To calculate the cross elasticity of demand for good x, we use the formula:

Cross Elasticity of Demand = (% Change in Quantity Demanded of x) / (% Change in Price of y)

First, let’s calculate the percentage change in quantity demanded of x:

% Change in Quantity Demanded of x = ((New Quantity Demanded - Old Quantity Demanded) / Old Quantity Demanded) * 100

% Change in Quantity Demanded of x = ((35 - 40) / 40) * 100 % Change in Quantity Demanded of x = (-5 / 40) * 100 % Change in Quantity Demanded of x = -12.5%

Next, let’s calculate the percentage change in price of y:

% Change in Price of y = ((New Price - Old Price) / Old Price) * 100

% Change in Price of y = ((20 - 10) / 10) * 100 % Change in Price of y = (10 / 10) * 100 % Change in Price of y = 100%

Now, we can calculate the cross elasticity of demand for x:

Cross Elasticity of Demand = (-12.5% / 100%) Cross Elasticity of Demand = -0.125

The cross elasticity of demand for x is -0.125.

To determine the type of goods x and y are, we need to consider the sign of the cross elasticity of demand.

If the cross elasticity of demand is positive, it means that x and y are substitute goods. This means that when the price of y increases, the quantity demanded of x also decreases.

If the cross elasticity of demand is negative, it means that x and y are complementary goods. This means that when the price of y increases, the quantity demanded of x also decreases.

In this case, since the cross elasticity of demand for x is negative (-0.125), x and y are complementary goods.