Kindly solve the following questions.

Production

Problem 1. Consider the Cobb-Douglas production function f(x,y) = 12x0.4y0.8.

(A) Find the intensities (? and 1 ? ?) of the two factors of production. Does this firm have decreasing, increasing, or constant returns to scale? What percentage of the firm's total production costs will be spent on good x?

(B) Suppose the firm decides to increase its input bundle (x, y) by 10%. That is, it inputs 10% more units of good x and 10% more units of good y. What is the percent increase in output?

(C) Suppose the firm has a production quota of q = 1000 units, and the firm inputs x = 100 units of the first good. How many units of the second good does it need to use to meet the quota?

(D) Assume the firm has a production quota of q = 2000 units, and the input prices are (px,py) = (7,19). Find the minimized cost C(2000) and the conditional factor demands (x?,y?).

Problem 2. Consider the linear (perfect substitutes) production function f (x, y) = 12.7x + 19.4y.

(A) How many units of good y would be a perfect substitute for 1 unit of good x? What is the slope of

the firm's isoquants?

(B) Suppose the input prices are (px,py) = (5,8). What is the slope of the isocost lines? How much output does the firm get when it inputs $1 worth of good x? How much output does the firm get when it inputs $1 worth of good y?

(C) Suppose this firm has a production quota of q = 500 units. Find the minimized cost C(500) and the corresponding conditional factor demands.

(D) Draw the firm's level-500 isoquant, as well as the isocost lines. Indicate the cost minimizer on your diagram.

Problem 3. Consider the Leontiev (perfect complements) production function f (x, y) = M in x , y . 9.6 5.2

(A) How many units of good y would be a perfect complement for 1 unit of good x? What is the equation of the firm's kink line?

(B) Assume the firm has a production quota of q = 400 units. Graph the firm's level-400 isoquant. What are the coordinates of the kink?

(C) Suppose the input prices are (px,py) = (16,9). Find the minimized cost C(400). What is the cost minimizing input bundle (x?, y?)?

(D) Give a complete geometric illustration of this firm's cost minimization. On a single diagram, draw the firm's level-400 isoquant, the isocost lines, and the cost minimizing input bundle.

Problem 4. Suppose that a firm's production plan is (x, y, z) = (102, 19, 957), and the market prices are (px , py , pz ) = (10, 5, 1.25). How much profit would the firm make if it carried out this plan?

Problem 5. Suppose that a firm's production function is f(x,y) = 20x0.7y0.3. Starting from the input bundle (x, y) = (40, 60), how much extra output will the firm get if it increases x from 40 to 41? How many units of output will the firm lose if x decreases from 40 to 39?

Problem 6. Suppose that the production of airframes (for aircraft) uses two inputs: capital (good x) and labor (good y). The production function is f(x,y) = xy. Assume that the price of capital is $1 per unit, and the price of labor is $10 per unit. The manufacturer wants to make 121,000 airframes. Find the cost-minimizing combination of capital and labor inputs.

Part 2.

Question 1

Use the Model of Demand and Supply to explain why the price of buffet dinners has decreased recently in Dhaka City. Your answer should include a well-labeled diagram.

Question 2

Two candidates, Mr A and Mr B, are running for presidency in Country Z. The people of Country Z can either vote for Mr A or Mr B.

We are interested to study and analyze the total number of votes received by each of the two candidates.

Discuss in detail how we can apply the model of Production Possibility Frontier (PPF) in this case. Your answer should include a well-labeled diagram.

Discuss how the definition of the PPF needs to be adjusted and modified in this situation.

Question 3

The president of Country Z wants to adopt the free market economic system and has come to you for advice. You are the economic advisor of Country Z.

a) What would be your advice to the president of Country Z? Discuss your point of view in detail.

b) The price of rice has been increasing rapidly in Country Z. Discuss all the possible ways Country Z can tackle (manage) the problem of increasing price of rice. No need to draw diagrams in this answer.

Question 4

You have decided to open a small business in Country Z and you want to hire some employees for your business.

a) Discuss why you will need a rationing device when hiring employees.

b) Discuss in detail about the rationing device you will use when hiring employees.

c) Discuss how your choice of rationing device might affect the society of Country Z.

d) Discuss how you can use the concept of incentives and negatives to get the best out of your employees. Is this situation related to optimization or efficiency? Discuss in detail.

Question 5

Mara and Dona are both consumers and producers of butter and bread. They are both living in a barter economy. The following are the production schedules of Mara and Dona:

Production schedule of Dona Butter (units per day) Bread (units per day) 8 0 4 4 0 8

Using the given situation show that specialization and trade can benefit individuals and societies. Show all steps in your analysis. Explain in detail.

You can assume that the terms of trade are 5 units of bread for 4 units of butter.

Question 6

Discuss in detail how the concept of transaction cost and economic growth may be connected. Try to explain the connection as clearly and precisely as you can. There is no need to draw any diagram.

Section ii.

5. Now suppose that instead of a luxury good, the consumer can chose between a consumption good c, and hours of work w. Here P: = $1, or: = 55D. and the consumer gets paid $2 for every hour of work they \"consume."r Further, assume work takes time and they can only consume at most 24 hours of work. Graph the consumption set with work on the '1" axis. What is the price of work: p\d. If after the tax the consumer consumes 3 units of the luxury good, how will the tax on the luxury good affect government revenue? If after the subsidy the consumer consumes 5 units of the consumption good, how will the subsidy affect government revenue? e. As discussed above, after the tax and subsidy have been implemented our consumer is consuming 3 units of the luxury good and 5 units of the consumption good. Suppose the growing US economy increases the consumer's income by $25. Graph the new budget constraint and write down the new budget constraint formula. Label where the constraint hits the axes. Assume that after the growth of the economy our consumer now consumes 5 units of the luxury good and 6 units of the consumption good. How has the growth in the economy affected government revenue? f. How would the increased income from the growing economy discussed above compare to the change in the budget constraint from an ad valorem sales subsidy of 10%? 5. Go back to the original budget constraint with P. = $1, , = $10, and m = $50. Imagine that the luxury goods did not only require money but also requires time to consume. This would be the case for luxury goods such as ski vacations. a. First assume each unit of a luxury good took 6 hours of time and a consumer only has at most 24 hours of time to spend. Graph the consumption set and label the axes. Graph both the budget constraint and the time constraint and label the points where they hit the X and Y axes. Shade the set of available bundles the consumer has to choose from. b. What if the luxury good took only 1 hour to consume. How would the choice set change from above? If this was the case, what would be an easy simplifying assumption to apply to this model?Objective: To give you experience solving budget constraint problems. To show how the budget constraint can be used to model different questions and applied to policy discussions. Imagine you are an economist working for the US Department of the Treasury. Part of your job is to predict how changes in tax policy affect government revenue and the typical consumer's wellbeing. For this exercise we will assume a hypothetical US consumer choses between two commodities: a general consumption good: c and a luxury good /. The luxury good is symbolic of any high end purchases consumers might buy such as Lamborghinis, yachts, concert tickets, etc.; whereas c represents necessities such as food, shelter, and clothing. 1. Graph the consumption set of a typical US consumer. Put the consumption good on the X axis and the luxury good on the Y axis. Label the axes. 2. Assume the price of a unit of the of the general consumption good is Pr = $1, the price for a unit of luxury good is P, = $10, and the hypothetical consumer's income is m = $50. Write out the equation for the budget constraint. Graph the budget line and the consumption set, labeling where the budget line hits the X and Y axes and the slope of the budget line. Shade the budget set. 3. Assuming the typical consumer spends all of their income, what is the opportunity cost in terms of the consumption good c for getting an additional unit of the luxury good /?1. Answer all ports (aj-(d) of this question. Let the utility function be given by 15051.32): \\/a:1+ 332- Let m be the income of the consumer, p1 and m the prices of good 1 and good 2, respectively. To simplify, normalize the price of good 1, that is p1 = .81. (a) [5 marks] Write down the budget constraint and illustrate the set of feasible bundles using a gure. (b) [11 marks] Suppose that m = .8103 and that p2 = .810. Find the optimal bundle for the consumer. In other words, nd the combination of 3:1 and 1:2 that maximizes the consumer's utility when the prices are m = .610, p1 = .61 and her income is m. 2 100. (c) [11 marks] Suppose still that m = .6100 but now the price of good 2 has increased to p2 = .630. Find the optimal bundle for the consumer. In other words, nd the combination of 3:1 and 3:2 that maximizes the consumer's utility when the prices are p; = .830, p1 = .E l and her income is m = .8100. (d) [6 marks] How can we explain the drastic change in demand for the goods when the price of good 2 increased from .810 to 30