A profit-maximizing firm equates the marginal rate of technical substitution of two inputs to: the ratio of marginal products of the inputs and the ratio of the costs of these inputs. the marginal cost ratio of the good being produced. All of the choices None of the choices the price ratio of the good being produced. the ratio of the inputs cost that satisfies the ratio of highest marginal products of the inputs. O the ratio of marginal products of the inputs
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- Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72Consider a factory that produces iPhones. This factory relies on both employees (labor) and machines (capital). Which of the following would decrease the demand forlabor?O a. Public taste shifts away from iPhones towards AndroidsO b. The price of capital falls and labor is easily substituted for capital.O c. The factory has trouble hiring competent workers (workers become less productive).O d. (b) and (a)O e. all of the aboveTripod Store has been so successful in Paris that it wants to set up a new operation in Nantes. Their long-run production func tion is Q = K2/3L1/3 The rental rate of capital is $12 and the wage is $10. The market price of cameras is $6, and Tripod expects to sell 1000 per month. a. What is the opti mal allocation of capital and labor (per month) for the new loc ation? b. In add ition to the price of labor and capital, Tripod will have to pay $8000 per month in fixed costs—rent, insurance, etc. Does this change your answer to part (A) above?
- Monique has a flock of six chickens in her backyard that she initially bought for $6 each. Theflock currently lays 20 eggs per week, which Monique and her family consume at home, andher current cost of feed is $2 per week. Monique has a job that pays $8/hour with flexiblehours, but she is thinking of selling her chickens’ eggs to earn extra income. To start sellingeggs, she would need to increase production to 30 eggs per week. She can do this by increasingthe chickens’ feed to $3 per week and taking an hour off work each week to devote to chickenrearing. If the market price of her farm-fresh eggs is $1 per egg, what would be Monique’sweekly economic profits from selling her chickens’ eggs? (Select one from below) (a) −$9: This is her revenue minus her accounting cost.(b) −$1: This is her revenue minus her production cost.(c) $0: Eggs are a constant-cost market so producers must earn 0 profits.(d) $1: This is her revenue minus her economic cost.(e) $7: This is her revenue minus her…Many businesses taco increasing marginal costs because___ O A. in order to increase output, you have to purchase more inputs.O B. a business may have to shift to more expensive sources of inputs in order to increase output.O C. most businesses are not near capacity.OD. when the price falls, output increases.For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and AverageTotal Cost (ATC) are given as follows:Marginal Cost (MC) = C'(0)Average Total Cost (ATC) = C(Q)/QProve that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at itsminimum value.(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
- 38. For the production function y = 3x₁ + 4x2 , which of the two inputs is more productive when x₁ is 1 and x₂ is 10 ? O. X1 O. X2 O. neither ; for this situation , they have equal marginal products O. cannot tell from the above information 39. Given the production function y = 3x₁ + 4x2 , what is the marginal rate of technical substitution of x₁ for x₂ ( MRSx1x2 ) when x₁ is 5 and x₂ is 5 ? O. -0.75 O. -x1 / 5 O. 5 O. -5Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?The nation of Ectenia has 20 competitive appleorchards, all of which sell apples at the world priceof $2 per apple. The following equations describethe production function and the marginal product oflabor in each orchard:100100 2 ,2 5 25 2Q L LMPL Lwhere Q is the number of apples produced in a day,L is the number of workers, and MPL is the marginalproduct of labor.a. What is each orchard’s labor demand as a functionof the daily wage W? What is the market’s labordemand?b. Ectenia has 200 workers who supply their laborinelastically. Solve for the wage W. How manyworkers does each orchard hire? How much profitdoes each orchard owner make?c. Calculate what happens to the income of workersand orchard owners if the world price doubles to$4 per apple.d. Now suppose that the price is back at $2 perapple but a hurricane destroys half the orchards.Calculate how the hurricane affects the income ofeach worker and of each remaining orchard owner.What happens to the income of Ectenia as a whole?
- The elasticity of substitution of a Cobb-Douglas production function is constant alongthe whole range of any isoquant, and is equal to 1. Can you show this property that the elasticityof substitution is equal to one everywhere? Is the elasticity of substitution for a CES (ConstantElasticity of Substitution) production function the same?Kindly explain the answer to me.Which of the following statements is not correct? Select one: O a When MC is below AVC, AVC is rising. O b. The total product curve shows how a firm's output changes when the quantity of labour changes. O c. Diminishing marginal returns occur when the marginal product of a worker is less than the marginal product of the previous worker. O d. The change in total product resulting from a one-unit increase in the quantity of labour is called marginal product. ous page Nextwhat is the marginal rate of substitution when the price of coffee is $1.00 per ounce? the prof said the answer is -2.