Question

Use the following information to answer the four questions that follow. Marcus has the following utility function for quantities of Apples (A) and Eggs (E): U(A,E)=A2E. The marginal rate of substitution is MRS=2E/A where A is the x-axis good. Apples sell for pA=10 and eggs sell for pE=20. His income which he spends on these two goods is m=600.

14) Marcus’ budget constraint can be written A) 10A+20E=600 B) 600+10A=20E C) 20+30=600(A+E) D) 600=20E=10A

15) If Marcus maximizes utility, how many Apples will he consume? A) 10 B) 20 C) 30 D) 40

16) If Marcus maximizes utility, how many Eggs will he consume? A) 10 B) 20 C) 30 D) 40

17) Suppose the price of Apples rises to pA=15 while at the same time Marcus’ income rises such that the original quantity of Apples and Eggs he consumed is still exactly affordable. Then we can conclude that Marcus is

A) no better or worse off from the income and price change. B) better off and will consume more apples and less eggs than before. C) better off and will consume less apples and more eggs than before. D) worse off and will reduce both consumption of eggs and apples.

Answer 1

14.
A) 10A+20E=600

Pa = 10, pE = 20 and m = 600
The budget equation is Pa*A +pE*E = 600

15 & 16:
MRS = MUa/MUE = 2E/A
The optimal bundle is defined as MRS = Pa/PE
2E/A = 10/20
2E/A = 1/2
A = 4E - substitute this in budget equation: 10A+20E=600
10*4E+20E=600
60*E = 600
E = 10 (Q16) and A = 40 (Q15)

17. A) no better or worse off from the income and price change.

Now pA=15 while PE = 20. His new income = 15*40 + 20*10 = 800
Recall the optimal condition: A = 4E - substitute this in new budget equation: 15A+20E=800 (notice that income has increased).
15*4*E + 20*E = 800
80*E = 800
E = 10 and A = 4*10 = 40.

We can see that optimal quantity has not changed. Hence, he's no better or worse off.