Question

I have a preferences over books (B) and journals (J). The price of books (P_B) is $40. The price of magazines (P_J) is $20. My income (m) is $240.

Given my utility preference is U(J,B)=min(2J,B).

A) Derive the function of the Engel curve for journals. Write the answer as the quantity of journals as a function income. N(m).

B) Derive the function for the Demand curve for journals. Write the answer as the quantity of journals as a function of price of journals, J(P_J)

Answer 1

Answer

A)

Utility is given by :

U(J,B)=min(2J,B)

In order to Maximize Utility for such a perfect complements function a consumer consumes that allocation where Kink of the isoquant intersects Budget line.

Kink of isoquant of this utility function will occur where 2J = B ----------------------------(1)

Budget line is given by :

JP_J + 40B = m ----------------------------(2)

From (1) and (2) we get :

JP_J + 40*2J = m

=> J = m/(P_J + 80) ----------------------------------(3)

Now, P_J = 20

=> J = m/(20 + 80) = m/100 -

Hence, Engel Curve is given by :

J = N(m) = m/100

B)

Now Let P_J be P_J but m = 240. Putting this in (3) we get :

J = 240/(P_J + 80)

Thus, Demand curve for journals is given by :

J = J(P_J) = 240/(P_J + 80)