Question

Consider the market for a homogeneous good (say bananas). The demand function is q ^d (p) = αp^ε , where α > 0 is a constant, and ε < 0 stands for the elasticity of demand. The supply function is q s (p) = p ^η , where η > 0 stands for the elasticity of supply. Write Python codes to analyze this market in the following cases.

(a) Set α = 1 and consider the following values for the elasticities: ε = −1 and η = 2. Plot the two indirect functions (note: the price has to be on the y-axis). Report the equilibrium price and quantity.

(b) Now set α = 2 and consider the following values for the elasticities: ε = {−2; −0.5} and η = {1; 3}. Write a do-loop where at each iteration the equilibrium price and quantity are computed and displayed (for all four combinations). Report these four set of values in a table and comment.

(c) Now consider a different demand function, namely q ^d (p) = e ^−p − 0.01p. The supply function is q ^s (p) = p ² . Adapt the code we discussed in class to find the numerical solution of the market equilibrium (note: the procedure might fail when using a poor initial guess). Report the solution.

Answer 1

What is 'Price Elasticity Of Demand'
Price elasticity of demand is a measure of the relationship between a change in the quantity demanded of a particular good and a change in its price. Price elasticity of demand is a term in economics often used when discussing price sensitivity. The formula for calculating price elasticity of demand is:

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

If a small change in price is accompanied by a large change in quantity demanded, the product is said to be elastic (or responsive to price changes). Conversely, a product is inelastic if a large change in price is accompanied by a small amount of change in quantity demanded.