Question

Consider the following demand and supply functions: where d is the quantity demanded, Q is the quantity supplied, P is the price, and all pa- rameters [ao, αι, βο'Al are positive constants unless otherwise stated. Denote θ as the partial derivative symbol, and Δ as the discretized units of change 1. (1 point) Derive the demand curve. What is the slope of the demand curve? A. 1 2. (1 point) What is the intercept of the demand curve (along the y axis)? ao 3. (1 point) Find the answer to this partial derivative A. -01 ao D. -20 4. (1 point) Suppose ai increases. What is the impact on the demand curve? A. Lower intercept; steeper curve B. Lower intercept; flatter curve C. Higher intercept; flatter curve D. Higher intercept; steeper curve 5. (1 point) Find the equilibrium price and quantity. D. P 6. (1 point) Suppose Bo decreases by one unit. What is the impact upon equilibrium price?

Answer 1

This is a simple question of Market equilibrium.

We have:

Qd = a0 - a1.P (Demand)

Qs = B0+B1.P (Supply)

Demand curve is written as P in terms of Q. So solving for P, we get :

P = a0/a1 - (1/a1)Q

1. Slope of demand curve = dP / dQ = - (1/a1) (ans D).

2. Intercept is the point where Q = 0 and that is a0/a1 (ans C).

3. Partial derivative dQ/dP = -a1 (ans A).

4. High a1 means lower intercept, lower absolute value of slope (ans B).

5. Equating Qd and Qs, we get equilibrium price :

a0-a1P = B0+B1P

P* = (a0-B0) / (a1+B1)

Putting this in Qs we get:

Q = B0+B1(a0-B0)/(a1+B1) = (a1B0+B1B0+B1a0-B1B0) / (a1+B1) = (a1B0+B1a0) / (a1+B1) = ans A.

6. dP*/dB0 = -1/(a1+B1)

Fall in one unit of B0 causes rise in equilibrium price by 1/(a1+B1) (ans C).