Suppose ?(?, ?) = ?3?

a) (3 pts) Write down the formula and calculate the marginal rate of substitution (MRS) of X for Y.

b) (1 pts) Denote the price for good X is ? , the price for good Y is ? , and income is I.?? Write down the budget constraint.

c) (5 pts) Derive the individual demand for good X and good Y as a function of prices and income. (hint: solve the utility maximization problem)

d) (2 pts) Explain the following statement: Individual demand function is homogeneous of degree 0 with respect to prices and income.

e) (2 pts) Verify the homogeneity property with your demand functions derived in part d).

f) (4 pts) Now suppose ? = 3, ? = 4, ? = 100. Find the optimal consumption bundle. ??

g) (2 pts) Show whether or not the consumer can afford the bundle (15, 20).

h) (2 pts) What is the maximum utility level?

2. Ted and Jane are buying a house for $280,000. They will make a 25% down payment. They will be able to obtain a loan at 8.5% per annum interest. What will be their annual payment if their loan is for 15 years? 25 years? What will be the monthly payment if their loan is for 15 years? 30 years?

The correct answers are below, I just need to know how to solve using a financial calculator

2. 25,288.3, 20,519.45, 2,067.95, 1,614.72

E. coli are able to break down lactose when present, and this is regulated by the lac Operon. Describe the mechanisms for the positive and negative control of this operon, and briefly discuss the advantages of both forms of control for this operon.

Using Behavorial VHDL, design a 4-bit up/down counter.

A car is traveling down the expressway at 31.7 ? with no acceleration. How far has the car? traveled in 3.9 hours? If the speed limit in such expressway is 70mph, should the driver receive a speed ticket?

A car is traveling down the same expressway as in the previous problem, it is traveling at 22.3 7 ?. If it constantly accelerates at a rate of 4.3 ?, in how many minutes is it going to pass the speed limit.

The price of a home is ​$120,000. The bank requires a​ 20% down payment and three points at the time of closing. The cost of the home is financed with a​ 30-year fixed-rate mortgage at

7​%.

a.  Find the required down payment.

​$

b.  Find the amount of the mortgage.

​$

c.  How much must be paid for the three points at​ closing?

​$

​(Round to the nearest dollar as​ needed.)

d.  Find the monthly payment​ (excluding escrowed taxes and​ insurance).

​$

​(Round to the nearest dollar as​ needed.)

e.  Find the total cost of interest over 30 years.

​$

​(Round to the nearest dollar as​ needed.)

What are the applications of 8051 microcontrollers that can be done on EdSim51? List down at least 5.

A tower worker at the top of a wind turbine tower is letting down a small broken part of mass 4.3 kg tied to a practically massless rope.

The top of the tower is 14.4m above the ground, and the wind is blowing at 6.3 m/s at the top of the tower and decreases linearly with height to 1.7 m/s at the ground.

She is letting the rope slide thru her leather gloves at a rate of 0.30 m/s, and the friction between the rope and her gloves is making the gloves warm. What power is being

dissipated as heat where rope is sliding on the gloves?

What determines the value of a bond? Write down the formula for determining the price of the bond and explain it briefly.