged. This will increase the equilibrium price and quantity. There will be an upward movement along with the supply due to a price increase. The interaction is illustrated below.

The intercept value of demand curves represents the factors that affect the demand other than the own price. An increase in intercept implies that the shift in the demand curve is due to the change in other factors responsible for changing the demand. Changes in the product's price will cause a movement along the demand curve, whereas other factors' changes will shift the demand curve parallel as there is no change in the slope.