Scenario 4.1:
Daniel derives utility from only two goods, cake (Qc) and donuts (Qd). The marginal utility that Daniel receives from cake (MUc) and donuts (MUd) are given as follows:
MUc = Qd MUd = Qc
Daniel has an income of $240 and the price of cake (Pc) and donuts (Pd) are both $3.
-See Scenario 4.1. Holding Daniel's income and Pd constant at $240 and $3 respectively, what is Daniel's demand curve for cake?

Question

Quizplus · Accepted Answer

Since Daniel only derives utility from cake and donuts, his budget constraint can be expressed as:
240 = 3Qc + 3Qd
But we know that MUc = Qd and MUd = Qc, so we can rewrite this as:
240 = 3Qc + 3(MUc)
240 = 3Qc + 3Qd
240 = 3Qc + 3(Qc/3)  (substituting Qd = Qc/3 from MUd = Qc)
240 = 4Qc
Qc = 60
So Daniel's demand curve for cake is:
Qc = 240/(3 + Pc) 
(substituting Qc = 60 from budget constraint)

Scenario 4.1: Daniel Derives Utility from Only Two Goods, Cake (Qc) and (Qc)