Answer to Question #231621 in Microeconomics for Anisha Kumar

Question

Suppose that the quantity of corn supplied depends on the price of corn (P) and the amount of rainfall (R). The demand for corn depends on the price of corn and the level of disposable income (I). The equations describing the supply and demand relationships are Q^s = 20R + 100P and Q^d = 4000 − 100P + 10I.

a)     Sketch a graph of demand and supply curves.

b)     Sketch a graph that shows the effect of an increase in rainfall on the equilibrium price and quantity of corn.

c) Sketch a graph of demand and supply curves that shows the effect of a decrease in disposable income on the equilibrium price and quantity of corn.

Answer 1

Part a

$Q^s = 20R+ 100P\\ When \space Q^s=0, P= -\frac{20R}{100}\\ Q^d= 4000-100P+10I\\ When \space Q^d=0, P= \frac{(-4000-10I)}{(-100)} = 400+0.1I\\ When \space P=0, Q^d= 4000+10I$

$At \space equilibrium : Q^s= Q^d\\ 20R+100P= 4000-100P+10I\\ 200P= 4000+10I-20R\\ P= (4000+10I-20R)/200\\ P= 20+0.05I -0.1R (Equilibrium \space price)\\ Q= 20R+100(20+0.05I-0.1R)\\ Q= 20R +2000+5I-10R\\ Q= 2000+10R +5I (Equilibrium \space quantity).\\$

Part b

Rainfall increases supply, reducing the equilibrium price and raising the quantity in equilibrium.

To clarify:

Corn supply is determined by corn (P) price and the amount of rainfall (R). The estimated supply curve is shown.

$$Qs = 20R + 100P$$

R and P both have a positive relationship with corn supply. It indicates that if the price of corn or the number of rain increases, so will the supply of corn. The essential point is that if maize prices move, the supply curve will not alter. We proceed along the supply curve, but the supply curve shifts to the right or left if the weather changes. The aforesaid scenario is depicted in the diagram.

As rainfall increases, the supply curve moves to the right, and market equilibrium prices decrease from P1 to P2. The quantity of equilibrium has risen from Q1 to Q2.

'S1' represents the new supply curve.

Part c

Maize demand is determined by the price of corn as well as disposable income. The demand function is as follows: $Q^d = 4000 - 100P + 10I$. In the demand function, the price of corn is inversely connected to the demand for maize, but disposable income (I) is inversely related to the demand for corn; if disposable income rises, the demand curve shifts to the right and vice versa.