SE THE FUNCTION BELOW (WHOSE PARAMETERS QUALIFY IT AS STC FUNCTION) TO ANSWER THE QUESTIONS SHOW WORK!!!!! STC = 190 + 17Q - 2Q^2 + 8Q^3 1) DEMONSTRATE THAT THE VALUE OF SMC EQUALS THE VALUE OF AVC AT THE VALUE OF Q WHERE AVC IS A MINIMUM HINT: THE LEVEL OF Q YOU FOUND IN F IS WHERE AVC IS A MINIMUM. IF YOU PLUG THIS LEVEL OF Q INTO AVC (SEE C) AND ALSO INTO MC (SEE D) THE TWO OUTCOMES SHOULD BE THE SAME IF SMC CROSSES AVC AT THIS LEVEL OF Q 2) WHY DOES THE DERIVATIVE OF SHORT RUN TOTAL COST (STC) EQUAL THE DERIVATIVE OF TOTAL VARIABLE COST (TVC)? STATED ANOTHER WAY WHY DOES dSTC/dq = dTVC/dQ? EXPLAIN IN A COUPLE OF SENTENCES (HINT SEE TRUETT PAGE 235 AND FOOTNOTE 16) 3)FIND THE VALUE OF Q WHERE INCREASING RETURN CEASES AND DIMINISHING RETURNS BEGINS. HINT: DIMINISHING RETURNS BEGINS AT THE LEVEL OF Q WHERE MC IS A MINIMUM
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Suppose that you are the manager of Rockford Enterprises in a competitive market. You are asked to estimate the average variable cost (AVC) function for the firm. Based upon the estimated AVC, you can obtain the predicted values of AVC and SMC. You should decide i) whether to produce output or go out of business; and ii) if you decide to produce output, how many units of output you would produce. Currently, the market price is given at $50. You have already paid the total fixed cost (TFC) of $2,000. The following table shows the output-cost data of Rockford Enterprises (see p. 377 in the textbook): Table 1: Output and Deflated Average Variable Cost ($) Quarter Output Deflated AVC ($) 2012-II 300 36.26 2012-III 100 37.33 2012-IV 150 27.10 2013-I 250 26.89 2013-II 400 45.10 2013-III 200 31.34 2013-IV 350 42.24 2014-I 450 55.13 2014-II 500 61.73 You are asked to estimate the following AVC function: AVC = a + bQ + cQ^2 (a) Using the data above, estimate the coefficients of AVC, b, and c in MS Excel, and check if you obtain the same regression result as that on page 377 of the textbook. Submit the printout of your own regression table. (b) Check if the estimated coefficients of AVC, b, and c are statistically significant at the 5% level, using the p-values shown in your regression tables. Explain why or why not. Using the estimated coefficients of AVC above, implement the profit-maximizing output decision for the firm. Refer to Chapter 11.6 of the textbook. When you know the estimated coefficients of AVC, you can obtain the predicted values of AVC and SMC. AVC = a + bQ + cQ^2 SMC = a + 2bQ + 3cQ^2 (a) Determine whether the firm should shut down or not, and explain why or why not. (b) Suppose that you decided to produce output in the short run. Find the firm's profit-maximizing output level. (Note: You can use the online quadratic equation calculator to solve the quadratic equation for Q. Refer to the following website: http://www.math.com/students/calculators/source/quadratic.htm)
Dominador T.
Question 1: Given the following cost function:TC = 1500 + 15Q – 6Q2 + Q3i. Determine the total fixed cost for producing 1000 units of output and 500 units of output.ii. What is AFC at:a) 1000 units of outputb) 500 units of outputiii. Determine TVC, AVC, MC and AC at 50 units of output. Question 2: The demand function equation faced by PTCL for its computers is given by:P = 50,000 – 4Qi. Write the marginal revenue equationii. At what price and quantity marginal revenue will be zero?iii. At what price and quantity will total revenue be maximized? Question 3: Suppose the following demand and supply function:Qd = 750 – 25PQs = -300 + 20 Pi. Find equilibrium price and quantityii. Find consumer and producer surplus Question 4: Given production function:Q = L 3/4 . K1/4Find out the optimal quantities of the two factors using Lagrangian method, if it is given that price of labor is Rs.6 and price of capital is Rs.3 and total cost is equal to Rs.120.Question 5: Given the cost function isTC = 6L + 3KFind out the optimal quantities of the two factor using Lagrangian method, if it is given thatoutput is equal to 13.46 = L3/4 . K1/4 Question 6: Suppose that the production function of the firm is:Q = 100L1/2.K1/2K= 100, P = $1, w = $30 and r = $40. Determine the quantity of labor that the firm should hire in order to maximize the profits. What is the maximum profit of this firm? Question7: Solve the above problem for w = $50. Question 8: Given TC = 100 + 60Q – 12Q2 + Q3Finda. The equations of the TVC, AVC, and MC functions.b. The level of output at which AVC and MC are minimum, and prove that the AVC andMC curves are U-shaped.c. Find the AVC and MC for the level of output at which the AVC curve is minimum. Question 9: Answer the same questions as in the above problem if:TC = 120 + 50Q – 10Q2 + Q3 Question10: If the demand function faced by a firm is:Q = 90 – 2PTC = 2 + 57Q – 8Q2 + Q3Determine the level of output at which the firm maximizes the profit.
Manasvee S.
Consider a firm which faces the following production function: Q = F(K, L) where Q is the firm's output, K is the firm's capital input, and L is the firm's labor input. This production function is assumed to have the following properties: FK > 0, FL > 0, FKK < 0, FLL < 0, FKL = FLK < 0, and FKK * FLL > FKL^2. Given (1), the firm's total revenue R is given by: R = PQ = PF(K, L) where P is the price of the firm's output (assume that P > 0), and the firm's cost C is given by: C = rK + wL where r is the interest rate, w is the wage, and C is the total cost. Given (3) and (4), the firm's profit function can be written as follows: ̴̵̶̷̸̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎̀́̂̃̄̅̆̇̈̉̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡π = PF(K, L) - rK - wL where π is the firm's profit. If the firm operates under perfect competition, the prices of output and inputs (P, r and w) are exogenous, and this implies that the firm chooses K and L which maximize π. Given this firm's profit-maximizing problem, answer the following questions: a) Obtain the FOC, πK = 0, which is expressed in terms of r (i.e. r is a function of other variables). b) Obtain the FOC, πL = 0, which is expressed in terms of w (i.e. w is a function of other variables). c) Obtain the SOC for maximum. From your answers in a) and b), there exist i) a value of K and ii) a value of L which optimize π; let them be denoted by K* and L*, respectively. Since the production function is stated in the general form, however, K* and L* cannot be derived explicitly. To get around this problem, let's assume a specific, Cobb-Douglas production function as follows: Q = K^1/3L^2/3 Then, the profit function becomes: π = PK^1/3L^2/3 - rK - wL
Sam S.
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