Suppose the current price and quantity of widgets is p = $50 and Q = 125
The demand for widgets is log-linear and the price elasticity of demand is E = -2. The supply of widgets is perfectly elastic.
a. Derive the equations for the demand and supply of widgets.
b. What would be the effect on the equilibrium price and quantity if demand were to increase by 500 widgets?
a. Because demand is log linear, the demand equation is of the form Q = Ape, where A is a positive constant and e is the price elasticity of demand. We can solve for A:
125 = A(50 )-2 A = 312,500
Demand is then given by Q = 312500p-2
Supply is horizontal and so the equation is p = 125.
b. An increase in demand will lead to Q* = 313,000 and p* = 125
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