Question

The marginal value equation is: MV=16.40-1.00*Q
The marginal cost equation is: MC=2.20+0.59*Q

1. What are the gains from trade?  

2. What is the price elasticity of demand at equilibrium (absolute value)?  

Answer 1

(1) In free trade equilibrium, MV = MC.

16.4 - Q = 2.2 + 0.59Q

1.59Q = 14.2

Q = 8.93

P (MV) = 16.4 - 8.93 = 7.47

From MV function, when Q = 0, MV = 16.4 (Vertical intercept).

Consumer surplus (CS) = Area between MV curve and price = (1/2) x (16.4 - 7.47) x 8.93 = (1/2) x 8.93 x 8.93 = 39.87

From MC function, when Q = 0, MC = 2.2 (Vertical intercept).

Producer surplus (PS) = Area between MC curve and price = (1/2) x (7.47 - 2.2) x 8.93 = (1/2) x 5.27 x 8.93 = 23.53

Gain from trade = CS + PS = 39.87 + 23.53 = 63.4

(2)

From MV function, Q = 16.4 - MV

Elasticity of demand = (dQ/dMV) x (MV/Q) = - 1 x (7.47 / 8.93) = - 0.84

Absolute value = 0.84