Question

The demand curve for grilled cheese sandwiches has been estimated using statistical techniques as follows: log(Q) = -1.10 - 0.18log(P) + 1.21log(I) + 0.84log(Ph) where Q is the quantity of grilled cheese sandwiches P is the price of grilled cheese sandwiches I is income Ph is the price of hamburgers. Thats all information

a. If P = $1,000, calculate the price elasticity of demand

b. Draw the Engel curve. (just show the shape, don’t need to show specific point)

c. What is the relationship between hamburgers and grilled cheese sandwiches?

Answer 1

Solution:

a) Price elasticity of demand, ed =

We can find as follows: differentiating the equation with respect to P

(1/Q)* = -0.18*(1/P)

So, = -0.18*Q/P

So, ed = -0.18*(Q/P)*(P/Q) = -0.18

So, a percentage increase in price results in a percentage decrease in quantity demanded by 0.18.

b) Engel curve depicts relation between income and quantity demanded, that is how income affect demand. Thus, from given equation, Engel curve can be drawn as:

c) Notice that price of hamburgers, Ph, has the coefficient estimate of +0.84. That is the price of hamburgers is positively related with the demand for grilled cheese sandwich. This indicates that hamburgers and grilled cheese sandwich are substitutes, and hence can be replaced for each other.

This is because as price of burgers go up, it becomes more expensive and so people reduce it's demand and increase demand for sandwich as they can be consumed in place of each other.