Aswer the attachment below.

6.7 The production function

Q=KaLb where 0? a, b?1 is called a Cobb-Douglas production function. This function is widely used in economic research. Using the function, show the following:

a. The production function in Equation 6.7 is a special case of the Cobb-Douglas.

b. If a+b=1, a doubling of K and L will double q.

c. If a +b

d. If a +b > 1, a doubling of K and L will more than double q.

e. Using the results from part b through part d, what can you say about the returns to scale exhibited by the Cobb-Douglas function?

6.8 For the Cobb-Douglas production function in Problem 6.7, it can be shown (using calculus) that MPK =aKa-1Lb MPL =bKaLb-1 If the Cobb-Douglas exhibits constant returns to scale (a +b=1), show that

a. Both marginal productivities are diminishing.

b. The RTS for this function is given by RTS=bK/aL

c. The function exhibits a diminishing RTS.

6.9 The production function for puffed rice is given by q=100?KL where q is the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour.

a. Calculate the q=1,000 isoquant for this production function and show it on a graph.

b. If K=10, how many workers are required to produce q=1,000? What is the average productivity of puffed-rice workers?

c. Suppose technical progress shifts the production function to q=200?KL. Answer parts a and b for this new situation.

d. Suppose technical progress proceeds continuously at a rate of 5 percent per year. Now the production function is given by q=(1,05)t q=100?KL, where t is the number of years that have elapsed into the future. Now answer parts a and b for this production function. (Note: Your answers should include terms in (1,05)t. Explain the meaning of these terms.)

7.5 A firm producing hockey sticks has a production function given by q=2?KL. In the short run, the firm's amount of capital equipment is fixed at K=100. The rental rate for K is v=$1, and the wage rate for L is w=$4.

a. Calculate the firm's short-run total cost function. Calculate the short-run average cost function.

b. The firm's short-run marginal cost function is given by SMC=q/50. What are the STC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks?

c. Graph the SAC and the SMC curves for the firm. Indicate the points found in part b.

d. Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC at its lowest point.

7.3 The long-run total cost function for a firm producing skateboards is TC =q3-40q2+430q where q is the number of skateboards per week.

a. What is the general shape of this total cost function?

b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output?

c. The marginal cost function for skateboards is given by MC= 3q2 -80q +430 Show that this marginal cost curve intersects average cost at its minimum value.

d. Graph the average and marginal cost curves for skateboard production.

Pick any three of the topics above and write a concise yet through response about each topic. Include how learning this information has broadened your understanding of CTE, how it has changed your thoughts about teaching or working in the CTE area, how it will change our classroom approach with your students and fellow CTE teachers (don't forget the Vocational Director and staff), include any other educational ponderings you encountered. Respond to all three topics in the same document The total of all three topics combined should be between 1000 to 1200 words. Topics 1. Name and describe the first five planning decisions every CTE teacher should make when planning a program or daily lessons. 2. Compare and contrast the different types of supervision and give an example of when each one has a place in your curriculum and setting. 3. Justify why including effort as part of your grading system is an important aspect of attribution retraining. 4. Describe a situation in which you use "wait time" to improve communication in your interactions with students in your CTE setting. 5. Identify two educational resources regarding safety in the classroom, lab or CTE setting that can provide training materials and/or curriculum content to assist you in educating students about safety practices. Describe each resource in detail. 6. Explain why continuing education and professional development for faculty in health and safety practices is essential for both the instructor and students of a CTE program. 7. Describe the four key components to an effective preventive maintenance program and describe one application in your current CTE program. 8. Justify the need for a Safety Checklist Program in any CTE setting 9. Justify why the philosophy of fact-finding is more important and effective in practice than faultfinding after an incident has occurred. 10. Describe the overall role of health and safety (prevention and response) in relationship to effective teaching and learning.16. Suppose that there are only two goods, books and coffee. Justine gets utility from both books and cof- fee, but her indifference curves between them are concave rather than convex to the origin. a. Draw a set of indifference curves for Justine. b. What do these particular indifference curves tell you about Justine's marginal rate of substitution between books and coffee? c. What will Justine's utility-maximizing bundle b. look like? (Hint: Assume some level of income for Justine and some prices for books and coffee, then draw a budget constraint.) C. d. Compare your answer to (b) to real-world behaviors. Does the comparison shed any light d. on why economists generally assume convex preferences? * 17. Chrissy spends her income on fishing lures (L) and gui- tar picks (G). Lures are priced at $2, while a package e. of guitar picks costs $1. Assume that Chrissy has $30 to spend and her utility function can be represented as 20. Che U(L,G) = 105Go5. For this utility function, MUZ = sub 0.51 05Gos and MUG = 0.5105G-05 wha