Q1 Suppose a market demand function is specified as QdX 600

Q1 Suppose a market demand function is specified as: QdX = 600-2 PX (a) What is the inverse demand function? (1 Points) (b) If sellers decide to charge $2 per unit for the product, what will be the point elasticity of demand? (3 Points) (c) What is likely to be the impact on total revenue after the price increase? (2 Points) (d) Suppose the market supply function is defined as: Qsx- 10+4 Px, what will be the equilibrium quantity in units? (2 Points) (e) Suppose policy makers determine that the per unit price of this product should be $50, how much will sellers be willing to offer? Explain the effect of the regulated price? (2 Points)

Solution

a)

Q_dx = 600 - 2P_x

2P_x = 600 - Q_dx

The inverse demand function is

P_x = 300 - 0.5 Q_dx

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b) Q_dx = 600 - 2P_x

when p = $ 2, Q = 596 units

dq_dx / dp_x = -2

e_p = (dq_dx / dp_x ) * (P/Q)

e_p = - 2 * ( 2/596)

e_p = -0.00671 ( point elasticity of demand)

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c) The price elasticity of demand is inelastic which means that a price increase will result in an increase in total revenue.

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d)

Q_sx = 10 + 4P_x

Equilibrium quantity is found by equating market demand and market supply equations

Q_dx = Q_sx

600 - 2P_x   = 10 + 4P_x

P = $ 98.33

Equilibrium quantity = 403.33 or ( 403 units)