a) Maximize the utility function U = X0°Y°25 subject to budget constraint 680 = 8X + 5Y Also show that above utility function is homogenous and homothetic.
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- You produce quesadillas (Q) with beef (B) and cheese (C). The production process is as so: Q = 60B - 1.5B2 + 50C - 1.5C2 The price of beef is $6 per box, and the price of cheese is $5 per box. The boxes are the same size and you only have room for 22 boxes in your freezer. How many boxes of cheese should be purchased?Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)Assume you own a copper mine. The mine has total known reserves of 500 (million metric tons). The market demand for the copper is estimated to be: P = -1.75Q + 1000 and the marginal cost curve is estimated to be: P = 1.25Q + 100. What is the efficient quantity of copper to extract if you need only consider the current period in your decision making? Assume you need to consider allocation of the mine’s resources across two periods of time—the present and the future. Assume the “future” period is 10 years from the present and you use a discount rate 7.5%. What would be the efficient (inter-temporal) allocation of the mine’s resources in each period? What would be the price in each period if demand is constant across time?
- The following accompanying table shows the relationship between the speed of a computer's CPU and its benefits and costs. Assume that all other features of the computer are the same (that is, CPU speed is the only source of variation), and only the CPU speeds listed below are available for purchase. CPU Total Marginal Total Marginal GHz Benefit Benefit Cost Costs 2.0 $1,000 $900 2.5 $1,400 $100 $1,200 $1,500 3.0 $300 3.5 $1,900 4.0 $2,000 $400 The total benefit of a 3.0GHZ computer is:The following accompanying table shows the relationship between the speed of a computer's CPU and its benefits and costs. Assume that all other features of the computer are the same (that is, CPU speed is the only source of variation), and only the CPU speeds listed below are available for purchase. CPU Total Marginal Total |Marginal GHz Benefit Benefit Cost Costs 2.0 $1,000 $900 2.5 $1,400 $100 3.0 $300 $1,200 3.5 $1,900 $1,500 4.0 $2,000 $400 Application of the Cost-Benefit Principle would lead one to purchase a computer.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 - 0.02 x Demand for an annual printing of this particular product. The fixed costs per year (ie., per printing) = $46,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 3,000 units per year. The maximum profit that can be achieved is $. (Round to the nearest dollar.) The unit price at the point of optimal demand is $ per unit. (Round to the nearest cent.) Enter your answer in each of the answer boxes.
- Please no written by hand solutions Suppose you own a store that sells top-of-the-line MP3 players. You have determined that the demand function for your MP3 players is Qd = D(P) = 1200 - 4P. At what price would you sell the MP3 players if you wanted to sell 200 of them?Which of the following conditions should hold for an interior optimum? Px MRSXY and PxX + PyY < I Py MUx and MUy should be maximized and Px X + PyY = I Px MRSXY and PxX + PyY = 1 Py MRSXY should be maximized and PxX + PyY = IHow did you arrive at -0.15 here? MB = (1/3)(90 - 0.6(9,588 + g)½- 0.3g½)To find Susan's optimal contribution, we need to calculate her marginal benefit, which is the derivative of MB with respect to g:MB' = (1/3)(-0.15(9,588 + g)(-1/2) - 0.15g(-1/2))
- Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.The accompanying table shows the relationship between the speed of a computer's CPU and its benefits and costs. Assume that all other features of the computer are the same (that is, CPU speed is the only source of variation), and only the CPU speeds listed in the table are available for purchase. CPU Total Marginal Total Marginal GHz Benefit Benefit Cost Costs 2.0 $1,000 $900 2.5 $1,400 $ 100 3.0 $300 $1,200 3.5 $1,900 $ 1,500 4.0 $2,000 $ 400 The marginal cost of upgrading from a 2.5GHz to 3.0GHz computer is O $400. O $300. $200. O $100.You run a coffee shop that is open all day. You are considering staying open in the evening. The total benefit (i.e.. Krevenue) from keeping your coffee shop open for each additional hour at night is shown in the table. Fill out the marginal benefit (the difference from one row to the next). (Enter your answers as a whole number. Include a negative sign (-) if the answer is negative but do not include a plus sign (+) if the answer is positive.) Hours per Night 0 1 2 3 4 5 6 Total Benefit $0 60 90 110 120 110 95 Marginal Benefit If your goal is to maximize total revenue, you should keep your store openhours. (Enter your answer as a whole number.) If you go beyond this amount, the marginal revenue Suppose it costs $25 for each additional hour that you keep the store open. If this is the case, you should keep your store open for hours at night. (Enter your answer as a whole number.) 11