# Saint Mary’s University Demand Function Utility Function Math Practice

### Question Description

I’m working on a micro economics discussion question and need a sample draft to help me study.

Question 2

Given the Utility function U(X,Y) = 6X + 5Y, where the MUx = 6 and MUy = 5

a)  If income was 1,050, and the price of X was 10.75 and Y was 4.25, How much utility would this consumer obtain given that he is maximizing utility ? (2 decimal precision)

b)  Illustrate 1 indifference curves for Utility equal to 120. Make sure to identify at least 3 sets of coordinates for the curve.

c)  Obtain the demand function for Y.

NOTE: Show all your work, even if you get it wrong you may get points for work done.

Question 4

The Bachelor Chow corporation sells dog food-like bachelor food. to produce the chow, the corporation needs to use a mix of kibles (K) and some water (W) in the following

a) If Bachelor chow wanted to produce 149 cans of chow, how many Kibbles would it need such that it minimized its cost (in the long run)?

b) Obtain the conditional factor demand function for kibbles: K.

c)  If the firm received an order for 149 Bachelor Chow, and only had W=12, would it be possible for it to meet its order? If so, how much Kibble would need to be used, and by how much would this cost more than the efficient long run input choice?

Question 6

Congratulations, you have been appointed the general manager of the Paradise Hotel, which is the only hotel on Paradise Island, located somewhere in the Pacific Ocean. This hotel also owns the only restaurant in town that serves breakfast.

The table below shows the willingness to pay of type 1 and type 2 hotel guests for hotel room (R) and for breakfast (B), as well as the expected number of guests of each type and the hotel’s marginal cost of providing each service.

Guest Type

Hotel Room (R)

Breakfast (B)

Expected # guests

Type 1

\$88

\$6

7

Type 2

\$64

\$7

5

Marginal Cost

\$13

\$3

As the hotel manager, your first responsibility is to decide whether to include breakfast in the standard hotel rate (breakfast +hotel room combo) or to charge extra for breakfast (breakfast is separate from hotel room). (Explain or /and show why – your work is worth 9 points)

hint: your asked whether you should price the goods separably or sell them as a bundle. You need to find prices and which is more profitable