1) The Demand and Supply Functions of a two-commodity market model are as follows: Qd1 =...

1) The Demand and Supply Functions of a two-commodity market model are as follows:

Qd1 = 10 - 2P1 +P2

Qs1 = -2 + 3P1

Qd2 = 15 + P1 - P2

Qs2 = -1 + 2P2

a. Find Pi* and Qi* (i = 1, 2). (Use fractions rather than decimals).

b. Based on this two-commodity model, what can you infer about the relationship between good 1 and good 2?

c. What is the economic meaning of the coefficient of P1 in the equation Qd1 = 10 - 2P1 + P2

Solutions

Expert Solution

a. Equilibrium occurs when Qd = Qs
At i = 1, Qd1 = Qs1 gives,
10 - 2P1 +P2 = -2 + 3P1
So, P2 = 3P1 + 2P1 -2 -10
So, P2 = 5P1 - 12

At i = 2, Qd2 = Qs2 gives,
15 + P1 - P2 = -1 + 2P2
So, 2P2 + P2 = 15 + P1 + 1
So, 3P2 = 16 + P1
So, 3(5P1 - 12) = 16 + P1 (as P2 = 5P1 - 12)
So, 15P1 - 36 = 16 + P1
So, 15P1 - P1 = 16 + 36
So, 14P1 = 52
So, P1* = 52/14 = 3.71

So, P2* = 5P1 - 12 = 5(3.71) - 12 = 18.55 - 12 = 6.55

Q1* = -2 + 3P1 = -2 + 3(3.71) = -2 + 11.13 = 9.13

Q2* = -1 + 2P2 = -1 + 2(6.55) = -1 + 13.1 = 12.1

b. We can find the cross price elasticity of demand to find the relationship between good 1 and good 2.
Cross price elasticity of demand of good 1 with respect to price of good 2, e = $\frac{\partial Qd1}{\partial P2}\times \frac{P2*}{Q1*}$

From demand equation, $\frac{\partial Qd1}{\partial P2} = 1$

So, e = (1)*(6.55/9.13) = 0.72
As cross price elasticity is positive so good 1 and good 2 are substitutes.

c. Coefficient of P1 in the equation Qd1 = 10 - 2P1 + P2 is -2. This means that as price of good 1 increases by 1 unit then quantity demanded of good 1 decreases by 2 units.

Rahul Sunny answered 1 year ago

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