Question

Demand for goods X with approval:

Qdx = 34 - 0.8Px + 0.3Py + 0.041

a) Determine the price elasticity of the demand for goods X at the price Px = 10; the price of goods Y at the price Py = 20 and consumer income = 5,000. Explain the coefficient of price elasticity of the demand for goods X.

b) Find the cross elasticity between item X and item Y at the price Px = 10; the price of goods Y at the price Py = 20; and Consumer income I = 5,000. Explain the value of the coefficient of elasticity between item X and item Y.

c) Determine the elasticity of consumer income against the demand for goods X at the price Px = 10; the price of goods Y at Py = 20; and consumer income | = 5,000.

d) Explain the value of the coefficient of elasticity of consumer income against the demand for goods X ...

Answer 1

Given,

Plug in the given values in the above equation

The elasticity of demand can be measured as

The first part of elasticity equation we can determine by differentiating Demand function wrt Px we get

Plug in these in spasticity equation we get

The elasticity of demand is less than 1 therefore it is price inelastic.

B. The quantity demanded we have already calculated in the above part here we are required to calculate the cross elasticity of demand between the two goods X and Y. First of all differentiate quantity demanded with respect to to price off Y we get

Differentiating the above equation with respect to Py

The cross elasticity of demand can be calculated using the following formula

Plug in The values in the above equation we get

The cross elasticity of demand between good X and Y is greater than zero, that is it is a positive number hence that too good are substitute to each other.

C. In this case we are required to calculate the income elasticity of demand the quantity demanded we have already calculated in the part A.

The income elasticity can be measured using the following

Demand function is as follows

Differentiating the above equation with respect to I we get

Plug in the calculated value into the equation

The income elasticity of demand is positive therefore the good is a normal commodity.

D. Income elasticity of demand we have calculated and it is equal to 0.862.

As we know the income elasticity of demand is defined as the percent change in quantity demanded due to the percent change in income mathematically it can be represented as follows

By the coefficient of income elasticity of demand we mean that if there is an increase of 1% in consumers income the demand of commodity X will increase by 0.862%.

Similarly if the consumers income increases by 10% then the quantity demanded of commodity X will increase by 8.62%.

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