1) For the following functions of production, find the functions of conditional input demand and the cost functions a. q = A min(azı, bz2}; b. q = Azfz; C. q = az, + bz2 d. q = az, + b(lnz,) a,b > 0 A, a, b >0 A, a, b > 0 a, b >0 |
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- 0.8₁ A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.)A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?12. Which of the following production function shows decreasing returns to scale? (a) f(r) = min{x1, 12}. 1/4 (b) f(z) = xỉ + x}/2 1/4 1/2 (c) f(x) = r1 + xj"x (d) f(x) = VE +a3.
- (a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
- (a) Suppose we have the following production function: Q=K²/³L2/³ Does the technology have constant returns to scale (CRS)? If not, what? Show your work and explain what it means.< (b) What is the firm's cost minimi on problem in the long-run? Explain and illustrate in a figure using isocost and isoquants how termine optimal inputs K and L. ← (c) Now, consider the short-run where K is fixed at 8 (so that K²/³ = 4). Let r = $20 and w = $10. Show then discuss how short-run average costs change as Qrises. You can use math or a table/figure to do this. (d) Suppose P = $15. Show that optimal Q = 64 in the short-run. You can use math or a spreadsheet. Show details. < (e) Now suppose P = $5. Should the firm shut-down and set Q=0? Explain. <A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.
- Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch It