The demand function for a good is: Q_d = a -bp and the supply function is: Q_s =

Question

The demand function for a good is: Q_d = a -bp and the supply function is: Q_s = c + ep where a, b, c, and e are positive constants. Calculate the current market equilibrium price (p) and quantity (Q). Illustrate this equilibrium on a well annotated graph. Illustrate graphically how and why the equilibrium would change if the price of a complementary good decreased. (Please do this on a graph of its own) Illustrate graphically how and why the equilibrium would change if the price of factor inputs increased. (Please do this on a graph of its own) How would von expect a to change (if at all), given an overall decrease in consumer wealth (or income). Illustrate graphically any change in the equilibrium price and quantity. (Please do this in a graph of its own)

Explanation / Answer

At equilibrium,

Qd=Qs

Or,a-bp=c+ep

Or,p(b+e)=a-c

Or,p=(a-c/b+e)

This is the equilibrium price.

Puttng value of p we get,Qd=a-bp=a-b*(a-c/b+e).

b) I am unable to show diagram as my system doesnot support it.

c)As we know that when complementary goods exhibit a negative cross elasticity of demand that means when the price of good Y rises, the demand for good X falls.Here the condition is given that price of complementary good decreased so the demand for other good will definately rise.Sorry as I failed to attach the diagram.

d)Input price refers to the factor price.For example in production we use capital and labour as input where cost of capital is rent and cost to labour is wage.When there is increase in factor input price then suppliers of final goods and services faced rising costs and had to reduce their supply at all price levels.The decrease in aggregate supply, caused by the increase in input prices, so AS curve will shift left.

e)When there is decrease in consumer wealth or income then Now if we have a change in people’s income --- the economy gets better or income tax goes down --- everything else equal we will see an increase in demand. An increase in demand results in a rightward shift of the demand curve. As soon as the demand curve shifts to the right, we are no longer in equilibrium at our current price and quantity.

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