3. In order to produce 28 widgets, a firm must use 14 workers in combination with 4 machines.

a. Let q denote the number of widgets, L denote the number of workers, and K denote the number of machines. Write down the production function that represents this technology for producing widgets. In a diagram with L on the horizontal axis and K on the vertical axis, draw the isoquant associated with q = 56.

b. Let w represent the wage rate and r represent the rental rate of capital. Solve for the firm’s factor demand functions for L and K.

c. Solve for the firm’s long run cost function. (2 points).

Problem 3: A firm has the following production function: ?(?, ?) = √?√?.

A) Show whether this firm’s technology exhibits constant, increasing, or decreasing returns to scale.

B) What is the firm’s Technical Rate of Substitution?

C) What is the optimality condition that determines the firm’s optimal level of inputs?

D) Is the marginal product of input ? increasing, constant, or decreasing in ??

E) Suppose the firm wants to produce exactly ? units and that input ? costs $?? per unit and input ? costs $?? per unit. What are the firm’s conditional input demand functions?

F) Using the information from part E), write down the firm’s total cost function as a function of ?? , ??, and ?.

Consider an oligopolist market with demand: Q = 18 – P. There are two firms A and B. The cost function of each firm is given by C(q) = 8 + 6q. The firms compete by simultaneously choosing quantities.

a. Write down firm A’s profit function and derive firm A’s reaction function.

b. Plot the reaction functions of both firms in a diagram.

c. What is the optimal quantity produced by firm A and firm B?

d. Now suppose firm B invests in a technology which doubles its fixed costs and lowers its marginal costs by half. Find Firm A and Firm B’s new optimal quantities and profits

a. Why is GPU important in a computer? Explain in your own words.

b. If you are visiting the your college campus with the help of a head mounted display (HMD) that feels like you are at your campus physically where you are attending classes and roaming around with your friends.

   i) What kind of technology can help getting you this kind of experience?

   ii) Justify your answer with the technological aspects whether it used virtual or augmented reality?

   iii) Compare, how virtual and augmented reality techniques differ from each other?

c. List down some remarkable AR applications that you might admire.

In the time that it takes a whiteboard marker of mass 12 grams to fall 1 meter down to the Earth of mass 6 × 10 kg, 24 (a) how far does the earth move up towards the whiteboard marker? Derive your answer from Newton’s laws, and state when you are using which law. (b) Given that the smallest scale we have measured to date is 0.00000000000000000001 meters = 10 -20 m, can we measure this distance from part (a) yet? (c) Therefore, is part (a) a scientific question? A “scientific question” has to be measurable or falsifiable “in principle” (not necessarily in practice according to current technology).

IDEO is a global award-winning design firm. Every year teams of people including psychologists, mechanical engineers, biologists, and industrial designers work on projects ranging from Apple's first computer mouse to heart defibrillators to the Neat Squeeze toothpaste tube.

IDEO's corporate philosophy is that teamwork improves innovation and creativity. Group brainstorming is used to spark a lot of new ideas at once. Project teams share and improve ideas by leveraging members' skills and solving problems together. The company believes that the diversity of interdisciplinary teams allows higher quality, faster innovation.

Regardless of the project, IDEO teams use the same process. First they identify similar products and experiences, then they observe people using them. The teams then visualize, evaluate, refine, and implement innovative solutions to their clients' problems drawing from their research and observations. IDEO team members lack status or formal titles, and every team member is given equal respect.

1. How does teamwork influence innovation at IDEO?

2. How does diversity influence the effectiveness of teamwork at IDEO?

3. What characteristics would you look for in staffing a project team at IDEO?

Please review carefully the data in “Data Table 1” below. These data are for actual mortgage products and rates offered by one of the largest banks in Canada on two different dates and were recorded in the morning of January 17, 2018 and February 11, 2018. Many questions in this assignment relate to the data in this table and also to the article “Everyone’s Mortgage is About to Get More Expensive,” published on Jan 17, 2018 in MacLean’s and appeared on the Internet. The announcement of the rate increase by the Bank of Canada occurred in the afternoon of the same day

2. What is the monthly mortgage payment for the 1-year fixed rate closed mortgage on January 17, 2018? The amortization period is 25 years and the mortgage amount to be loaned out is $750,000.

3. What is the monthly mortgage payment for the 1-year fixed rate closed mortgage on January 17, 2018? The amortization period is 20 years and the mortgage amount to be loaned out is $750,000.

4. What is the semi-annual mortgage payment for the 1-year fixed rate closed mortgage on January 17, 2018? The amortization period is 25 years and the mortgage amount to be loaned out is $750,000

5. Provide the amortization schedule in an Excel sheet format for the 1-year fixed rate closed mortgage for the first years, based on 25 years of amortization periodand $750,000 mortgage loan.
You MUST show or describe sufficiently every detail of your computational work on each column of the amortization schedule.

6. Reconsider Question 2 and suppose that the interest rate for the 1-year fixed rate closed mortgage goes up to 4% at the end of the year (or the beginning of the second year). What is the monthly mortgage payment for the same 1-year fixed rate closed mortgage in the second year of the mortgage?

7. Provide the amortization schedule in an Excel sheet format for the same 1-year fixed rate closed mortgage above for the second year. You MUST show or describe sufficiently every detail of your computational work on each column of the amortization schedule

8. Consider a borrower who is contemplating either the 5-year variable open mortgage or the 5-year variable closed mortgage in the amount of $750,000 over the 25-year amortization periodon January 17, 2018. Compute the prepayment penalties as a percent of the mortgage amount.

9. On January 17, 2018, the interest rate difference is (i) 1.60% between the 5-year variable open and the 5-year variable closed contracts and (ii) 1.46% between the 1-year fixed closed and 1-year fixed open contracts. Both differences are supposed to capture the effect of the pre-payment penalties on the interest rates. One would expect a relatively constant premium for the prepayment penalties on the same day. Explain why the pre-payment premium is not constant on January 17, 2018.

2. Walmart can use either self-service check out machines or cashiers to process customer purchases. For Walmart, self-service checkout machines and cashiers are perfect substitutes. Suppose that self-service checkout machines can process the purchases of 100 customers per hour and that a cashier can process the purchases of 60 customers per hour. Suppose that the price of operating a self-service checkout machine is 20 dollars per hour and that cashiers are paid an hourly wage of 10 dollars per hour. Answer the following questions:

a) Write down Walmart’s production function for processing customers’ purchases.

b) What is Walmart’s demand for cashiers given the production technology and input prices?

c) What is Walmart’s demand for self-service check out machines given the production technology and input prices?

d) How much will it cost Walmart to process the purchases of 400 customers in an hour?

e) Suppose the minimum wage for workers is increased to 15 dollars per hour. What is the cost to Walmart of processing 400 customers in a hour?

Discuss the difference in their structures that explain these differences between a closed-end fund and an open-ended mutual fund:

a) When investors buy shares of the open-end mutual fund (in the aggregate), the number of fund shares increase. But, this is not the case with a closed-end fund. Why?

b) An open-end mutual fund keeps a larger % cash (or cash-equivalent) allocation in the portfolio than the closed-end fund does. Why?

12)

?(Analyzing market values using financial? ratios) On August? 1, 2007 the Dell Computer? Corporation's stock closed trading at $27.76 per share while Apple? Corporation's shares closed at $133.64. Does this mean that because? Apple's stock price is roughly four times that of? Dell's, Apple is the more valuable? company? Interpret the prices for these two firms using the information found? here:

It appears that Apple enjoys a ______ (higher/lower) price per share when compared to its 2007 earnings but a _______ (lower/higher) price when compared to the book value of the? firm's equity. The ______ (lower/higher) market-to-book ratio for Apple reflects that fact that Apple has used a great deal ______ (more/less) equity? (and _____ (more/less) debt) to finance its operations. ?(Select from the? drop-down menus.)