Given the demand functions and the total cost function two goods: X and Y Px 164-&r Py = 81-2y TC = 800+ 4x + y +2.xy %3D where x and y are the number of units of goods X and Y respectively Determine the values of x and y for which profit is a maximum. What is the maximum profit? A production requirement is that 80x+20y = 640. Find the maximum profit subject of this constraint.
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- 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)omly typed answer he cost of ingredients for a turkey sandwich at The Pit Room is $5, and the daily demand function for this sandwich is d(p) =1200 - 100p. What price should the seller charge to maximize its daily total contribution? Round your final answer to two decimal places.Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost). (d) Find the average and marginal cost functions.
- Given U = (x + 2) (y + 1) and Px = 4, Py = 6, and B = 130; (a) Write the Lagrangian function (b) Find the optimal levels of purchase x* and y*. (c) Is the second-order sufficient condition for maiximum satisfied? (d) Does the answer in (b) give any coparative-static information?Suppose the supply function for product X is given by QXS = − 30 + 2Px − 4Pz. Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place.a. How much of product X is produced when Px = $600 and Pz = $60?b. How much of product X is produced when Px = $80 and Pz = $60?c. Suppose Pz = $60. Determine the supply function and inverse supply function for good X. Graph the inverse supply function. Supply function: Inverse supply function: Graph the inverse supply function from QX = 0 to QX = 200A movie theater has been charging $ 10.00 per person and selling about500 tickets on Saturday and Sunday nights. After surveyingtheir customers, theater owners estimate that for every 50 cents theylower the price, the number of attendees will increase by 50 per night.Find the demand function and calculate the consumption surplus whentickets are sold for $ 8.00.
- Let a firm’s production function be f(K,L) = min{2K,L}.a) Solve for the contingent demand functions for Kand L.b) Substitute the contingent demand functions in the total cost that you minimized in parta) to obtain the total cost function.c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 andw= 1 (with minimal possible cost).d) Suppose the price wincreases from 1 to 2. What happens to the demands for KandLand the total cost?Let a firm’s production function be f(K,L) = √2K1/2L1/2.a) Solve for the contingent demand functions for Kand L.b) Substitute the contingent demand functions in the total cost that you minimized in parta) to obtain the total cost function.c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 andw= 1 (with minimal possible cost).d) Suppose the price wincreases from 1 to 2. What happens to the demands for KandLand the total cost? e) Explain the difference in results between your answers to part d) in this question andthe previous question. Why do the impacts on demands and costs differ?What is the conditional demand for input 1? Use cost function c(w1;w2; y) = w11/2w21/2y2
- The marginal and average total cost curves for barbers in an area are cosntant at $12.00/haircut. The daily demand curve for haircuts in the area is given by: P = 22 - 0.001Qd where P is the price in dollars per haircut and Qd is the daily quantity demanded in number of haircuts. Haircuts are provided in a perfectly competitive market and each barber can provide exactly 25 haircuts daily. Suppose that the government decides to limit the number of barbers to 320. Each year, barbers must obtain a government-issued license to cut hair. Based upon the previous information: a. What will be the long-run equilibrium price for a haircut given there are only 320 licensed barbers?b. How much economic profit will each licensed barber earn daily?The demand function for a certain product is? = 86 − ?2and the supply function is? = ?2 + 6? + 30where p is in millions of dollars and x is the number of thousands of units. Find the equilibriumpoint (x, p), then find the consumer’s surplus and producer’s surplus. Round your answer to thenearest unit (the nearest million dollars).K Given the input-output matrix below, find the output matrix if final demand changes to 400 for water, 180 for electric power, and 700 for agriculture. Industry: Water Electric Power Agriculture Other Water 120 120 240 720 The output matrix is X = (Round to two decimal places as needed.) Industry Electric Power 400 200 100 300 8 Agriculture Final Demand 180 240 120 60 260 170 500