Question

The table below shows total utility in utils that a utility maximizing consumer receives from consuming two goods: Carrots and Cakes

       Carrots                                                   Cakes

Quantity            Total Utility                      Quantity         Total Utility

0                          0                                           0                    0

1                          20                                         1                    30

2                          35                                         2                    50

3                          45                                         3                    65

4                          50                                         4                    75

5                          52                                         5                    80

Assume that Carrots cost 1$ each, Cakes cost $2 each, and the consumer spends the entire income of $7 on Carrots and Cakes.

a. What is the maximum amount of cakes and carrots that this person can consume.

i. Cakes: ___________________

ii. Carrots: __________________

b. Determine what level of utility each of these bundles gives this person.

i. 5 carrotts and 1 cake: ________________

ii. 1 carrot and 3 cakes: _________________

c. Which bundle will maximize utility for this person?

This person will consume  carrots and  cakes: __________________

please help!!! this is econ 2302

Answer 1

a.

i. Maximum amount of cakes = Income/Price of cakes = 7/2 = 3.5
ii. Maximum amount of carrots = Income/Price of carrots = 7/1 = 7

b.
i. 5 carrots and 1 cake: Total utility from carrots + Total utility from cakes = 52 + 30 = 82
ii. 1 carrot and 3 cakes: Total utility from carrots + Total utility from cakes = 20 + 65 = 85

c. When carrots = 3; MU/Price = Change in total utility/Price = (45-35)/1 = 10/1 = 10
When cake = 2; MU/Price = Change in total utility/Price = (50-30)/2 = 20/2 = 10
Total cost = Price of carrots*Quantity + Price of cakees(Quantity) = 1*3 + 2*2 = 3 + 4 = 7 = income
So, this is the utility maximizing affordable bundle.
Thus, this person will consume 3 carrots and 2 cakes.